  For a periodically shaken optical lattice, effective time-reversal is
investigated numerically. For interacting ultra-cold atoms, the scheme of [J.
Phys. B 45, 021002 (2012)] involves a quasi-instantaneous change of both the
shaking-amplitude and the sign of the interaction. As the wave function returns
to its initial state with high probability, time-reversal is ideal to
distinguish pure quantum dynamics from the dynamics described by statistical
mixtures.
