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Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly whereas long range correlations require longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy, and their respective currents, the local compressibility, the local excess energy, the heat and single particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization group technique and comparisons with time-evolutions done within the Gutzwiller approximation are provided.