Frequency shifts during spin-exchange optical pumping of 3He and 129Xe and applications of hyperpolarized 129Xe

This thesis is focused on the fundamental physics of spin-exchange optical pumping (SEOP) and a few applications of the resultant hyperpolarized 129Xe. During SEOP, noble-gas and Rb atoms repeatedly collide. During these collisions the Rb valence-electron wavefunction overlaps with the noble-gas nucleus and if either the noble-gas nuclei or Rb electrons are highly spin-polarized then the other will experience, on average, a small additional magnetic field that will manifest itself as a shift in the Larmor frequency. The size of the frequency shift is proportional to the magnetization of the polarized atoms and consequently can be used to perform polarimetry. In this thesis, pulsed NMR was used to measure 3He and 129Xe Larmor frequency shifts, and optically detected continuous-wave electron paramagnetic resonance (EPR) was used to monitor the 87Rb hyperfine transition frequencies. A successful calibration of the size of the frequency shift due to 129XeRb collisions was done and, using this calibration, preliminary 129Xe polarimetry data were acquired by monitoring the 87Rb EPR frequency inside the Utah flow-through polarizer. The 129Xe polarimetry results were inconclusive due to an unexplained result regarding the sign of the frequency shift; however extensive progress was made in understanding the systematics associated with this type of measurement. Hyperpolarized 129Xe from the Utah flow-through polarizer was also used to perform measurements with unprecedented precision of the T1 time of 129Xe in Xe frozen as "ice" and "snow." In addition, hyperpolarized 129Xe was also used in a study focused on interaction of dissolved Xe with wild-type and several mutants of bovine pancreatic trypsin inhibitor (BPTI) protein.

FREQUENCY SHIFTS DURING SPIN-EXCHANGE OPTICAL PUMPING OF 3He AND 129Xe AND APPLICATIONS OF HYPERPOLARIZED 129Xe by Zayd Ma A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Department of Physics and Astronomy The University of Utah Dcember 2012 Copyright c Zayd Ma 2012 All Rights Reserved The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL This dissertation of Zayd Ma has been approved by the following supervisory committee members: Brian Saam , Chair September 25, 2012 Date Approved Christoph Boehme , Member September 25, 2012 Date Approved Oleg Starykh , Member September 25, 2012 Date Approved Stephan LeBohec , Member September 25, 2012 Date Approved David Goldenberg , Member September 25, 2012 Date Approved and by David Kieda , Chair of the Department of Physics and Astronomy and by Charles A. Wight, Dean of the Graduate School. ABSTRACT This thesis is focused on the fundamental physics of spin-exchange optical pumping (SEOP) and a few applications of the resultant hyperpolarized 129Xe. During SEOP, noble-gas and Rb atoms repeatedly collide. During these collisions the Rb valence-electron wavefunction overlaps with the noble-gas nucleus and if either the noble-gas nuclei or Rb electrons are highly spin-polarized then the other will experience, on average, a small additional magnetic field that will manifest itself as a shift in the Larmor frequency. The size of the frequency shift is proportional to the magnetization of the polarized atoms and consequently can be used to perform polarimetry. In this thesis, pulsed NMR was used to measure 3He and 129Xe Larmor frequency shifts, and optically detected continuous-wave electron paramagnetic resonance (EPR) was used to monitor the 87Rb hyperfine transition frequencies. A successful calibration of the size of the frequency shift due to 129XeRb collisions was done and, using this calibration, preliminary 129Xe polarimetry data were acquired by monitoring the 87Rb EPR frequency inside the Utah flow-through polarizer. The 129Xe polarimetry results were inconclusive due to an unexplained result regarding the sign of the frequency shift; however extensive progress was made in understanding the systematics associated with this type of measurement. Hyperpolarized 129Xe from the Utah flow-through polarizer was also used to perform measurements with unprecedented precision of the T1 time of 129Xe in Xe frozen as "ice" and "snow." In addition, hyperpolarized 129Xe was also used in a study focused on interaction of dissolved Xe with wild-type and several mutants of bovine pancreatic trypsin inhibitor (BPTI) protein. "If your mother says she loves you, make sure you check it out." - B.T.S. CONTENTS ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii CHAPTERS 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Spin-Exchange Optical Pumping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Brief History of Optical Pumping and Spin Exchange . . . . . . . . . . . . . . 1 1.1.2 Optical Pumping of Rb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.3 Rb-Noble-Gas Spin Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Practical SEOP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Spins in a Magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 Excitation and Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2. MEASUREMENT OF THE FREQUENCY SHIFT ENHANCEMENT FACTOR DURING RB-XE COLLISIONS . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Experiment Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5 Data Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.5.1 129Xe Diffusion Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.5.2 "Chemical" Exchange Between Regions of Polarized and Unpolarized Rb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.2.1 129Xe Flip Angle Dependence of (κ0)RbXe . . . . . . . . . . . . . . . . . . . 34 2.5.3 129Xe Imaging to Verify Noble Gas Homogeneity . . . . . . . . . . . . . . . . . . 34 2.5.4 SEOP at High Field: σ+ and σ− Energy Shift . . . . . . . . . . . . . . . . . . . . 35 2.5.5 Numerical Modeling of the Geometric Effect . . . . . . . . . . . . . . . . . . . . . 36 2.5.6 High Xe Concentration Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.5.7 Molecular Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3. 129XE POLARIMETRY USING THE SHIFT OF 87RB HYPERFINE TRANSITION FREQUENCIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2 The Utah Flow-Through Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.3 87Rb in a Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.4 Steady State Excitation of Rb Hyperfine Transitions While Optically Pumping 50 3.5 Alkali Spin Precession Detected via Transverse Faraday Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.6 87Rb EPR Detection Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.6.1 Simple and Inexpensive High-Current Stabilization with an Inductive Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.7 Data and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.7.1 Light Shifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.7.2 Alkali-Alkali Spin Exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.7.3 Hyperfine Resonance Shift Due to Collisions With Buffer Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.7.4 Attempts at Destroying the 129Xe and 131Xe Polarization via NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.7.5 Hyperfine Transition Linewidths During Frequency Shift Measurements 70 3.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 4. MEASUREMENTS OF FROZEN 129XE T1 RELAXATION. . . . . . . . . . 73 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.3 Method Used to Generate Xe Snow or Ice . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5. CHARACTERIZATION OF ENGINEERED CAVITIES IN PANCREATIC TRYPSIN INHIBITOR BY NMR-DETECTED XE BINDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.2 Hyperpolarized 129Xe NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.2.1 Overview of Spin-Exchange Optical Pumping . . . . . . . . . . . . . . . . . . . . 88 5.2.2 129Xe Delivery System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.3 129Xe NMR Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 5.2.4 Interpreting the 129Xe Chemical Shift as a Function of Protein Molarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2.5 Analysis of 129Xe NMR Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3 1H-15N HSQC Under Varying Molarity of Dissolved Xe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.4 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 APPENDICES A. CONSERVATION OF THE SPECTRAL CENTER OF MASS . . . . . . 101 vi B. NUMERIC INTEGRATION OF A SPHERICAL DISTRIBUTION OF DIPOLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 C. CELL FABRICATION PROCESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 D. HYPERFINE SUBLEVEL TRANSITIONS AT LOW FIELD . . . . . . . . 110 E. EQUIPMENT AND ELECTRONICS USED TO MEASURE 87RB EPR FREQUENCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 F. PDB ENTRIES USED FOR CAST CALCULATIONS . . . . . . . . . . . . . . 117 vii LIST OF FIGURES 1.1 Basic concept of depopulation optical pumping in an alkali vapor with zero nuclear spin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 87Rb ground and first excited state hyperfine energy levels at 30 G. . . . . . . . . 5 1.3 Schematic of how a pulsed NMR experiment works. . . . . . . . . . . . . . . . . . . . . . 12 2.1 Experiment concept to measure (κ0)RbXe without the need to measured the Rb polarization or density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Photograph of the 10 mm NMR probe and Cell 155B used in the measurement of (κ0)RbXe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Photograph of the 35 mm NMR probe used in the measurement of (κ0)RbXe. . 20 2.4 795 nm Optical pumping laser and associated optical in front of supercon-ducting magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5 Representative 129Xe and 3He FIDs acquired with the Rb in the high and low energy states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6 Fourier transforms of 129Xe and 3He FIDs acquired with the Rb in the high and low energy states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.7 Typical 3He and 129Xe raw spectra from cell 155B acquired under steady-state SEOP conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.8 Enhancement factor (κ0)RbXe plotted vs. temperature. . . . . . . . . . . . . . . . . . . 28 2.9 CPMG decay acquired on cell 150A at 170◦C to measure the 129Xe diffusion coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.10 Simulated NMR spectra with two distinct resonant frequencies and varying exchange rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.11 129Xe 1D image to verify the 129Xe magnetization is homogeneous. . . . . . . . . . 35 2.12 Demonstration of the 129Xe spectrum dependence on the pump laser frequency. 37 2.13 Numerical integration of the through space dipole field for a sphere with different magnetization distributions verifying the through space dipole field does not appreciably affect the 3He frequency shift. . . . . . . . . . . . . . . . . . . . . . 39 2.14 Enhancement factor (κ0)RbXe plotted vs. temperature for high-[Xe] cells. . . . . 40 3.1 Schematic and photograph of the Utah flow-through polarizer. . . . . . . . . . . . . 46 3.2 87Rb 5S1/2 hyperfine structure as a function of field from 0 to 30 G. . . . . . . . . 48 3.3 Overview of the electronics used to measure a 87Rb hyperfine transition frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.4 Photograph of the inside of the oven on the polarizer where the RF coils (F) excite the 87Rband are probed with a weak transverse D2 laser. . . . . . . . . . . . 56 3.5 87Rb hyperfine sublevel transition spectra acquired on an oscilloscope using the high frequency electronics and the VCO set to sweep frequency. . . . . . . . . 58 3.6 Circuit design to regulate the current through an inductive load powered by a DC power supply in voltage control mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.7 87Rb F = 2, ¯m = 3/2 hyperfine transition frequency as a function of time demonstrating the stability of the magnetic field. . . . . . . . . . . . . . . . . . . . . . . . 61 3.8 87Rb hyperfine sublevel transition frequency as a function of time when cycling Xe into and out of the gas stream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.9 Plot of the additional effective magnetic field from the AC-Stark effect. . . . . . 66 3.10 Plot of the 87Rb F = 2, ¯m = −3/2 hyperfine sublevel transition frequency as a function of time while changing the pump laser characteristics. . . . . . . . . 67 3.11 87Rb hyperfine sublevel transition spectra under different pump laser powers and Xe gas densities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.1 Schematic of the Pyrex condenser/cryostat used to measured frozen 129Xe T1 relaxation times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 Photograph of the cryostat/condenser used in the 129Xe T1 measurements. . . . 77 4.3 129Xe NMR spectra acquired during the transition of the Xe sample from accumulated snow, to liquid, and then to ice. . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4 129Xe FIDs acquired during the transition from accumulated snow, to liquid, and then to ice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.5 129Xe T1 decay measurements demonstrating the difference between Xe frozen as snow or ice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.1 Structure of wild-type BPTI and three-cavity forming variants. . . . . . . . . . . . . 86 5.2 Schematic of complete system to deliver hyperpolarized 129Xe to a protein solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.3 129Xe NMR spectra of hyperpolarized Xe in 25 mM phosphate buffer with different concentrations of wild-type BPTI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.4 129Xe chemical shift vs protein concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.5 1H and 15N amide chemical shift changes due to the Y23A substitution and binding of Xe to Y23A BPTI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.6 1H-15N chemical shift changes due to Xe binding to Y23A BPTI mapped onto the protein crystal structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.7 Binding isotherms for Xe binding to Y23A BPTI. . . . . . . . . . . . . . . . . . . . . . . 98 C.1 Schematic of gas handling system used to clean and to fill cells with various gas mixtures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 ix E.1 Photograph of most of the electronic equipment used to monitor the 87Rb frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 E.2 Control circuit used to condition the lock-in amplifier output before being fed to the VCO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 x LIST OF TABLES 1.1 Table of typical parameters that can be changed in SEOP experiments and some of the effects they may have inside an optical pumping cell. . . . . . . . . . . 9 2.1 Summary of cell contents used in this experiment. All cells are sealed, uncoated Pyrex spheres with inner diameters of ∼7 millimeters. Quoted pressures are referenced to 20 ◦C and the Xe pressure is subject to ∼ 50% uncertainty due to the filling procedure. Cells 155A-C are referred to as low-[Xe] cells and Cell 150A-C are referred to as high-[Xe] cells. . . . . . . . . . . . 