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

Quantum relaxation and metastability of lattice bosons with cavity-induced long-range interactions