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Quantum unitary evolution typically leads to thermalization of genericinteracting many-body systems. There are very few known general methods forreversing this process, and we focus on the magic echo, a radio-frequency pulsesequence known to approximately "rewind" the time evolution of dipolar coupledhomonuclear spin systems in a large magnetic field. By combining analytic,numerical, and experimental results we systematically investigate factorsleading to the degradation of magic echoes, as observed in reduced revival ofmean transverse magnetization. Going beyond the conventional analysis based onmean magnetization we use a phase encoding technique to measure the growth ofspin correlations in the density matrix at different points in time followingmagic echoes of varied durations and compare the results to those obtainedduring a free induction decay (FID). While considerable differences aredocumented at short times, the long-time behavior of the density matrix appearsto be remarkably universal among the types of initial states considered -simple low order multispin correlations are observed to decay exponentially atthe same rate, seeding the onset of increasingly complex high ordercorrelations. This manifestly athermal process is constrained by conservationof the second moment of the spectrum of the density matrix and proceedsindefinitely, assuming unitary dynamics.

Multispin correlations and pseudo-thermalization of the transient density matrix in solid-state NMR: free induction decay and magic echo