17 2.2 Sample frequency shift data after processing described in Section 2.5. ¯x is the average, and σ¯x is the standard deviation of the mean. The error in (κ0)RbXe is the statistical error of each nucleus added in quadrature. There is an error associated with (κ0)RbHe. However, this has been added to the final result and not to the individual values. For every point in Figure 2.8, a similar set of data was acquired. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3 Summary of cell contents and (κ0)RbXe results. (κ0)RbXe is computed for each of the low-[Xe] cells from the weighted average of that cell's data; we have excluded the high-[Xe] cells because of their anomalous behavior at high temperature (see Section 2.5.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1 Components of the EPR frequency counting apparatus. . . . . . . . . . . . . . . . . . . 57 4.1 T1 results of 129Xe in natural abundance Xe at 77 K. Each measurement is a completely new accumulation of frozen Xe from the polarizer. The stated errors are from least squares fits. The repeatability of these measurements is unprecedented, and the difference between ice and snow, while not under-stood at this point, is a possible explanation for variability in all previously published results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1 Table of 129Xe NMR chemical shift results from data shown in Figure 5.4 . . . . 95 5.2 Table comparing 129Xe binding sites in this work to prior publications . . . . . . 99 ACKNOWLEDGMENTS First and foremost, I need to thank my family for their love and support during graduate school. My mother and father have unconditionally supported me throughout my life whether I was pursuing my dreams in the pool or in the classroom. Without these two amazing people in my life, nothing I have accomplished would have come to pass. My sister was and remains a constant, friendly reminder that I really am an idiot and I am grateful to have her humbling presence. My cousin's frequent calls always made me laugh, even when nothing was working in the lab. I hope I have convinced my family that I did not get my doctorate in telemark skiing. I want to thank Monica Allen, my girlfriend of four years, for standing by my side as I struggled through several experiments and writing this thesis. Her passion for life constantly reminds me that I don't have to spend 12 hours a day in the lab to be successful. I am very fortunate to have her love, and my time in Utah would not have been the same without her. While I was spending long days in the lab, there were a few people I came to rely on very frequently. I thank Ed for his patience with my constant questioning and helping me with many of my machining projects. Harold was always around with a good idea or information on the right people to call to get things working when the South Physics building was going through its daily death throes. The front office made my life much easier by helping me navigate the plethora of paperwork over the years. The last set of acknowledgements is dedicated to the Saam research group. I want to thank Geoff Schrank for helping me get my feet wet with my first project. Eric Sorte provided invaluable help during the (κ0)RbXe experiment, and I have many fond memories of rock climbing with him in Big Cottonwood Canyon. Mark Limes was a constant source of impossible questions and I couldn't ask for a better labmate. Lastly, I thank my advisor, Brian Saam, for giving me the chance to join and excel in his research group. I have never met anyone who loves teaching more than Brian. His excitement for experimental atomic physics is truly infectious. I hope I have learned his lessons well, and I promise to not "make him look bad" in whatever I do in the future. CHAPTER 1 INTRODUCTION Spin-Exchange Optical Pumping (SEOP) and Magnetic Resonance (MR) will be briefly discussed in this introduction in order to provide the background for understanding the experiments presented in this dissertation. 1.1 Spin-Exchange Optical Pumping SEOP is a two-step process in which an alkali vapor is spin polarized by optically pumping with circularly polarized light at a resonant atomic transition. The alkali spin polarization is then transfered to noble-gas nuclei through spin-exchange collisions. This process can produce noble-gas samples with nuclear spin polarizations approaching 100% under certain conditions and has been given the catchy name "hyperpolarized noble-gas via SEOP." 1.1.1 Brief History of Optical Pumping and Spin Exchange The history of optical pumping, the connection with the Overhauser effect, and the discovery of spin-exchange between alkali metals and noble-gas nuclei is an entire book in itself. The rich history of the field and the people involved cannot be adequately covered in one paragraph; nevertheless, a brief summary follows. In 1952, A. Kastler published a paper in which he pointed out that absorption and scattering of resonant light leads to large population imbalances in atomic spin ground states of alkali atoms [14]. At almost the same time, A. Overhauser predicted that saturation of the electron resonance in metals will create an enhanced nuclear polarization on order of the ratio between the electron and nuclear gyromagnetic ratios [50]. The enhancement arises when the electrons attempt to relax back to thermal equilibrium and spin-flip nuclei. In 1956, the Overhauser effect was first observed in Lithium powder by C. Slichter and T. Carver [15]. T. Carver then moved to Princeton where the first attempts were made to realize the Overhauser effect in alkali-noble-gas mixtures. However, instead of saturating the alkali spin polarization, the alkali vapor was polarized by optical pumping. To further 2 this work, the first female post-doc at Princeton, M. Bouchiat, was hired to build the apparatus to polarize 3He using SEOP. This was ultimately successful and they polarized 3He to ∼0.01% (4 orders of magnitude over the thermal polarization) [12]. M. Bouchiat then began work on measuring the relaxation rate of Rb vapor in the presence of other noble gases. She discovered the existence of Rb-Xe van der Waals molecules and published two seminal papers on Rb-Xe molecular formation around 1970 [11, 10]. These papers were crucial to the theoretical work published by W. Happer in 1984 [31] that laid the foundation for almost all the work in SEOP that followed. W. Happer, who took over T. Carver's lab, was Brian Saam's doctoral advisor at Princeton University. 1.1.2 Optical Pumping of Rb An excellent description of the optical pumping and subsequent spin-exchange process can be found in references [30] and [72]; only the highlights will be recounted here. When resonant light is absorbed by an alkali atom, an electron will be moved into an excited state. From the excited state, the electron can relax back to different spin ground-states with probabilities given by matrix elements of the dipole operator [66]. If the resonant light is circularly polarized, then only a subset of the spin ground-states will be excited and a spin population will accumulate in the other ground states as the electrons relax. This is known as "depopulation pumping." In practice, a typical optical pumping experiment is as follows. A Pyrex cell is filled with a few milligrams of Rb metal and some additional buffer gases (typically He, N2, and Xe). The cell is heated to 100-200 ◦C which drives the Rb into vapor according to [38] [Rb] = 1 T 1026.41+4132/T (1.1) where T is the temperature in Kelvin, and the numbers have been chosen to make [Rb] have units of atoms per cubic centimeter. This Rb vapor is then irradiated with circularly polarized D1 light (σ+ or σ−). D1 light excites the valence electron from the 5S1/2 to the 5P1/2 state and the circular polarization, due to selection rules, forces the quantum number defining the spin state of the Rb atom to change by ±1 depending on the helicity of light polarization. While in the excited state the Rb atoms collide with buffer gas and, only very occasionally, other Rb atoms. These collisions rapidly mix and equilibrate the excited state populations. At this point, if the Rb atoms are allowed to relax radiatively, an unpolarized D1 photon will be emitted that can scatter several times. Repeated scattering of unpolarized light in the Rb vapor will ruin the ground state population imbalance because unpolarized 3 light excites out of all spin-ground states with equal probability. The process of repeated scattering is known as radiation trapping. To avoid radiation trapping, 50-200 Torr of nitrogen is added to the buffer gas mixture. The N2 molecule has rotational-vibrational states equivalent to the Rb D1 energy and can carry away the energy of an excited Rb atom allowing it to relax nonradiatively back to the ground state. This optical pumping process is then continued, and eventually a steady state balance is reached between the optical pumping rate and various relaxation rates. In typical optical pumping experiments, the Rb polarization can reach nearly 100% under certain conditions. Figure 1.1 illustrates the optical pumping process for a group of fictitious alkali atom with no nuclear spin (I = 0) and zero magnetic field. Many current optical pumping experiments use Rb for several practical reasons. First, The D1 and D2 resonances are far enough apart that, while pumping with D1 light from typical diode lasers, very little optical pumping power is at the D2 transition frequency. Pumping with D2 light is very inefficient because both spin-ground states shown in Figure 1.1 can be pumped out of with either σ+ or σ− light. Second, in typical optical pumping cells the Rb vapor pressure at easily attainable laboratory temperatures (100-200 ◦C) is hundreds of optical depths thick for D1 light. Lastly, the D1 transition is very close to inexpensive high-powered (30-1000 Watt) solid-state laser-diode arrays. While the description above is sufficient to understand most aspects of optical pumping, the description is a simplified semi-accurate physical picture. In reality, alkali atoms have nuclear spin and almost all optical pumping is done in a nonzero magnetic field. While, optical pumping can be done in zero magnetic field where the quantization axis and direction will be defined by the direction and helicity of pumping light, respectively, any small fluctuating field in the sample will quickly reorient the spins and possibly ruin the ground state population imbalance. To avoid this, the optical pumping setups used in this dissertation use a minimum magnetic field of ∼30 gauss (G) dominates any stray fields in the lab. All alkali atoms have nuclear spin and a magnetic hyperfine interaction I · S between the nucleus spin I and the electron spin S (see Section 3.3). A 30 G magnetic field will resolve the hyperfine structure and can potentially complicate the optical pumping. If the optical pumping laser has a narrow spectral width compared to the zero field hyperfine splitting and the Rb D1 resonance is not broadened in any way, then selectively pumping out of only a few hyperfine states is possible. Selectively pumping out of only a few ground states will decrease the optical pumping efficiency as the atomic spin F can 4 Figure 1.1. Basic concept of depopulation optical pumping in an alkali vapor with zero nuclear spin. Each arrow represents the electron spin of a single alkali atom. The diagram is split vertically in energy by the D1 transition (7947 ˚A for Rb) and horizontally by the quantum number mJ of the total angular momentum J = L+S. The alkali vapor is excited by D1, σ− light that can only pump out of one of the mJ = +1/2 states due to the selection rule imparted by the helicity. The mJ states rapidly mix and equilibrate in the excited state due to collisions with buffer gas and other alkali atoms. The vapor can then relax nonradiatively when colliding with N2 molecules which have rotational-vibrational states with energies close to the D1 transition. In the picture shown, the Rb electron spins will then accumulate in the mJ = −1/2 state. accumulate and distribute among states that are not the maximum or minimum spin angular momentum states ( F = 2, mF = ±2 for 87Rb). Figure 1.2 illustrates this point by showing the atomic levels including hyperfine coupling that can be excited by σ− light (the values for 87Rb in Figure 1.2 are from reference [66]). To ensure that optical excitation has an equal probability from all possible spin-ground states, one or more atmospheres of buffer gas is added to the optical cell which broadens the Rb D1 transition by ∼20 GHz/amagat [55] (an amagat is the density of an ideal gas at standard temperature and pressure). In addition, solid-state diode lasers typically have ∼100 GHz widths with in-lab after-market narrowing. With lasers this broad, covering the hyperfine structure is no longer a concern. The major concern becomes broadening the D1 transition enough with buffer gas to ensure 5 Figure 1.2. 