Recent experiments on ultracold atomic gases in an optical lattice potential have produced a Mott insulating state of ${}^{87}\mathrm{Rb}$ atoms. This state is stable to a small applied potential gradient (an “electric” field), but a resonant response was observed when the potential energy drop per lattice spacing $\mathrm{}\left(E\right),$ was close to the repulsive interaction energy (U) between two atoms in the same lattice potential well. We identify all states which are resonantly coupled to the Mott insulator for $E\approx U$ via an infinitesimal tunneling amplitude between neighboring potential wells. The strong correlation between these states is described by an effective Hamiltonian for the resonant subspace. This Hamiltonian exhibits quantum phase transitions associated with an Ising density wave order and with the appearance of superfluidity in the directions transverse to the electric field. We suggest that the observed resonant response is related to these transitions and propose experiments to directly detect the order parameters. The generalizations to electric fields applied in different directions and to a variety of lattices should allow study of numerous other correlated quantum phases.

• Received 18 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.075128