Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance

The many body quantum dynamics of dipolar coupled nuclear spins I = 1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance (NMR). By increasing the signal-to-noise ratio by two orders of magnitude compared with previous reports for the free induction decay (FID) of 19F in CaF2 we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second universal decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.