87Rb ground and first excited state hyperfine energy levels at 30 G (not to scale). The arrows represent the allowed transitions under irradiation of D1, σ− light. The atomic states are denoted by F = I + J with azimuthal quantum number mF. The ground state hyperfine splitting at zero magnetic field is 6835 MHz, and hyperfine sublevel transitions are ΔF = 0, ΔmF ± 1. With a sufficiently narrow laser selecting only a few of the allowed transitions is possible which will permit the atomic spin F to accumulate in ground states that are not maximum or minimum spin angular momentum states. This is avoided in two ways: first, spectrally narrowed solid-state diode lasers are typically 100 GHz FWHM which is much broader than the zero-field hyperfine splitting of 6.8 GHz; second, the presence of buffer gas broadens the Rb D1 resonance by about 20 GHz/amagat. most of the laser light is used to optically pump Rb and not heat the oven wall behind the cell. 1.1.3 Rb-Noble-Gas Spin Exchange The depopulation optical pumping process described in Section 1.1.2 can highly polarize a Rb vapor. However, the Rb has several relaxation pathways back to thermal equilibrium and has many mechanisms to do so. These mechanisms include but are not limited to collisions with the container walls, diffusion through magnetic field gradients, radiation trapping, spin-rotation interaction, and spin-exchange [30]. The mechanism that dominates 6 all others at low magnetic fields is the spin-rotation interaction which occurs when a Rb atom forms a molecule with another atom, and the Rb electron spin S precesses about the rotational angular momentum of the molecule N. Another possible relaxation pathway is spin-exchange. Spin-exchange conserves the total internal spin of the colliding atoms and can occur between two Rb atoms or Rb and a noble gas atom. Spin exchange between Rb atoms does not change the overall Rb polarization but rather aids in pushing the entire Rb vapor towards a single spin-temperature distribution. Spin exchange between a Rb electron and a noble gas nucleus can randomize the Rb electron spin but it also, as Overhauser predicted, spin-polarizes the noble gas nuclei. The Rb-noble-gas collisional Hamiltonian consistent with known relaxation mechanisms is [2] H = AI · S + γ(R)N· S + α(R)K· S + gsμBSzBz − μI I IzBz (1.2) where AI · S is the coupling between the alkali nuclear spin I and the alkali electron spin S which gives rise to the akali hyperfine structure; gsμBSzBz and −μI I IzBz are the magnetic dipole couplings of the alkali electron and nuclear moments to the applied magnetic field (taken in the z-direction); γ(R)N · S is the spin-rotation interaction between the alkali electron spin S and the relative angular momentum N of the colliding atoms; and α(R)K·S is the magnetic dipole coupling between the noble-gas nucleus and the alkali electron. Both the spin-rotation coefficient γ(R) and the spin-exchange coefficient α(R) depend on the interatomic distance R between the alkali and noble gas atom. This Hamiltonian has been studied extensively with both perturbative and numerical methods in references [31] and [2]. The details will not be discussed here. However, the qualitative features of the collisional process will be discussed and are essential to understand the experiments presented in this dissertation. When Rb atoms collide with a buffer gas, two types of collisions are possible: binary and molecular. Binary collisions typically last for a picosecond and can be pictured as two atoms simply "flying by" each other. Whereas, molecular collisions can last from 1-10 nanoseconds depending on gas pressure and occur when a van der Waals molecule is formed between a Rb atom and a noble gas atom. The difference in whether a collision will be molecular or binary depends on the van der Waals potential attracting the two atoms and whether a third body is present. Rb-He van der Waals potentials have no attractive well and therefore the collisions are always binary. In addition to having a short interaction time, a He atom has a low polarizability compared to the other noble gases, and the Rb 7 electron cannot penetrate the He electron cloud easily to couple to the He nucleus, making the α(R)K · S coupling very weak. This weak coupling is reflected experimentally by Rb-3He spin-exchange times on the order of tens of hours. Rb-Xe, on the other hand, has an attractive potential well where the well depth is about one third of kT at typical optical pumping temperatures. Thus even with an attractive potential the vast majority of Rb-Xe collisions will be binary unless a third body is present. The third body can carry away some of the kinetic energy allowing a stable Rb-Xe molecule to form. Molecular formation increases the Rb-Xe interaction time by several orders of magnitude over binary collisions and therefore makes Rb spin-destruction much more rapid. However, Xe is highly polarizable, and the Rb electron can easily penetrate the Xe electron cloud and couple to the nucleus resulting in a much stronger spin-exchange coupling. Numerical calculations of the Rb valence electron in the presence of Xe show that the probability of the electron to be at the Xe nucleus during a collision can be as much as 50%. In contrast to 3He, this strong coupling results in typical Rb-129Xe spin exchange times on the order of minutes. See also references [11, 31, 72, 2]. The term responsible for spin-exchange, α(R)K · S, is a magnetic dipole interaction that has both a through-space interaction that depends on direction and a Fermi-contact interaction that arises because of the wave function overlap of the Rb electron and the noble gas nucleus. The through-space interaction can potentially contribute a 2% effect during spin exchange and is generally ignored [31], whereas the wave function overlap of the Rb electron and noble-gas nucleus can produce a much stronger effect and is the basis for pursuing the measurements presented in Chapters 2 and 3. Averaged over many collisions, both the alkali electron, and noble-gas nucleus will experience a small nonzero magnetic field if the colliding spins are polarized. This additional magnetic field will shift any Zeeman energies in the noble-gas and alkali atom, and can be experimentally detected by a shift in the Larmor frequency that will be proportional to the polarization of the opposing species. Chapter 2 uses the change in the nuclear magnetic resonance (NMR) frequency of 129Xe and 3He due to collisions with polarized Rb atoms to calibrate the size of the shift for Rb-129Xe collisions [46]. Chapter 3 describes the experiment in which the frequency shift of the 87Rb Zeeman hyperfine sublevels were used to make the first attempts to date at measuring 129Xe polarization inside an optical pumping cell using the frequency shift of the Rb Larmor frequency. 8 1.1.4 Practical SEOP The previous sections provided an overview of the most relevant physics in SEOP. However, successfully connecting these concepts to experimental conditions in a lab can be challenging. Table 1.1 is a list of typical operating parameters that can be changed, the effect they will have on the spins in the optical pumping cell, and the associated observables in the lab. 1.2 Magnetic Resonance Every experiment in this dissertation uses the well known phenomena of magnetic resonance to probe both atomic and molecular interactions. References [64] and [1] have excellent descriptions of many aspects of magnetic resonance as well as detailed mathe-matical formalisms. While mathematical formalisms are useful for understanding details, a simplified physical picture will be discussed here to give the reader a picture to keep in mind when viewing the data and results of the various experiments. 1.2.1 Spins in a Magnetic field For the purposes of this discussion, spin is an arrow and the head of the arrow denotes either the north or south end of a tiny bar magnet or magnetic moment. Without a magnetic field a spin has no preferred direction and all spin states are degenerate. The application of a magnetic field B0 lifts the degeneracy and splits the spin-up and spin-down states (known as the Zeeman effect) by an energy E = ¯hγB0. γ is the "gyromagnetic ratio" which sets the scale for the size of the Zeeman energy splitting and has units of 1 (sec)(G) . Electrons and many nuclei have intrinsic spin J that is related to their magnetic moments by μ = γ¯hJ. The frequency γB0/(2π) is called the Larmor frequency. For reference it is 24.5 MHz for 129Xe in a 20,000 G magnetic field and ∼19 MHz for a 87Rb hyperfine sublevel transitions in a 30 G magnetic field. The previous paragraph explains in very basic terms how the energies of an isolated single spin behaves in a magnetic field. Practically, for a sample consisting of a many-spin system where the spins can interact and exchange energy, two macroscopic observables are always relevant. The thermal spin-polarization of the sample and the longitudinal relaxation time (T1). The thermal polarization of the sample is given by a Boltzmann distribution, and for spin 1/2, this is the difference in population between spin-up and spin-down normalized by the total number of spins: 9 Table 1.1. Table of typical parameters that can be changed in SEOP experiments and some of the effects they may have inside an optical pumping cell. SEOP parameter change Result Increase pumping laser power Increases optical pumping rate Can potentially cause massive local heating in the cell Can cause Rb hyperfine frequency shifts (Section 3.7.1) Change pumping laser tuning Changes the absorption of light that can change the optical pumping rates and light penetration Can cause Rb hyperfine frequency shifts (Section 3.7.1) Increase oven temperature Increases [Rb] according to equation 1.1 Increases Rb-Rb spin-exchange and spin-destruction rates [34] Increases Rb-129Xe and Rb-3He spin-exchange rates [18, 17] Decreases the characteristic optical depth of the cell potentially leading to significant laser attenuation Increase magnetic field Decreases Rb spin-destruction from molecular forma-tion [11] Increases the splitting between the Zeeman hyperfine sublevels in Rb (Section 3.3) Addition of N2 into cell Allows Rb to relax nonradiatively (Section 1.1.2 and [30]) Broadens the Rb D1 and D2 absorption width [55] Aids in formation and breakup of Rb-Xe van der Waals molecules Increases Rb hyperfine splitting [47] Addition of He into cell Broadens Rb absorption lines [55] Aids in formation and breakup of Rb-Xe van der Waals molecules Increases the Rb hyperfine splitting [47] Addition of Xe into cell Dramatically increases Rb spin-destruction [48] which has the possibility of affecting laser attenuation Aids in formation and breakup of Rb-Xe van der Waals molecules Broadens Rb absorption lines [55], but typical Xe concentrations are too low to see an effect Decreases Rb hyperfine splitting [47] 10 P = N ↑ −N ↓ N ↑ +N ↓ = tanh μB0 kT (1.3) where B0 is the magnetic field, k is the Boltzmann constant, and T is the absolute temper-ature of the sample. Typical thermal polarization for nuclear spins in a modest magnetic field (2 T) at room temperature is 10−5 to 10−6. In experiments where the spins are being detected directly, the size of the signal will be proportional to the magnetization which is the product of the magnetic moment, polarization, and density of the spins. Typical gas densities are of order 1019 atoms per cubic centimeter (compared to 1022 hydrogen atoms per cubic centimeter of water) and detecting 129Xe or 3He nuclei through induction (see Section 1.2.2) is impossible unless the nuclear spin polarization is at least 0.01 which can lift the signal above typical electronic noise, hence the need for hyperpolarized gas. The temperature T in Equation 1.3 is generally considered to be the sample temperature, which is correct for thermally polarized samples. However, T can also be used to describe the spin polarization of the sample. For example, hyperpolarized 129Xe in a glass cell at room temperature has a much lower "spin temperature". For particles that do not have spin 1/2, the definition of "polarization" must be gen-eralized. A sample of non-spin 1/2 particles will have a population distributed through the Zeeman states described by a Boltzmann distribution and the polarization is defined as P = Iz I . For example, in a Rb vapor the atomic polarization is described by Fz F , and the electron spin polarization is Sz S . The longitudinal relaxation time T1 is the characteristic time for a sample to relax up or down to its thermal polarization described above. This process requires local oscillating transverse magnetic fields at the Larmor frequency which will induce transitions from spin-up to spin-down and vice versa. The possible sources of energy to modulate the magnetic field and induce spin flips are very diverse. In a solid insulator, the mechanism is usually lattice vibrations from phonons; in a liquid sample it can be from spin-rotation modulated by collisions or dipole-dipole interactions with other spins; in a gas sample spin-rotation, spin-exchange, diffusion through field gradients, and wall interactions are all possible mechanisms. 1.2.2 Excitation and Detection To induce transitions between energy levels split by the Zeeman effect, a second (RF) magnetic field B1 oscillating at the Larmor frequency is applied transverse to the static magnetic field B0. This application of RF, viewed in a reference frame rotating at the 11 Larmor frequency (called the rotating frame), will torque the magnetization away from the static magnetic field direction towards the transverse plane. The RF can be stopped at a time when the magnetization lies in the transverse plane and the spins will then precess about the main magnetic field B0 at approximately the Larmor frequency. Deviations from the exact Larmor frequency occur because the magnetic field at each point in the sample will not be identical because of dipole fields from nearby spins or magnetic field inhomogeneities. This difference in magnetic field across the sample will cause some spins to precess faster than others. The difference in precession frequencies dephases the spins resulting in a decay of the magnetization coherence in the transverse direction with a characteristic time T∗ 2. This method of inducing transitions between Zeeman energy levels for a finite time to tip the spins in a sample to a specific angle then monitoring the transverse decay is referred to as pulsed MR. The duration of the RF excitation is called the pulse length, and the angle the magnetization resides at with respect to the static magnetic field is called the flip angle. The nuclear MR (NMR) experiments in this dissertation are all done with pulsed NMR. The remainder of this section will describe pulsed NMR and how T∗ 2 relates to spin dynamics in a sample. In all pulsed NMR experiments, a collection of electronics referred to as the spectrometer outputs an RF pulse with a specific frequency, shape, and duration. The pulse is amplified, and sent to an inductor that is oriented perpendicular to the main magnetic field and also contains the sample. To minimize the transmission loss between the amplifier and inductor, the inductor is capacitively coupled such that the impedance at the desired frequency matches the output impedance of the amplifier. The capacitive and inductive structure is called the probe and typically contains tunable capacitors that can change the probe impedance at specific frequencies. This impedance matching is typically narrow in frequency ( f Δf is usually 50-100, where f is the resonant frequency and Δf is the FWHM) which makes the probe an excellent notch filter that is highly sensitive to induction at only the resonant frequency. After the RF pulse ends, the magnetization will precess at the Larmor, frequency and this precessing magnetization will induce an oscillating voltage in the probe. The typical induced voltage in the probe is not much more than a few microvolts, and an NMR spectrometer essentially acts as a high-frequency, high-gain, high-fidelity lock-in amplifier to lift the signal out of the noise and demodulate it down to audio frequency. This demodulated signal, known as a free induction decay or FID, can then be outputted to an oscilloscope 12 or a computer. A FID is a decaying oscillation at the precession frequency in the rotating frame, which has a frequency set by the central excitation frequency, and the envelope decay is the magnetization coherence loss in the transverse direction. See Figure 1.3 for a schematic of the pulse-receive process and a sample FID from a hyperpolarized 3He sample. Since the FID is a measure of the loss of spin-coherence vs time, it can be Fourier Figure 1.3. Simplified NMR experiment. The spectrometer provides an RF pulse that is amplified and transmitted to the probe which is impedance matched to spectrometer and frequency tuned to the the Larmor frequency of the spins in the sample. After the RF pulse finishes the spins precess in the sample. This precession is picked up by the same inductor that delivered the RF and is transmitted back to the spectrometer to be amplified and mixed down to audio frequency. The spectrometer outputs the free induction decay (FID) to an oscilloscope or computer (upper right). The FID shown is from a hyperpolarized 3He sample in a 2 T magnetic field. This FID can be Fourier transformed (FT) to give a frequency spectrum of the resonant frequencies in the sample. In this case the FT results in a single resonance frequency with a width that is determined by magnetic field inhomogeneities. 