  It is now widely accepted that quenches through the critical region of
quantum phase transitions result in post-transition states populated with
topological defects -- analogs of the classical topological defects. However,
consequences of the very non-classical fact that the state after a quench is a
{\it superposition} of distinct, broken-symmetry vacua with different numbers
and locations of defects have remained largely unexplored. We identify coherent
quantum oscillations induced by such superpositions in observables
complementary to the one involved in symmetry breaking. These oscillations
satisfy Kibble-Zurek dynamical scaling laws with the quench rate, with an
instantaneous oscillation frequency set primarily by the gap of the system. In
addition to the obvious fundamental significance of a superposition of
different broken symmetry states, quantum coherent oscillations can be used to
verify unitarity and test for imperfections of the experimental implementations
of quantum simulators.
