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