13 transformed to generate the spectrum of the frequencies required to generate the coherence loss. R. Norberg and I. Lowe proved that that a Fourier transform of the FID contains all of the same frequency information as monitoring the absorption of continuous-wave (CW) RF by a sample as spins are brought into and out of resonance by slowly sweeping the magnetic field. This discovery revolutionized the fields of high resolution NMR spectroscopy and magnetic resonance imaging as well as opened the doors to complex structural and molecular dynamic information about molecules in solution using multidimensional Fourier transform spectroscopy. The Fourier transform of an FID is a frequency spectrum comprised of one or more resonance peaks with associated widths. The width of the resonances are inversely related to the characteristic decay time T∗ 2 of the FID envelope which can be affected by many physical processes. A few of these processes will be mentioned here and then discussed in more detail in the relevant chapters. T∗ 2 is generally expressed as 1 T ∗ 2 = 1 T2 +Γi, (1.4) where T ∗ 2 is the experimental decay constant, T2 is the decay time from microscopic interactions in the sample, and Γi is the dephasing caused by inhomogeneity in the main magnetic field B0. In all experiments presented here, T∗ 2 is minimized by a process called shimming in which the homogeneity of the main magnetic field B0 is adjusted by adding small additional fields in different directions. If T∗ 2 → T2, linewidths have physical signif-icance relevant to the spin dynamics in the sample. The analysis in Chapter 2 used 3He and 129Xe NMR spectra that were field-inhomogeneity and chemical-exchange broadened respectively. The frequency shift measurements in Chapter 3 followed the frequency of a 87Rb hyperfine sublevel transition frequency with linewidths determined by optical pumping and collisional relaxation rates. In Chapter 4, frozen 129Xe T1 was measured using the decay of dipolar-broadened resonance lines. Lastly, in Chapter 5, one aspect of the protein characterization used the frequency shift of a dissolved 129Xe resonance that was broadened by inhomogeneity. CHAPTER 2 MEASUREMENT OF THE FREQUENCY SHIFT ENHANCEMENT FACTOR DURING RB-XE COLLISIONS In 1978 while doing measurements to detect nuclear 129Xe polarization via Rb electron paramagnetic resonance (EPR), B. C. Grover noticed that the magnetic field induced by the noble-gas polarization experienced by the Rb atoms was two orders of magnitude larger than what was classically predicted [29]. He immediately hypothesized that this was due to a strong Fermi-contact interaction during binary collisions; while we now understand that Xe and Rb undergo both binary and molecular collisions, his explanation of the effect was correct. This enhancement is characterized by a dimensionless factor κ, and we have successfully measured it to be [46] (κ0)RbXe = 493 ± 31 . (2.1) This chapter is devoted to the motivation, background, experimental details, and data analysis associated with this measurement. 2.1 Introduction Much of the physics and theory of SEOP has been worked out in great detail [31, 2], and is well understood. However, the problem of optimizing SEOP equipment to produce large volumes of highly polarized 129Xe efficiently remains open. Many current methods exists to characterize an optical pumping apparatus [61]. However, the ability to measure the 129Xe polarization inside an optical pumping cell (without a thermal NMR reference) while actively pumping has not been realized. This measurement of (κ0)RbXe provides the crucial missing link to make measuring the 129Xe polarization possible. As discussed in Section 1.1.3, the Fermi-contact hyperfine interaction αK · S between the noble-gas nuclear spin K and the alkali-metal electron spin S is responsible for alkali- noble-gas spin-exchange. In addition, if the Rb vapor and the noble-gas are highly polarized, 15 then a Larmor frequency shift (relative to zero polarization) will occur in the alkali EPR frequency and the noble-gas NMR frequency. This shift in frequency is due to repeated collisions with spins aligned in the same direction which will, on average, provide a small additional non-zero magnetic field. The shift in the nuclear Larmor frequency due to the hyperfine interaction was first observed by W. D. Knight while doing an NMR experiment on powdered 63Cu [39]. However, the observed effect in 63Cu was due to the intra-atomic hyperfine interaction between Cu conduction electrons and Cu nuclei. In this measurement the hyperfine interaction is interatomic between polarized Rb electrons and noble-gas nuclei. The small collisionally averaged additional field seen by the noble gas and the resulting frequency shift has been calculated in spherical geometry to be [59] Δ|νX| = −1 h |μK| K 8π 3 μBgSκXA[A] Sz , (2.2) where X is the noble gas species, A is the alkali metal species, h is Planck's constant, μK is the nuclear magnetic moment, μB is the Bohr magneton, gS ≈ 2 is the Land´e factor, [A] is the alkali-metal number density, and Sz is the volume-averaged expectation value of the z-component of the alkali-metal electron spin (in units of ¯h). κXA = ( XA − 1)κ1 + κ0 is the complete enhancement factor which contains both molecular (κ1) and binary (κ0) collision contributions and a supression factor XA that depends on the gas pressure [59]. Our measurement was done in the regime where the enhancement is solely due to κ0, and a complete discussion of neglecting the molecular contribution is given in Section 2.5.7. An equation analogous to 2.2 for the EPR shift at low magnetic field where the alkali hyperfine splitting is much greater than the Zeeman energy is given by [59] Δ|νA| = 1 h μB |gs| (2I + 1) 8π 3 μK K κAX[X] Kz . (2.3) where I is the alkali metal nuclear spin, [X] is the noble gas number density, and Kz is the ensemble averaged expectation value of the nuclear spin in units of ¯h. An accurate measurement of κ0 can provide important constraints on the problem of calculating Rb valence electron wavefunctions during a van derWaals collision or computing the van der Waals potential numerically. However, the most immediate application of this measurement is in situ noble gas polarimetry. Equation 2.3 is proportional only to known fundamental constants, κ0, and the noble gas magnetization. Therefore with knowledge of κ0, the noble gas number density, and an accurate measurement of the Rb EPR frequency the polarization of the noble gas can be deduced. Using the classical through-space dipole 16 field (non-zero for all geometries not a sphere) of a cylinder, a 1.5% measurement of (κ0)RbHe was done [8, 54] and (κ0)RbHe has been used to measure 3He polarization in neutron spin structure experiments [65]. All 129Xe polarization measurements prior to this dissertation have been done by refer-encing a thermal NMR signal and suffer from several shortcomings. The measurements rely on a comparison of the 129Xe NMR signal intensity to a thermally polarized sample with a known spin density that fills the exact same volume as the 129Xe sample. If the hyper-polarized (HP) 129Xe signal is compared to a thermally polarized 1H sample, the different gyromagnetic ratios requires electronics that respond identically to a frequencies that are different by a factor of four or the static magnetic field must be adjustable. If the HP 129Xe signal is compared to thermally polarized 129Xe, then the thermal sample must be filled with ∼10 atmospheres to get any usable signal. Guaranteeing the thermal sample occupies the same volume as the hyperpolarized sample can indeed become a dangerous endeavor as any nonspherical geometry is very susceptible to explosions. Furthermore, thermal NMR polarimetry must be done at relatively high-fields where the thermal polarization is high enough to induce a measurable voltage in the probe. Optical pumping experiments are generally done in low fields (∼30 G) for practical reasons and moving the polarized gas to a higher field and then measuring the polarization will provide a reasonable estimate of the noble gas polarization, but will not provide time resolved information regarding the dynamics inside of the optically pumping cell. (κ0)RbHe has been measured before to be (κ0)RbHe = 4.52 + 0.00934T [54] (where T is temp in Celcius) and (κ0)RbXe has been measured to be 650 ± 350 [59] respectively. The measurement of (κ0)RbXe has a very large error dominated by models of the Rb polarization used in the measurement of (κ0)RbXe. 2.2 Experiment Design As can be seen in Equation 2.2, a direct measurement of the enhancement factor κ requires knowledge of the Rb magnetization, the frequency shift of the noble gas, and the precise values of the fundamental constants. To avoid measuring the Rb density (difficult for several experimental reasons) stable optical pumping conditions were prepared and the NMR frequency of the 3He and 129Xe shift was recorded before and after a reversal of the Rb magnetization direction. If the Rb magnetization does not change between the frequency shift measurements for 129Xe and 3He then the ratio of the enhancement factor for Rb-129Xe 17 to Rb-3He is (κ0)RbXe = (κ0)RbHe γHe γXe 2ΔνXe 2ΔνHe . (2.4) where γX are the noble-gas gyromagnetic ratios and 2ΔνX are the shifts in the respective noble-gas NMR frequency when the Rb vapor is exactly flipped from the low- to high-energy Zeeman polarization state. This procedure has several advantages. With a reversal of the Rb magnetization from the high energy state (HES) to low energy state (LES) the frequency shift will be twice as large as the shift from zero Rb polarization. If the procedure takes much less time than the drift of the applied magnetic field B0, the individual shift measurements can be averaged together as independent measurements (Note: the shift is independent of field). Many acquisitions of identical shift measurements permits the use of the average for each nucleus to be used in equation 2.4. Figure 2.1 shows a graphical representation of the experimental concept. 2.3 Apparatus Six sealed, uncoated Pyrex-glass spheres with an inner diameter d of 7 millimeters were fabricated. Each cell contained a few milligrams of natural isotopic abundance Rb metal along with 3He, Xe (enriched to 86% 129Xe), and N2 in the various ratios shown in Table 2.1. The cells were prepared with the method briefly outlined in Appendix C. During the experiment these cells were placed in a safflower oil bath, heated by an aluminum block that was heated by air blown over an external filament heater outside the magnet. The oil was found to be necessary as measured temperature gradients were as much as 20 ◦C across the cell while heating the cell directly with forced air. The cells Table 2.1. Summary of cell contents used in this experiment. All cells are sealed, uncoated Pyrex spheres with inner diameters of ∼7 millimeters. Quoted pressures are referenced to 20 ◦C and the Xe pressure is subject to ∼ 50% uncertainty due to the filling procedure. Cells 155A-C are referred to as low-[Xe] cells and Cell 150A-C are referred to as high-[Xe] cells. Cell Xe:N2:He (Torr) % Xe 155A 5:160:2200 0.2 155B 10:250:2300 0.4 155C 10:168:2300 0.4 150A 50:175:1000 4.1 150B 110:350:2040 4.4 155D 50:172:1200 3.5 18 Figure 2.1. Experiment Concept. By measuring both the 129Xe and 3He NMR frequency before and after Rb reversal from HES to LES, (κ0)RbXe can be deduced by multiplying the ratio of the frequency shift with (κ0)RbHe and the ratio of the gyromagnetic ratios (Equation 2.4). Rb is reversed by a rotation of the λ 4 plate in the optic train of the pumping laser. NMR spectra shown are for illustration of the frequency shift only. The spectra are not actual data and are not representative of experimental lineshapes. were placed in the center of the NMR coil which was wound in a single-turn Helmholtz configuration. When using the ∼10 mm diameter coil (Figure 2.2), the cell was held in place with the coil. When using the ∼35 mm diameter coil a stand was glued in the center of the oil bath to support the cell (Figure 2.3). All results presented here are from the 35 mm probe as (κ0)RbXe results from the 10 mm probe showed a flip angle dependence that is well explained by B1 inhomogeneity and the model of chemical exchange invoked to explain the two peak structure present in the 129Xe spectra (see Section 2.5.2 and 2.5.2.1 for further discussion). In both situations the coil was tuned to both the 129Xe (24.5 MHz) and 3He (67.6 MHz) NMR frequencies with tunable capacitors mounted behind the aluminum block. A switch was added to the tuning circuit that enabled switching between the two nuclei without disturbing the experiment in any other way. The NMR probe (Figure 2.3) was placed in a horizontal 2 T superconducting magnet 19 Figure 2.2. Photograph of the 10 mm NMR probe and Cell 155B. (A) Switch to add/remove capacitance in order to change between 129Xe and 3He resonances without disturbing the apparatus. (B) Capacitors to tune the resonance frequency of the tank circuit. (C) NMR coil (∼10 mm diameter) holding the cell immersed in safflower oil (D). (E) Optic window to admit pumping laser light. (F) Hollowed out aluminum housing heated by external filament heater. (Oxford) that also contained a set of gradient coils (SGRAD MKII 250/150, Techtron 7000 amplifiers) for imaging and a set of rooms temperature shims (Oxford) to homogenize the applied magnetic field. A high-resolution Apollo (Tecmag) NMR spectrometer was used to excite the noble gas and record the FIDs. The FIDs were then outputted to NTNMR software on a computer. To optically pump the Rb vapor, a 30 W diode-laser array model A317B (QPC Lasers) was used. The laser was tuned to the 795 nm D1 resonance and narrowed to ∼0.3 nm (∼130 GHz) with a Littrow cavity [19] with a maximum narrowed output of ∼20 W. The Littrow cavity employs an adjustable diffraction grating that allows tuning of the output wavelength by selectively feeding back a specific wavelength into the diode array. The laser was mounted on an optical table with the optical axis aligned with the magnet bore. The optic axis aligned with the magnet bore will henceforth be referred to as horizontal. The 20 Figure 2.3. Photograph of the 35 mm probe NMR used in the experiment. (A) NMR Coil and (B) stand to support the cell. (C) Resistive thermal device to monitor the oil temperature. (D) Electronics box with the same tunable capacitors and switch shown in Figure 2.2. final optical element before the last collimating lens was a quarter wave plate that could be easily rotated 180◦ about an axis through its optical post (perpendicular to horizontal). When the circular polarizer is set at 45◦ with respect to incident linear polarization, a 180◦ rotation about the optical post is identical to a 90◦ rotation of the fast axis about the horizontal axis. The result of either of these rotations is a reversal of the helicity of light. The reversal of the helicity of the pumping light will reverse the Rb magnetization by 180◦ with respect to the static magnetic field. Figure 2.4 is an image of the laser and associated optics. 