Self-trapping dynamics in a two-dimensional optical lattice

We describe theoretical models for the recent experimental observation of macroscopic quantum self-trapping (MQST) in the transverse dynamics of an ultracold bosonic gas in a two-dimensional lattice. The pure mean-field model based on the solution of coupled nonlinear equations fails to reproduce the experimental observations. It greatly overestimates the initial expansion rates at short times and predicts a slower expansion rate of the cloud at longer times. It also predicts the formation of a hole surrounded by a steep square fortlike barrier which was not observed in the experiment. An improved theoretical description based on a simplified truncated Wigner approximation (TWA), which adds phase and number fluctuations in the initial conditions, pushes the theoretical results closer to the experimental observations but fails to quantitatively reproduce them. An explanation of the delayed expansion as a consequence of a type of self-trapping mechanism, where quantum correlations suppress tunneling even when there are no density gradients, is discussed and supported by numerical time-dependent density matrix renormalization group (t-DMRG) calculations performed in a simplified two coupled tubes setup.