Phase relationship between the long-time beats of free induction decays and spin echoes in solids

Recent theoretical work on the role of microscopic chaos in the dynamics and relaxation of many-body quantum systems has made several experimentally confirmed predictions about the systems of interacting nuclear spins in solids, focusing in particular on the shapes of spin echo responses measured by nuclear magnetic resonance. These predictions were based on the idea that the transverse nuclear spin decays evolve in a manner governed at long times by the slowest decaying eigenmode of the quantum system, analogous to a chaotic resonance in a classical system. The present paper extends the above investigations both theoretically and experimentally. On the theoretical side, the notion of chaotic eigenmodes is used to make predictions about the relationships between the long-time oscillation phase of the nuclear free induction decay and the amplitudes and phases of spin echoes. On the experimental side, the above predictions are tested for the nuclear spin decays of 19F in CaF2 crystals and 129Xe in frozen xenon. Good agreement between the theory and the experiment is found.