2.4 Data Acquisition The following procedure was used to acquire data. 1) Heat the oil and cell to the desired temperature. 2) Check that the probe is correctly tuned for both 129Xe and 3He. 3) Optically pump for 1-2 hours to allow the 3He polarization to build up. 4) Use the auto- 21 Figure 2.4. 30 W, 795 nm optical pumping laser and optics. (A) 2 T superconducting magnet. (B) Room temperature shims and gradient coils. (C) Pipe carrying warm air from the heating element to probe. (D) λ 4 plate rotated to reverse Rb magnetization. (E) External Littrow cavity to narrow the pumping light from the diode array. (F)Watercooling block to which the diode array is mounted. shimming procedure provided with the NTNMR software to control the room temperature shims and maximize the 3He T∗ 2. The 3He FID was used to shim because it is unaffected by diffusion of 3He through regions of polarized and unpolarized Rb and guarantees the most homogeneous field across the cell. 5) Acquire 20-80 FIDs with a rapid reversal of the Rb magnetization between each acquisition (∼10 minutes). 6) Switch the NMR probe to the other nucleus without otherwise changing the apparatus. 7) Acquire 20-80 FIDs again with a rapid reversal of the Rb magnetization between each. 8) Switch back and forth between 3He and 129Xe to improve statistics if desired. The idea behind this procedure of rapid switching of the Rb magnetization between acquisitions was to remove any effects of a slow drift of the applied magnetic field, i.e., the frequency shift is independent of magnetic field and as a long as the FIDs are acquired rapidly (1-2 seconds) compared to any static field drift, the shifts measured between any two consecutive shots can be averaged together as identical independent measurements. Figure 22 2.5 and 2.6 show a simple schematic of this procedure as well as representative data. Reversal of the Rb magnetization was done "by hand" by rotating the λ 4 plate 180◦ about it's vertical axis as fast as possible. The Rb optical pumping time is of order milliseconds and thus the Rb magnetization is reversed instantaneously relative to the 129Xe (∼5-30 seconds) and 3He (∼60 minutes) spin-exchange times allowing NMR spectra to be acquired after rotation of the λ 4 plate before any appreciable loss of the noble gas magnetization. Figure 2.5. Graphical representation of the experiment and representative data. An FID is acquired, the λ 4 plate is rotated (reversing the Rb magnetization), and another FID is immediately acquired. The entire procedure (acquire-reverse-acquire) takes ∼1-2 seconds This is done for 129Xe and 3He 10-40 times to allow for averaging. The 3He FID's exhibit smooth exponential decays in all cases. The 129Xe FID's were acquired in identical experimental conditions as the 3He FID's and show a beating which is characteristic of two resonances. The data shown are from Cell 150A at 200 ◦C. 23 Figure 2.6. FFT of the data shown in Figure 2.5. The 3He spectra show a single, narrow peak that shifts slightly under Rb magnetization reversal as opposed to the Xe where the spectrum is reversed and shifts by ∼50 Hz, but the peak near 0 Hz does not shift much. The 129Xe peak that stays near 0 Hz is from 129Xe colliding with unpolarized Rb, and the peak that shifts by ∼100 Hz is from 129Xe colliding with polarized Rb. See Section 2.5 for further discussion about the exchange broadened 129Xe spectra. 2.5 Data Analysis and Discussion With a high precision measurement of the noble-gas NMR frequency and knowledge of (κ0)RbHe Equation 2.4 can be used to obtain values for (κ0)RbXe. However, given the shape of the spectra demonstrated in Figure 2.6 the analysis of the NMR frequency shift requires careful handling of several subtleties. Figures 2.6 and 2.7 show typical FFT spectra prior to any data analysis. The 129Xe and 3He have decidedly different structures with the following characteristics: 1) the 3He spectra always exhibit a single, narrow resonance that never changes shape; 2) the 129Xe spectra always exhibit two peaks; 3) the 129Xe peak separations and widths increase with 24 Figure 2.7. Typical 3He and 129Xe raw spectra from cell 155B acquired under steady-state SEOP conditions. The narrow 129Xe peak at 0 Hz was acquired with the laser blocked; it has been amplitude-normalized to appear on the same graph. The double peak in the 129Xe spectra at all but the lowest temperatures represents regions of highly polarized and nearly unpolarized Rb vapor; the lines are broadened and begin to coalesce due to diffusion of 129Xe between these two regions. For 3He, the much smaller frequency-shift dispersion and more rapid diffusion yields a single narrow peak in all cases. The respective shifts in the spectral center of mass upon reversal of the Rb magnetization were used in Eq. 2.4 to extract (κ0)RbXe. 25 temperature; 4) the relative strength of the two peaks becomes more equal at higher temperatures; 5) when blocking the laser the 129Xe peak is always very narrow (∼2-4 Hz), single resonance directly between the HES and LES spectra. The 129Xe peak structure is due to Xe diffusing between regions of polarized and unpolarized Rb much more rapidly than the Rb-Xe spin exchange rate and on the order of the difference in resonance frequency between regions of polarized and unpolarized Rb as defined by Equation 2.2. This is identical to the NMR phenomena known as chemical exchange [5], except instead of exchanging between two chemically distinct sites, the 129Xe is diffusing between regions of polarized and unpolarized Rb in the cell (see Section 2.5.2). These distinct regions of polarized and unpolarized Rb are due to attenuation and lensing of the optical pumping laser inside the optical pumping cell. Since Equation 2.2 is a collisionally averaged shift that is proportional to the volume averaged expectation value of the a electron spin, the correct frequency shifts to use in Equation 2.4 are the spectral center-of-mass (COM) or "first moment" [64] shifts. However, using a COM analysis to compensate for an inhomogeneous Rb magnetization has three requirements. 1) The 3He and 129Xe magnetization distributions must be identical in the cell. That is, the 129Xe spectrum must not be weighted incorrectly towards the polarized Rb peak when compared to the 3He spectrum. Another way to view this is that the 129Xe must diffuse around the cell much faster than the characteristic 129Xe-Rb spin-exchange time. This was found to be true as the characteristic spin-exchange time was measured to be 3-20 seconds, compared to the diffusion time measured at ∼150 ms (see Section 2.5.1). 129Xe was also found to be homogeneous with imaging (see Section 2.5.3). (2) The Rb magnetization distribution must not change between measurements of the 129Xe and 3He shifts (typically 10-15 minutes). This could not be determined experimentally since Rb electron resonances at 2 T are well into microwave frequencies and pose many experimental difficulties. However, stability of the Rb magnetization between 3He and 129Xe measurements was inferred from the repeatability and stability of the measured value of (κ0)RbXe. Over 3000 frequency shifts were measured at different temperatures over the course of several months. (3) Since the Rb magnetization is inhomogeneous there is a through space magnetic field inside of the cell generated by the Rb atoms. If this through space field, on average, generates a 3He frequency shift on order of the contact shift due to (κ0)RbHe, then the 3He 26 shift cannot be easily related to the 129Xe shift and Equation 2.4 is no longer valid. To determine if this was indeed the case, numerical modeling was done of the through-space dipole field inside of a sphere with various magnetization geometries (see Section 2.5.5). The most extreme geometries yielded, at most, less than a 1% effect. Given the above conditions were satisfied, the COM shift can be used in equation 2.4. Measuring the 3He spectral COM is simple since 3He is undergoes fast exchange (see Section 2.5.2), and consequently the position of the peak corresponds to the spectral COM. The 129Xe spectral COM were not so simple. The first attempts were numeric integrals over a chosen frequency range, but the results were wildly inconsistent due to integration of the noise not resulting in zero, and the integrals were also dependent on the phase of the real signal relative to the spectrometer reference. Attempts were also made at fitting the peaks to two-site chemical exchange models; however, the expression is complicated (Equation 2.5) and the assumption that only two sites exist is not true, although it is a reasonable simimation (see Section 2.5.2). Instead the 129Xe FIDs were multiplied by an exponential (apodization) with a time constant approximately four to five times the resonance splitting, Fourier transformed, and the position of the maximum value of the magnitude signal was recorded. This procedure conserves the COM information (Appendix A) and the maximum value of the magnitude will correspond to the peak position of a correctly phased real spectrum. Thus, a comparison of the 3He peak shift to the 129Xe apodized peak shift can be done to extract (κ0)RbXe. Table 2.2 shows sample frequency shift data. Six cells were made and they can be broadly divided into two categories: high Xe-concentration with 50-100 Torr (high-[Xe]), and low Xe-concentration with 5-10 Torr (low-[Xe]). See Table 2.1 for a complete description of the cell contents. The calculated values of (κ0)RbXe are plotted vs. temperature T for the three low-[Xe] cells in Figure 2.8. The error bars shown reflect only the statistical uncertainty in the measured frequency-shift ratio and do not include the uncertainty in (κ0)RbHe; at the lower temperatures the error is dominated by the large relative uncertainty in the small 3He frequency shifts. The low-[Xe] cells (both individually and collectively) show no significant temperature dependence be-tween 140-220 ◦C; the weighted average of all of these points yields an uncertainty of < 1%. If we take the same weighted average on a cell-by-cell basis, a larger spread is observed (see Table 2.3), suggesting some unknown systematic errors of a few-percent. These errors could include small cell-dependent geometrical effects. In some cases, residual asymmetries were apparent in the HES and LES 129Xe spectra with respect to the unpolarized-Rb peak 27 Table 2.2. Sample frequency shift data after processing described in Section 2.5. ¯x is the average, and σ¯x is the standard deviation of the mean. The error in (κ0)RbXe is the statistical error of each nucleus added in quadrature. There is an error associated with (κ0)RbHe. However, this has been added to the final result and not to the individual values. For every point in Figure 2.8, a similar set of data was acquired. Experiment #61: 201◦C Experiment #61a: 190◦C Δν 3He (Hz) Δν 129Xe (Hz) Δν 3He (Hz) Δν 129Xe (Hz) 3.052 91.6 1.908 56.9 3.242 95.6 1.812 61 3.147 85.5 1.812 52.9 3.243 99.8 1.812 55 3.242 91.6 1.812 56.9 3.147 111.8 1.908 52.9 3.433 91.6 1.908 52.9 3.243 97.7 2.098 50.8 3.052 86.8 1.811 56.9 3.147 95.6 1.716 56.9 ¯x ± σ¯x 3.19±.04 94.8±2.7 1.86±.03 55.3±1.0 (κ0)RbHe 6.397 6.295 (κ0)RbXe 519±16 512±12 Table 2.3. Summary of cell contents and (κ0)RbXe results. (κ0)RbXe is computed for each of the low-[Xe] cells from the weighted average of that cell's data; we have excluded the high-[Xe] cells because of their anomalous behavior at high temperature (see Section 2.5.6) Cell Xe:N2:He (Torr) (κ0)RbXe 155A 5:160:2200 495±6 155B 10:250:2300 490±5 155C 10:168:2300 530±9 150A 50:175:1000 − 150B 110:350:2040 − 155D 50:172:1200 − (Figures 2.7 and 2.6). These may be due to imperfections or drifts in laser tuning (see Section 2.5.4) or power and may introduce some additional error at the ∼1% level. However, we found the two spectral COMs to be equidistant from the unpolarized-Rb peak in all data used to measure (κ0)RbXe. For the above reasons, the error was accordingly increased in the shift ratio, which is represented by the hatched range in Figure 2.8. Finally, we add the 1.8% uncertainty in the value of (κ0)RbHe [54] in quadrature to this range to arrive at our final result in Equation 2.1. 28 Figure 2.8. Enhancement factor (κ0)RbXe plotted vs. temperature for three low-[Xe] cells. The weighted average of all the low-[Xe] data points is 493, with the estimated uncertainty shown by the gray hatched region. This uncertainty is estimated from cell-to-cell variations in the weighted average of (κ0)RbXe (see Table 2.3). These temperature-independent data represent the best estimate of (κ0)RbXe. 29 Theoretical calculations in reference [59] resulted in (κ0)RbXe ≈700 with little to no temperature dependence. The discrepancy from our value is most likely due to imprecise knowledge of the molecular van der Waals potentials and unperturbed valence electron wavefunction enhancement values. The remainder of this chapter will be broken into sections to discuss several control experiments, chemical exchange, additional experimental observations, and the anomalous high-[Xe] measurements. 2.5.1 129Xe Diffusion Measurement A measurement of the 129Xe diffusion coefficient will provide two pieces of information. First, it will provide a check on the assumption that 129Xe diffuses across the cell faster than the spin-exchange time resulting in a homogeneous noble-gas magnetization. Second, it can provide an estimate of the exchange rate to support the hypothesis of chemical exchange broadened 129Xe spectra. Measurement of the diffusion coefficient DXe was performed using the Carr-Purcell- Meiboom-Gill (CPMG) pulse sequence [64]. The CPMG sequence is a 90◦ pulse followed by a series of 180◦ pulses of alternating phase all done while applying a Z-gradient of known value. The 180◦ pulses refocuses transverse coherence loss due to magnetic field inhomogeneities into echos between pulses, and the resulting echo decay envelope is due to diffusion through the applied gradient. The phase alternation removes the error ac-cumulated from sequential imperfect 180◦ pulses. The CPMG was performed six times under varying conditions: an identical pulse sequence (same echo delay) was done with the pump laser on and off, and with the Z-gradients set to 0%, 4% (.81 G/cm), and 6% (1.21 G/cm) of their maximum operating range. The result for DXe from the 4% and 6% gradients were averaged together and assigned a 10% error from the equipment manufacturers specifications. Figure 2.9 shows sample data. The average of all the different CPMG runs together yielded DXe = 0.51±0.05 cm2/s. The diffusion coefficient is highly dependent on the gas composition and using previously measured values from the literature to estimate the diffusion coefficient for the gas composition in this experiment demonstrated reasonable agreement. The diffusion coefficient of Xe in 1 atmosphere of N2 is ∼0.21 cm2/s [74] when scaled for temperature (D ∝ T3/2 [52]). In reference [37], the calculated diffusion coefficient for a 25%-75% mixture of Xe-He at 175 ◦C is stated to be ∼1 cm2/s. Scaling the diffusion coefficients for pressure 30 Figure 2.9. CPMG decay taken on cell 150A at 170◦C. The error bars are from finding the standard deviation of the top 11 points of each echo. The parameters D and M0 are allowed to float; T2 was found by plotting the data with no gradient, setting D and H to zero, and allowing T2 to float. and the gas ratio in this experiment, and then adding them in reciprocal, gives .54 cm2/s. This is probably an underestimate of the diffusion coefficient given the gas composition in this experiment since cell 150A does not have a 25%-75% Xe-He gas ratio; however, the results are consistent. The spherical measurement cells had an inner diameter of ∼7 millimeters, and the characteristic diffusion rate 1/τd ≈ 6DXe/d2 ≈ 10 hz. This is on the order of the typical resonance splitting seen in the 129Xe spectra and the characteristic diffusion time (∼100 ms) is much faster than the measured Rb-129Xe spin-exchange times (which were 3-20 seconds depending on temperature). 