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We study the many-body state of ultracold bosons in a bistable opticallattice potential in an optomechanical resonator in the weak-coupling limit.New physics arises as a result of bistability and discontinuous jumps in thecavity field. Of particular interest is the situation where the optical cavityis engineered so that a single input beam can result in two radically differentstable ground states for the intracavity gas: superfluid and Mott-insulator.

Bistable Mott-insulator to superfluid phase transition in cavity optomechanics