2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167070Recent experiments on strongly-interacting bosons in optical lattices have revealed the co-existence of spatially-separated Mott-insulating and number-fluctuating phases. The description of this inhomogeneous situation is the topic of this Letter. We establish that the number-fluctuating phase forms a superfluid trapped between the Mott-insulating regions and derive the associated collective mode structure. We discuss the interlayer's crossover between two- and three-dimensional behavior as a function of the lattice parameters and estimate the critical temperatures for the transition of the superfluid phase to a normal phase.Other Condensed MatterMesoscale and Nanoscale PhysicsAtomic Physicstext