2.5.2 "Chemical" Exchange Between Regions of Polarized and Unpolarized Rb The well-known NMR phenomenon of chemical exchange [5, 58] has been studied ex-tensively and can provide much physical insight into the dynamics of spin systems. This 31 effect manifests itself when spins move between distinct resonances on T2 timescales, i.e., timescales that correspond to the difference in precession frequencies across the sample. Depending on the exchange rates relative to the difference in frequencies, the NMR spectrum can be drastically different. The equation for a NMR spectrum where spins are exchanging between two distinct resonant frequencies can be acquired by solving the modified Bloch equations with 2-site chemical exchange [58]: f(ν) = iγB1M0 1 T2 − 2iπ (ΔνB) PA + kA + kB + 1 T2 − 2iπ (ΔνA) PB 1 T2 − 2iπ (ΔνB) 1 T2 − 2iπ (ΔνA) + kB 1 T2 − 2iπ (ΔνA) + kA 1 T2 − 2iπ (ΔνB) , (2.5) where ν is the excitation frequency, i = √ −1, γ is the gyromagnetic ratio, B1 is the RF field strength, M0 is the magnetization, ΔνB = νB − ν and ΔνA = νA − ν, νA and νB are the rotating-frame precession frequencies while in site A and B, respectively, T2 is the relaxation in the absence of exchange which can be different for the two sites but has been chosen to be equal for simplicity, kA and kB are the exchange rates per atom from A to B and B to A, respectively, and PA is the relative population of A with PA + PB = 1. A plot of this function with different exchange rates is shown in Figure 2.10. In terms of shaping an NMR spectrum, three different chemical-exchange regimes exist which are demonstrated in Figure 2.10. The "slow exchange" regime where two distinct resonant peaks are apparent with minimal broadening is defined by τex (Δω) 1 where Δω is the difference between the two resonant frequencies. The "intermediate exchange" regime where the two resonances begin to broaden and coalesce is defined by τex (Δω) 1. The "fast exchange" regime is when the individual resonances have narrowed to a single resonance positioned at the population-weighted average of the two resonances. Fast exchange is defined by τex (Δω) 1. These different exchange regimes can be thought about qualitatively by picturing spins (or arrows) dephasing in the rotating frame. After a 90◦ pulse the spins are all in the transverse plane in the same direction. The two resonant frequencies will each have a given population that can be thought of as two groups of spins and each group has their own T2 determined by the sample environment. In the slow exchange regime, the two groups of spin never exchange and the transverse coherent magnetization will "beat" with the difference in precession frequency in the rotating frame 32 Figure 2.10. Simulation of two site chemical exchange using equation 2.5. The average exchange rate per atom is shown in the legend. The population ratio of the two sites is 60/40 with a resonance splitting of 30 Hz. Actual 129Xe spectra are similar in shape to the intermediate exchange (black line) where it is clear the peaks are broadening and moving towards each other with increasing exchange, whereas 3He data are better represented by the fast exchange peak (blue). and dephase with a combination of the T2s from the different resonances. In the fast exchange regime, the spins are mixed too fast to generate a coherent difference between the two resonances resulting in an average of two frequencies. Intermediate exchange is a combination of slow and fast exchange. While the concept of exchange broadening has been introduced in the context of two distinct resonant frequencies, it should be understood that any number of resonances can be present, but the physical picture will not change much. However, Equation 2.5 will no longer be valid and picturing the spins bouncing between different resonances in the rotating frame becomes confusing. The connection to chemical exchange in an optical pumping cell is best thought of in terms of where the optical pumping light is inside the optical pumping cell. The cell is spherical and will focus the incoming optical pumping light, which will create a sharp boundary between regions of light and no-light as the laser propagates towards the back of the cell. In addition to lensing, the pumping laser can be attenuated by the Rb vapor. 33 At typical running temperatures, the cell is hundreds of optical depths thick. Because the absorption of the laser light is polarization dependent once the photon flux drops below the necessary threshold to polarize the Rb vapor, the light will penetrate about only one optical depth further into the cell [72]. Given that our cells were ∼7 millimeters in diameter, one optical depth would be ∼100 micrometers thick. Thus, the two effects that shape the laser profile inside the cell will both create sharp boundaries between regions of polarized and unpolarized Rb, which can lead to an exchange broadened spectrum because, according to Equation 2.2, the resonant frequency for 129Xe is dependent on the Rb polarization. The 129Xe spectra always have two peaks. One of the two peaks is close to 0 Hz and when the Rb is reversed only moves a small amount to the other side of 0 Hz. If this peak is due to contact with unpolarized Rb, it should not move when the Rb is reversed. However, if the 129Xe is exchanging with a different resonant frequency (namely coming in contact with polarized Rb), the unpolarized peak that should be at 0 Hz can be shifted slightly slightly off of 0 Hz towards the other resonance. The shift of the 129Xe resonance in contact with unpolarized Rb is evidence that strongly indicates the 129Xe spectra are, in fact, exchange broadened. Additional qualitative proof of exchange broadened 129Xe spectra is that the simulated intermediate-exchange spectrum (black line in Figure 2.10) is very similar to actual 129Xe spectra (Figures 2.6 and 2.7) at higher temperatures. The change in the 129Xe spectra as a function of temperature (Figure 2.7) is easily understood in the context of chemical exchange. At the lowest temperatures (Figure 2.7 150 ◦C) the contribution from the unpolarized Rb peak is small and results in just a "shoulder" towards 0 Hz on the main peak, and at the highest temperatures, the spectra exhibit two distinct peaks mirrored about zero. The reason for this change as a function of temperature is twofold. First, the Rb number density increase exponentially with temperature [38], and for a given polarization the difference in 129Xe frequency when in contact with polarized and unpolarized Rb should increase exponentially as well. Second, because the Rb number density increases with temperature the pumping laser cannot penetrate as deep into the cell at the higher temperatures making the region of polarized Rb much smaller. The diffusion coefficient will change by only about 15% from 150 ◦C to 200 ◦C and as a result, the lower temperature 129Xe spectra more closely represent fast-exchange, whereas at higher temperatures, the spectra become distinctly reminiscent of the intermediate-exchange regime. That is, the increase in diffusion coefficient cannot keep up with the increase in frequency difference as the temperature increases. 34 2.5.2.1 129Xe Flip Angle Dependence of (κ0)RbXe While making early measurements of (κ0)RbXe, a dependence on the size of the 129Xe flip angle was noticed. This dependence does not make sense from the theory that yields Equation 2.2. The frequency shift is dependent only on (κ0)RbXe and the Z-component of the Rb magnetization. For a transverse noble gas magnetization to appreciably effect its own frequency shift, the Rb magnetization would have to be affected on T2 timescales. This cannot be true since the fastest measured spin-exchange times were of order 5 seconds and T∗ 2 with the laser blocked (no Rb polarization) was never longer than a few hundred milliseconds. The cause of this flip angle dependence was due to the RF field strength being inho-mogeneous across the sample, which caused a difference in the flip angle between 129Xe in regions of polarized and unpolarized Rb. Even though the 129Xe magnetization is uniform across the cell, the time required to rehomogenize the cell by diffusion after disturbing the magnetization is on the order of 100 ms (see Section 2.5.1). Therefore, if the 129Xe that is in contact with unpolarized Rb is flipped by the RF pulse slightly less than 129Xe in contact with polarized Rb, then the spectrum will be weighted towards the polarized Rb peak. This, in turn, will give an incorrect result for (κ0)RbXe when compared to 3He, which homogenizes instantaneously on all timescales relevant to this experiment. With the the 10 mm coil (Figure 2.2) at small 129Xe flip angles (less than 20◦), the effect was found to disappear. However, to avoid this issue completely, a bigger Helmholtz coil was constructed (Figure 2.3) to generate a homogeneous RF field strength across the entire cell. 2.5.3 129Xe Imaging to Verify Noble Gas Homogeneity The assumption that the 129Xe magnetization distribution must be identical to the 3He (i.e., it must be uniform) is essential to perform a first-moment analysis. The CPMG diffusion measurements provide strong evidence for 129Xe homogeneity, however, imaging provided direct verification. 1-D slice selection MRI was done on cell 150A at 170◦C. 1-D slice select in the Z-direction selects slices and collapses all the signal amplitude from the X and Y directions to a single point. Therefore the signal strength S of an image of a uniformly magnetized sphere is S(z) ∝ π R2 − z2 where z is the position along the sphere with the center of the sphere at 0, and R is the radius of the sphere. Figure 2.11 shows the images acquired with 35 Figure 2.11. 129Xe signal strength as a function of position along the z-axis (along the magnetic field and optical pumping axis). The signal strength represents all the signal from 129Xe in the x and y directions at a chosen z value. The signal with the laser on has been scaled to amplitude match the signal with the laser off. No significant difference between signals with the laser on and laser off indicates the 129Xe frequency shift data is not preferentially weighted towards the polarized Rb peak. no difference within error between the images acquired with the pump laser on or off and both images are parabolic as expected. If the Xe magnetization is inhomogeneous while optically pumping, then there would be a difference between the images with the laser on or off. 2.5.4 SEOP at High Field: σ+ and σ− Energy Shift In early measurements, after extensive shimming of the main magnetic field using the 3He T∗ 2, an asymmetry in the spectrum shape was sometimes still observed between the 129Xe LES and 129Xe HES spectra. The cause of this asymmetry was traced back to the tuning of the optical pumping laser. To reverse the Rb magnetization, the pumping laser is switched from σ+ to σ− or vice versa (Section 1.1.2), and because the alkali vapor is 36 being optically pumped at 2 T, the mj = −1/2 → mj = 1/2 transition selected by σ+ will be shifted in energy relative to the mj = 1/2 → mj = −1/2 transition selected by σ− by ∼30 GHz. The pumping laser had a narrowed width of ∼0.3 nm at 795 nm which is ∼140 GHz. If the spectrum of the pumping laser is such that the absorption of σ+ light is different than σ− then the penetration depth of the laser will change and consequently the NMR spectrum will change as it depends heavily on the ratio of polarized to unpolarized Rb in the cell. Figure 2.12 shows 129Xe spectra as a function of laser tuning. In all data presented in this dissertation, the laser was tuned prior to data acquisition to ensure the HES and LES spectra were symmetric and, more importantly, the COM was positioned an equal amount away from zero for both HES and LES spectra. 2.5.5 Numerical Modeling of the Geometric Effect The imaging and diffusion measurements provide strong evidence that the noble gas magnetization is uniform and will therefore not have a through-space effect on the NMR shift. However, a through-space magnetic dipole field from the nonspherical geometry of the Rb magnetization can possibly have an effect on the noble-gas NMR. To test this, numerical modeling was done on several geometries, and the averaged through-space magnetic field was compared to 8π 3 (κ0)RbHe. In the most extreme cases, the numerical modeling results showed the effect would be negligible. The magnetic field due to a magnetized object discretized as a collection of magnetic dipoles is written as [33] B = 3n(n ·M) +M |x − x |3 d3x + 8π 3 δ(x − x ) , (2.6) where x is the field point, x is the source point, n is the unit vector in the x−x direction, and M is the magnetization of the infinitesimal volume d3x . The first term in the through space dipole field generated at any point in space is due to a magnetized object. However this integral cannot include the point x = x since the field will diverge. To complete the description, a second term is added to include "contact" with the piece of magnetization at the field point. This contact term is identical to what one finds for the field inside of a uniformly magnetized sphere when performing a surface charge integral; As the sphere volume is decreased, the description becomes a delta function. A comparison of the first term to the second was done to test the possible contribution from an inhomogeneous Rb magnetization. To perform the numeric integration of the first term in Equation 2.6, a 43x43x43 array 37 Figure 2.12. Demonstration of the 129Xe spectrum dependence on the pump laser tuning. The wavelength listed on the right is the peak of the laser spectrum viewed on an Ocean Optics Spectrometer, in all cases the laser has a spectral width of ∼0.3 nm FWHM with an approximate Lorentzian/Gaussian lineshape. As the laser is tuned through the D1 resonance (∼794.7 nm) the HES and LES spectra swap characteristics. This dependence of the 129Xe spectrum on the pump laser tuning is a result of the σ− and σ+ absorption energy being shifted when a Rb atom resides in a 2 T magnetic field. 