Expansion dynamics of strongly correlated lattice bosons: A selfconsistent density-matrix approach

TL;DR

This paper introduces a selfconsistent density-matrix approach to study the expansion dynamics of strongly correlated lattice bosons, capturing both condensate and non-condensed fluctuations beyond mean-field theories.

Contribution

The authors develop a novel quantum master equation method that extends beyond Gutzwiller mean-field theory to analyze real-time dynamics of strongly interacting bosons on a lattice.

Findings

Ballistic expansion of condensate observed

Slow, diffusive transport of normal bosons detected

Robustness and melting of Mott insulator discussed

Abstract

We study the spatio-temporal dynamics of interacting bosons on a two-dimensional Hubbard lattice in the strongly interacting regime, taking into account the dynamics of condensate amplitude as well as the direct transport of non-condensed fluctuations. To that end we develop a selfconsistent density-matrix approach which goes beyond the standard Gutzwiller mean-field theory. Starting from the Liouville-von-Neumann equation we derive a quantum master equation for the time evolution of the system's local density matrix at each lattice site, with a dynamical bath that represents the rest of the system. We apply this method to the expansion dynamics of an initially prepared cloud of interacting bosons in an optical lattice. We observe a ballistic expansion of the condensate, as expected, followed by slow, diffusive transport of the normal bosons. We discuss, in particular, the robustness of the Mott insulator phase as well as its melting due to incoherent transport. The method should be applicable to various models of lattice bosons in the strongly correlated regime.