  The coupling of cold atoms to the radiation field within a high-finesse
optical resonator, an optical cavity, induces long-range interactions which can
compete with an underlying optical lattice. The interplay between short- and
long-range interactions gives rise to new phases of matter including
supersolidity (SS) and density waves (DW), and interesting quantum dynamics.
Here it is shown that for hard-core bosons in one dimension the ground state
phase diagram and the quantum relaxation after sudden quenches can be
calculated exactly in the thermodynamic limit. Remanent DW order is observed
for quenches from a DW ground state into the superfluid (SF) phase below a
dynamical transition line. After sufficiently strong SF to DW quenches beyond a
static metastability line DW order emerges on top of remanent SF order, giving
rise to a dynamically generated supersolid state.
