  It was recently discovered that atoms subject to a time-periodic drive can
give rise to a crystal structure in phase space. In this work, we point out the
atom-atom interactions give rise to collective phonon excitations of
phase-space crystal via a pairing interaction with intrinsically complex phases
that can lead to a phonon Chern insulator, accompanied by topologically robust
chiral transport along the edge of the phase-space crystal. This topological
phase is realized even in scenarios where the time-reversal transformation is a
symmetry, which is surprising because the breaking of time-reversal symmetry is
a strict precondition for topological chiral transport in the standard setting
of real-space crystals. Our work has also important implications for the
dynamics of 2D charged particles in a strong magnetic field.