38 was set up with the coordinate system origin and center of the sphere placed at the center of the array. A magnetization M = 1 in the Z-direction was assigned to each point with the option to cutoff the magnetization and make it 0 at any point. This roughly simulates the pumping laser magnetizing the Rb and then being quickly attenuated. Then each point was stepped through and the field calculated by summing the contributions from all other dipoles in the array. A series of If-Then statements were used to determine whether magnetization existed at a given point. The X,Y, and Z components at each field point were outputted to a text file and then analyzed. The code used is shown in Appendix B. No susceptibility effect of the glass was taken into account, and the permeability of the sphere was neglected as a dilute gas has essentially zero permeability. Figure 2.13 shows the results. The numerical modeling is conclusive evidence that the Rb through-space fields can be neglected while analyzing the 3He frequency shift. The through-space effect on the 129Xe can be neglected in all cases because (κ0)RbXe is two orders of magnitude larger than (κ0)RbHe (i.e. the second term in 2.6 is large compared to the first no matter what geometry of the Rb magnetization is present). Additional proof the numeric integral was done correctly is in the lower right figure where the magnetization is cylinder-like. A uniformly-transverse magnetized cylinder has a total magnetic field (inside) of −2πM with a through space field of −2π 3 M. In the numeric results, the regions of most negative values of field, Bz ≈ −0.18π 3 (κ0)RbHeM = −4.8π 3 M, which is on order of what is expected for a perfect cylinder. 2.5.6 High Xe Concentration Data Below T≈175 ◦C, the data for the high-[Xe] cells (Figure 2.14) are generally consistent with the hatched range (Figure 2.8) that characterizes the low-[Xe] data. However, at the highest temperatures the measured shift ratio drops by about 20%. These 10 or so data points out of 60 acquired for all six cells are at the extremes of high temperature, high [Rb], and rapid Rb spin-destruction (due to higher [Xe]); yet we are unable to connect these physical conditions in a plausible way to the observed systematic depression of the shift ratio. We considered whether fast Rb-129Xe spin exchange might lead to a violation of our fundamental assumption of uniform nuclear magnetization, but this would increase the shift ratio by preferentially weighting the regions of higher Rb magnetization in the 129Xe spectrum. We also tested for extreme geometrical effects by remeasuring the shift ratio for both high- and low-[Xe] cells at a given temperature after significantly decreasing the laser 39 Figure 2.13. Numerical integration of Equation 2.6. All figures are Y-Z slices down the middle of sphere with each showing the through-space field for different depths of magnetization. The colors show the direction and magnitude of Bz only. By is not zero throughout this slice, however Bx and By both average to zero over the sphere and only the contribution to Bz is the quantity of interest. (Bz)AV G is the average over the entire sphere, not just the slice shown. Even the decidedly nonspherical magnetization distribution show a negligible effect when averaged over a sphere including local regions with 15% deviations from 8π 3 (κ0)RbHe. 40 Figure 2.14. (κ0)RbXe vs. temperature for the high-[Xe] cells. The method used to generate the data points is the same method used in Figure 2.8, and the gray hashed box covers the same area on the graph as in Figure 2.8 as well. These high-[Xe] data are consistent with the low-[Xe] data up to about 175 ◦C where the ∼20% drop-off at the highest temperatures is not understood. power. The 129Xe spectrum changed dramatically under these conditions, but the shift ratio was unchanged within error. The anomalous high-[Xe] high-temperature data points were excluded from the main result because they are neither consistent from cell to cell nor consistent with a plausible theoretical temperature dependence (reference [59] calculates a zero or very weakly positive temperature dependence). 2.5.7 Molecular Considerations Rb-Xe molecular formation can have an effect on 129Xe frequency shifts. Recall the shift is due to a collisionally averaged field seen by the 129Xe nucleus due to spin polarized Rb atoms. If during a collision the Rb electron spin is torqued appreciably (more than a 41 radian), the average field seen by the 129Xe nucleus will be decreased. The effective field due to formation of Rb-Xe molecule is about 100 G [11] and this experiment was done at 20,000 G. Therefore, the molecular contribution to this experiment is zero for any gas pressure. Reference [59] presents a very thorough discussion of the molecular contribution to the enhancement factor κ, and only the necessary highlights will be recounted here. The expressions for the alkali and noble-gas frequency shifts (Equations 2.3 and 2.2) contain the enhancement factors κAX and κXA respectively, and not the measured κ0. κ0 is just the enhancement due to binary collisions between Rb and Xe atoms. κXA is the complete enhancement factor and takes the form κXA = (κ0 − κ1) + XAκ1 which includes the contribution from long lived molecules κ1 and a suppression factor XA. The reason for the separation of these two enhancement factors is simply to account for the two regimes where calculation is possible: the high-pressure regime defined by κ0 where, during a collision, the alkali electron-spin evolution angle about the molecular angular momentum is small (much less than a radian), and the low pressure regime defined by a κ0 − κ1 where the alkali-spin is torqued significantly during a molecular collision. The suppression factor XA can vary between 0 and 1, and is a convenient way to treat the intermediate regime when the system is transitioning from a frequency enhancement described by κ0 − κ1 to only κ0. If the experiment were done at low field (comparable to the molecular field) the frequency enhancement would then depend on the cell pressure relative to the "characteristic pres-sure." The characteristic pressure is the gas pressure at which the Rb-Xe molecular lifetime is such that the Rb electron spin will, on average, precess by a radian about the molecular angular momentum [59, 74]. Characteristic pressures depend on what types of atoms are forming and breaking up Rb-Xe van der Waals molecules, but all are ∼300 Torr [74]. For reference, when a cell pressure is half of the characteristic pressure, the enhancement factor κXA is within 1% of κ0. 2.6 Conclusions This chapter describes in detail our successful measurement of (κ0)RbXe. This measure-ment will allow for 129Xe polarization measurements to be done inside of optical pumping cells potentially providing more insight into the physics of spin-exchange between Rb and 129Xe. This additional insight will allow for much more precise optimization of the output 129Xe polarization from modern flow-through polarizers. 42 Several experimental facts relevant to practical SEOP were also observed. At high mag-netic fields, the Rb D1, σ− and σ+ energies are shifted in energy by a non-negligible amount when using solid-state diode arrays. A 20 ◦C temperature gradient across ∼1 centimeter was measured when heating the cell with forced air. The 129Xe magnetization does not mirror the Rb magnetization under any of the experimental conditions in this measurement. Lastly, the results for (κ0)RbXe from the high-[Xe] cells are very intriguing and no plausible explanation has been put forward at this point. Further experimentation, possibly at lower magnetic fields, is necessary to find an explanation for these data. CHAPTER 3 129Xe POLARIMETRY USING THE SHIFT OF 87Rb HYPERFINE TRANSITION FREQUENCIES Many applications of hyperpolarized gas rely on rapid, continuous production of po-larized 129Xe [36, 67, 75] where the current state-of-the-art technology is flow-through polarizers [61, 57, 23]. This technology has the ability to provide several (1-10) liters per hour of hyperpolarized 129Xe when the 129Xe is a small percentage (1-3%) of the total gas density. However, all the current designs seem unable increase the 129Xe polarization beyond ∼40% (under reasonable running conditions) for reasons that are not completely understood. A detailed analysis of the 129Xe polarization inside the optical pumping region under different conditions would greatly improve our understanding of the underlying physics and experimental realities of flow-through polarizers. The previous chapter described the method by which a successful calibration of (κ0)RbXe was done. This chapter focuses on using (κ0)RbXe to measure the 129Xe polarization by monitoring the 87Rb hyperfine electron paramagnetic resonance (EPR) frequency while actively optically pumping. A Rb EPR frequency counting apparatus was developed on the Utah flow-through polarizer that fell short of a definitive 129Xe polarization measurement, but produced several interesting and unexpected results. The data collected, while still preliminary, point towards the possibility of probing fundamental atomic physics and is an essential first step for future 129Xe polarimetry measurements. 3.1 Introduction As stated in Chapter 2 (Equation 2.3) the alkali-metal EPR frequency in the presence of noble-gas is given by the following: Δ|νA| = 1 h μB |gs| (2I + 1) 8π 3 μK K κAX[X] Kz . (3.1) 44 This gas-phase shift of the alkali metal EPR frequency is caused by a Fermi-contact interaction between the alkali valence electron and noble gas nucleus experienced during many rapid collisions that result in an average additional magnetic field experienced by the alkali valence electron. For a given noble-gas magnetization, μK K [X] Kz , the scale of the shift is determined by κAX and the size of the Rb gyromagnetic ratio, 1 h μB|gs| (2I+1) . Everything is known in Equation 3.1 except the noble gas magnetization. Therefore, with knowledge of the noble gas density, which is typically known in most optical pumping experiments, and with an accurate measurement of the alkali EPR frequency, the polariza-tion of the noble gas Kz K can be determined. Estimating the size of the alkali EPR shift is instructive for understanding the difficulty of this measurement. Equation 3.1 can be rewritten in terms of 129Xe quantities to be Δ|νRb| = 4 3 μBgs (2I + 1) γXeK (κ0)RbXe [Xe] |PXe| . (3.2) where I = 3/2 for 87Rb, μB = 9.274 × 10−21 erg G , (κ0)RbXe = 493 ± 31, γXe = 7393 rad s×G, gs ∼2.002, K =1/2, PXe = KZ K is the polarization of the 129Xe and can vary from 1 to -1, and [Xe] is the Xe gas number density. These values yield Δ|ν87Rb | ∼ 80kHz × [Xe] × |PXe| , (3.3) where [Xe] is now the density of isotopically natural Xe in amagats. For typical optical pumping mixtures of lean Xe concentration (0.01-0.03 amagats), this yields a shift of ∼1 kHz at 50% polarization. The 87Rb EPR resonance is about 20 MHz at 30 G so, from the theoretical predictions, the magnetic field must be stable to one part in 105, or 300 μG. This is very challenging, but not impossible. For the reader's reference, a high-resolution NMR magnet and spectrometer can typically be stabilized to ∼10 ppb, however apparatus of that type are typically at much higher fields (100,000 G) where 10 ppb is ∼1 mG. This experiment has a simple design: Monitor the Rb EPR frequency as function a of the Xe density in order to to back out the 129Xe polarization. The remainder of this chapter will discuss in detail the Utah flow-through polarizer, some theory behind Rb hyperfine structure in a magnetic field, the EPR detection apparatus used, and results. 3.2 The Utah Flow-Through Polarizer The Utah flow-through polarizer was initially designed and built by Geoff Schrank and resides in the Saam Labs at the University of Utah. My initial graduate work was helping 45 in a fairly thorough characterization (only lacking the in situ 129Xe polarization) of the polarizer which was published in Physical Reveiw A [61] and Geoffry Schrank's thesis [60]. In this dissertation I will discuss only the details necessary to understand the work presented. A comprehensive discussion of the flow-through polarizer can be found in the thesis of G. Schrank [60]. The idea behind a flow-through polarizer is to generate a continuous gas stream that is free of alkali metal and contains hyperpolarized 129Xe. This is accomplished by flowing a gas stream containing 129Xe through a polarized alkali-metal vapor that is kept spatially contained by large temperature gradients and gravity. The alkali vapor is highly polarized by continuous optical pumping with circularly polarized D1 light (see Section 1.1.2), and as the gas flows through the polarized alkali vapor the 129Xe becomes polarized and then remains polarized as it flows into cooler parts of the system where the alkali metal sticks to the glass was leaving an alkali-free gas stream. In addition the optical pumping cell is long (∼1m) which helps mitigate localized heating by the pumping laser. Localized heating can cause undesirable pockets of very high Rb number density which can cause significant laser attenuation and create regions of unpolarized Rb that will hinder the capability of the device to output maximum 129Xe polarization. The important experimental features of the polarizer relevant to the measurement of the Rb EPR frequency are: (1) The relative gas composition and total pressure inside the optical pumping cell can be controlled precisely. Mass flow controllers (1.5% full-scale) admit a precise (1.5% full-scale) flow to the input of the optical pumping cell and a pressure regulator (Bellofram T77 506) backed by a vacuum pump controls the pressure inside the optical pumping cell. In addition, a high precision (±0.01 psi) pressure gauge (Ashcroft) was installed at the optical pumping cell inlet to monitor the pressure inside the cell where the EPR measurements were done. (2) The Xe can easily be cycled into and out of the gas stream which enables comparing the Rb frequency with and without Xe inside the cell. This Xe cycling should have no time-transient effect on the pressure or flow rate as the Xe is a very small fraction of the total gas composition. (3) The optical pumping laser is tunable in frequency about the Rb D1 resonance, and the power incident on the optical pumping cell can be adjusted, as well (0-38 W). (4) The oven, where the cell is heated, has two windows that run along the optical pumping cell to allow a probe laser to pass through the cell and out the other side transverse to the main magnetic field. (5) The main magnetic field provided by the four hoops is ∼27 G. Figure 3.1 shows a schematic of the design as 46 Figure 3.1. Schematic and photograph of the Utah flow-through polarizer. (A) DILAS 50 watt continuous wave 795 nm diode array narrowed with an external Littrow cavity. The laser is circularly polarized, shaped, and then aimed through the pumping cell from the top of the polarizer. (B) Mass-flow controllers (AALBorg) that control the volume flow of a specific gas at room temperature to 1.5% full-scale (C) Forced air oven to drive Rb into vapor phase. This oven is capable of temperatures exceeding 200 ◦C, but typical running temperatures range from 100-140 ◦C (D) Water jacket at 16 ◦C to aid in removing the Rb quickly out of the gas stream and keeping it contained in the oven (E) Cell 156. ∼1 meter long, 4.5 cm diameter optical pumping cell containing ∼1 gram Rb of natural isotopic abundance. (F) 1 cm glass window in oven to admit the probe laser transverse to the main magnetic field and monitor the precession frequency of the Rb atoms. (G) The static magnetic field B0 is supplied by four, 1 m diameter, 200 turn coils with each adjacent pair satisfying the Helmholtz condition. 