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Recent experiments on strongly-interacting bosons in optical lattices haverevealed the co-existence of spatially-separated Mott-insulating andnumber-fluctuating phases. The description of this inhomogeneous situation isthe topic of this Letter. We establish that the number-fluctuating phase formsa superfluid trapped between the Mott-insulating regions and derive theassociated collective mode structure. We discuss the interlayer's crossoverbetween two- and three-dimensional behavior as a function of the latticeparameters and estimate the critical temperatures for the transition of thesuperfluid phase to a normal phase

Coexistence of superfluid and Mott phases of lattice bosons