  Quantum unitary evolution typically leads to thermalization of generic
interacting many-body systems. There are very few known general methods for
reversing this process, and we focus on the magic echo, a radio-frequency pulse
sequence known to approximately "rewind" the time evolution of dipolar coupled
homonuclear spin systems in a large magnetic field. By combining analytic,
numerical, and experimental results we systematically investigate factors
leading to the degradation of magic echoes, as observed in reduced revival of
mean transverse magnetization. Going beyond the conventional analysis based on
mean magnetization we use a phase encoding technique to measure the growth of
spin correlations in the density matrix at different points in time following
magic echoes of varied durations and compare the results to those obtained
during a free induction decay (FID). While considerable differences are
documented at short times, the long-time behavior of the density matrix appears
to be remarkably universal among the types of initial states considered -
simple low order multispin correlations are observed to decay exponentially at
the same rate, seeding the onset of increasingly complex high order
correlations. This manifestly athermal process is constrained by conservation
of the second moment of the spectrum of the density matrix and proceeds
indefinitely, assuming unitary dynamics.