47 well as a picture of the actual polarizer. 3.3 87Rb in a Magnetic Field Since the Rb atom will experience, on average, a small additional magnetic field from repeated collisions with polarized 129Xe, the energy of the Rb hyperfine sublevel transitions will change and can be used to measure a small change in magnetic field. The hyperfine sublevel transitions are also experimentally convenient because at ∼30 G, they are distinct and accessible with radio frequency photons. The calculation of the hyperfine energy levels of an alkali atom in a magnetic field can be done from first principles. The Hamiltonian describing a Rb atom in a magnetic field is H = He + A(SpinOrbit)L · S + A(Hyperfine)I · J − μI · B − μJ · B (3.4) where He contains all interactions that do not involve spin, L and S are the valence electron orbital and spin angular momentum respectively, J = L + S, I is the nuclear spin (87Rb I=3/2, 85Rb I=5/2), and B is the external magnetic field. If one ignores non-spin dependent interactions and considers the ground state where L=0 and J=1/2 (5S1/2 for Rb) then this Hamiltonian can be diagonalized analytically as a function of magnetic field for arbitrary nuclear spin I. This was done in 1931 by G. Breit and I. I. Rabi [13] and the eigenenergies are E h = − νHF 2(2I + 1) ± νHF 2 1 + 2mF I + 1/2 gsμB hνHF B + gsμB hνHF B 2 1/2 , (3.5) where h is Plank's constant, μB is the Bohr magneton, νHF is the zero-field hyperfine splitting in Hz, I is the nuclear spin, gs ∼ 2, B is the external magnetic field, mF is the azimuthal quantum number of the atomic angular momentum F = J+I, and ± distinguishes between the F = I + 1/2 and F = I − 1/2 hyperfine manifolds. F provides good quantum numbers when the applied magnetic field is much less than the hyperfine field (∼1 kG for 87Rb). At much higher fields (>5 kG), product states with quantum numbers mI and mJ are the eigenstates that diagonalize Equation 3.4. Figure 3.2 shows a plot of Equation 3.5 as a function of field for 87Rb. The hyperfine states are denoted by F,mF and the transition between different hyperfine states (denoted hyperfine sublevel transitions) can be written F,mF ↔ F,mF± 1 . However, this can become cumbersome and the notation convention adopted by almost all of the SEOP literature uses ¯m, a, and b which are defined in the following way: 48 Figure 3.2. 87Rb 5S1/2 hyperfine structure as a function of field. Each line represents a different hyperfine state denoted by mF with the upper manifold being F = 2 and the lower manifold being F = 1. The gray dashed line is 27 Gauss where almost all frequency shift data were taken. At 27 Gauss the F=2, ¯m = −3 2 transition is ∼19 MHz which is easily accessible with lab-built and inexpensive RF equipment. The experiment is to monitor one of the hyperfine transitions and try to detect the small change in energy associated with collisions with polarized 129Xe. The energies in this diagram are all visibly linear, however, when the applied magnetic field is on order of the hyperfine field, the energy levels begin to distort appreciably and become decidedly nonlinear. ¯m = mF − 1/2 (3.6) ¯hωf, ¯m = Ef,mF − Ef,mF−1 (3.7) f = a = I + 1/2 (3.8) f = b = I − 1/2. (3.9) For example, the 2, 1 ↔ 2, 0 transition will be denoted by 2, 1 2 and edge transitions in the f = a = I +1/2 manifold are ¯m = ±I. Edge transitions refer to sublevel transitions that correspond to transitions between the states denoted by mF = ±F and the immediate 49 adjacent mF state. The hyperfine sublevel energies computed from Equation 3.5 have a nonlinear depen-dence on the external field, whereas Equation 3.2 is linear with no dependence on the hyperfine structure. This is because Equation 3.2 is valid only in the regime where the hyperfine states are degenerate (<1 G) and the factor 1 h μB|gs| (2I+1) is the gyromagnetic ratio for all hyperfine sublevel transitions. The ground-state hyperfine sublevel transition energies can be found for an arbitrary magnetic field by taking the difference between two adjacent mF levels in equation 3.5. However, the experimental magnetic field is ∼30 G, and con-sequently, the math can be substantially simplified by keeping only the terms linear in B and expanding the square root to second order in gsμB hνHF B . Differentiating the transition energy with respect to magnetic field and multiplying by the 129Xe magnetization results in the alkali EPR shift due to collisions with polarized 129Xe for a specific sublevel transition when the applied magnetic field is much less than the Rb hyperfine field (see Appendix D). Thus, the expression correct to second order in magnetic field for the Rb EPR shift at low magnetic field is ΔνRb = 4 3 μBgs (2I + 1) γXeK (κ0)RbXe [Xe]PXe 1 ± 4I (2I + 1) μBgs hνHF B0 . (3.10) As written, Equation 3.10 only applies to the F = a edge-transitions (+: 2,−3 2 and −: 2, 3 2 for 87Rb). Equation 3.10 has been written in terms of the edge transitions because the process of optical pumping continuously adds angular momentum to the alkali vapor; depending on the helicity of light, the Rb atoms accumulate in either the a,±(I + 1/2) states. With this accumulation, the EPR signal from the edge transitions dominates the spectrum and provides the peak used to monitor the EPR frequency. Equation 3.10 is identical to Equation 3.2 with a small correction that is 1.7% for 87Rb at 27 G and depends on the strength of the hyperfine field relative to the applied field. Up to this point, only 87Rb has been discussed. We have neglected the other naturally occurring isotope, 85Rb. η87 = .2783 and η85 = .7217 (NIST) are the naturally occurring isotopic fractions of Rb and consequently the signal from the precessing magnetization will be ∼2.5 times bigger for 85Rb than 87Rb. However, the signal of interest is not the magnitude of the precessing magnetization, but the frequency of precession. Since 87Rb has a larger gyromagnetic ratio, for a unit change in applied magnetic field, 87Rb will exhibit a bigger shift than 85Rb. 50 3.4 Steady State Excitation of Rb Hyperfine Transitions While Optically Pumping All the other experiments described in this dissertation are pulsed NMR experiments where the goal is to rotate the spins into the transverse plane as quickly as possible and monitor the transverse magnetization via induced voltage in a coil surrounding the sample. In contrast, the experiment here aims to maintain a coherent precession of 87Rb atoms with continuous-wave (CW) RF excitation of hyperfine sublevel transitions and use optical detection to monitor the precession. As described in Section 1.2.2, the Zeeman splitting of a spin in a static magnetic field can be excited by a transverse oscillating magnetic field at the Larmor frequency. This excitation will torque the spin, and it will precess around the magnetic field resulting from the vector sum of of the static magnetic field, B0, and the oscillating transverse field, B1. In the rotating frame when exactly on resonance, the spin simply rotates around the X or Y direction moving between +Z and -Z at the Rabi precession frequency. If the longitudinal relaxation rate 1/T1 is on order of the Rabi frequency, the competition between B1 rotating the spin off of Z and relaxation mechanisms pushing it back will result in the spin residing at a specific angle with respect to Z. This coherent steady state precessing magnetization will have a component in the transverse direction that rotates at the Larmor frequency and can be described by the Bloch equations. The classically derived phenomenological Bloch equations, while in general not a com-pletely accurate model of a spin system, provide the correct description for a polarized vapor of 87Rb atoms under steady state RF excitation and various relaxation mechanisms. The rotating frame solutions to the Bloch equations in the limit of a small B1 field are [64] MX ∼ B1 (ω0 − ω) γ2 + (ω0 − ω)2 MY ∼ B1 γ γ2 + (ω0 − ω) , (3.11) where M is the magnetization, B1 is the amplitude of the oscillating magnetic field in the X direction, ω0 is the center of the resonance, ω is the excitation frequency, and γ is T2-relaxation that defines the width of the resonance. The absorptive (MY ) and dispersive (MX) peaks are only 90◦ out of phase and experimentally either one can be selected. For this reason only the absorptive shape will be discussed. When calculated from first principles using the evolution of the density matrix, the exact solution for the expectation value of 51 the transverse spin in a 100% polarized Rb vapor under weak-RF excitation takes the same form as MY in Equation 3.11. This calculation was published in [2] and takes the form S = gsμB 2(2I + 1)¯h B1 γa,I (ωa,I − ω)2 + γ2 a,I , (3.12) where S is the expectation value of the alkali electron spin, I is the nuclear spin, ωa,I is the center frequency of the hyperfine sublevel transition defined by a, I , ω is the excitation frequency, and γa,I is the relaxation rate of the resonating hyperfine sublevel. In this case I can be used to denote the hyperfine sublevel transition because Equation 3.12 has been written for edge transitions as the Rb vapor is assumed to be 100% polarized. In reality, the Rb is never 100% polarized and a full treatment can be found in reference [6] for an expression of S for arbitrary Rb polarization where the other hyperfine peaks will contribute to the overall spectrum. However, that level of sophistication is not necessary for this discussion. The linewidths of the hyperfine sublevel transitions are integral to the accuracy of this measurement, because, for a given signal-to-noise ratio, the width of the hyperfine sublevel transition controls the precision of the determination of the peak frequency. The linewidths, without shimming the magnetic field, are dominated by magnetic field inhomogeneities and can render the hyperfine peaks indistinguishable in some cases. The magnetic field was shimmed with a neodymium permanent magnet suspended with a clamp next to the oven. To do this, the hyperfine spectrum was viewed on an oscilloscope while moving the magnet around until the peaks were as narrow as possible, and then the magnet was fixed in place. The advantages of using a permanent magnet for shimming are two-fold. It is simple, and the magnetic field produced by a permanent magnet is very stable. In absence of magnetic field inhomogeneities, the linewidth for a given hyperfine sublevel transition is determined by the resonance damping rate γf, ¯m and is given by [6] γf ¯m = 1 Tex + 1 TSD + R 3[I]2 + 1 − 4 ¯m2 4[I]2 − P Tex + Rsz ¯m [I] (−1)a−f + 1 TFD − ηQ¯m Tex (2f + 1)2 − 4 ¯m2 4[I]2 (3.13) where a = I + 1/2, f = I ± 1/2 , [I] = 2I + 1, R is the optical pumping rate where the Rb is being sampled, sz is the mean photon spin of the pumping laser (∼ ±1), 1 TSD is the S-damping rate, 1 TFD is the F-damping rate, 1 Tex is the alkali-alkali spin-destruction rate, η is the isotopic fraction of the Rb being excited, Q¯m depends on the polarization of the 52 Rb and is the probability that the azimuthal quantum number of the Rb nuclear spin is ¯m. Each of these relaxation processes and their relevance to this experiment will be discussed in the following paragraphs. The local optical pumping rate R is given by [71] R = ∞ 0 ψ(ν)σR(ν) dν. (3.14) where σR(ν) is the Rb absorption profile, and ψ(ν) is the incident photon flux defined by the output spectrum of the pumping laser. Numeric estimations of Equation 3.14 range from 10 Hz to 100 kHz [60] depending on the experimental conditions, and consequently this relaxation process can play a major role in the hyperfine sublevel transition linewidths. 1 Tex is alkali-alkali spin destruction rate and will not contribute significantly to the linewidths in this experiment. The gas composition in this experiment was roughly 50% N2 and 50% He at ∼675 Torr, and at these pressures, the collisional Rb relaxation is dominated by buffer gas collisions [34]. 1 TFD is the F-damping rate from interactions that only mix states in a single hyperfine manifold, i.e., Δf = 0. These type of interactions arise from alkali-buffer gas collisions that are long compared to the hyperfine period, namely Rb-Xe van der Waals molecules formed by three body collisions at low pressures (5-10 Torr). Rb-Xe van der Waals molecules typically live for 10−8 seconds [11]. These lifetimes are two orders of magnitude longer than the the hyperfine period in Rb (∼10−10 seconds), which means the alkali metal electron can recouple to the nucleus during the lifetime of the collision. The consequence of this recoupling is the two f manifolds cannot mix, and only Δf = 0 transitions are allowed. The third body is necessary to carry away some of the energy allowing the molecule to form; this process is rare. In reference [59], the maximum value of the fraction of Xe bound in molecules at the deepest part of the van der Waal's potential was calculated to be 13%. The fraction of Rb-Xe molecules will not increase with an increase in third body gas pressure, however the lifetime of the collisions will decrease as 1/p, where p is third body gas pressure. At high enough gas pressures (200-300 Torr [74]), all of the collisions become sudden with respect to the hyperfine period, and 1 TFD no longer contributes to the hyperfine transition linewidth. 1 TSD is the S-damping rate from interactions which are much faster than the hyperfine period and can mix the hyperfine manifolds during a collisions, i.e. Δf = ±1. At the gas pressures in our experiment (∼675 Torr), this relaxation will dominate over F-damping. In 53 terms of the Rb electron spin state, the main difference between S- and F-damping is the amount the electron is torqued about the internuclear axis during collisions. During an S-damping collision, the Rb precesses much less than a radian about the molecular angular momentum and the electron will undergo a "random walk" around the Bloch sphere where each collision can be considered a step. In contrast, during an F-damping collision the electron precesses many times about the internuclear axis and is consequently completely randomized after every collision. Equations 3.13 and 3.12 are calculated under the assumption that the hyperfine popu-lations of the Rb atoms in the optical pumping cell are well defined by a spin-temperature. ρ = eβFz Z (3.15) where ρ is the density matrix, Z is the partition function, and β is the spin-temperature parameter. The spin temperature condition will prevail as long as all of the interactions that the Rb atoms undergo are sudden with respect to the hyperfine period [2]. Once again, for the pressures in our cell, this is always the case. Neglecting 1 TFD