  We predict the existence of novel collapse and revival oscillations that are
a distinctive signature of the short-range off-diagonal coherence associated
with particle-hole pairs in Mott insulator states. Starting with an atomic Mott
state in a one-dimensional optical lattice, suddenly raising the lattice depth
freezes the particle-hole pairs in place and induces phase oscillations. The
peak of the quasi-momentum distribution, revealed through time of flight
interference, oscillates between a maximum occupation at zero quasi-momentum
(the $\Gamma$ point) and the edge of the Brillouin zone. We show that the
population enhancements at the edge of the Brillouin zone is due to coherent
particle-hole pairs, and we find similar effects for fermions and Bose-Fermi
mixtures in a lattice. Our results open a new avenue for probing strongly
correlated many-body states with short-range phase coherence that goes beyond
the familiar collapse and revivals previously observed in the long-range
coherent superfluid regime.
