Dynamics of correlations in shallow optical lattices

Abstract

We explore the time evolution of correlations in a homogeneous gas of lattice bosons with filling factor ${n}_{0}$, following a sudden reduction in the lattice depth to a regime where the interactions are weak. In the limit of vanishing interactions, we find a simple closed-form expression for the static structure factor. The corresponding real-space density-density correlation function shows multiple spatial oscillations which disperse linearly in time. By perturbatively including the effect of interactions, we study the evolution of boson quasimomentum distribution following the quench. In one dimension, the quasimomentum distribution develops peaks at finite momentum which disperse towards $q=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. In two dimensions, the momentum occupation rapidly approaches a steady-state distribution characterized by a broad peak at $q=0$. Quasi-long-range order is never found at finite time. Our studies provide insight into the dynamics of isolated quantum systems.