Dynamics of correlations in shallow optical lattices

TL;DR

This paper investigates the evolution of correlations in a lattice boson gas following a rapid lattice depth reduction, providing analytical expressions for static structure factors and analyzing interaction effects on momentum dynamics.

Contribution

It introduces a closed-form expression for the static structure factor in the non-interacting limit and studies the real-space correlation oscillations and their dispersion, including perturbative interaction effects.

Findings

Derived a simple expression for the static structure factor at zero interactions.

Showed that density correlations exhibit multiple oscillations that disperse over time.

Calculated the evolution of boson quasi-momentum considering weak interactions.

Abstract

We explore how correlations evolve in a gas of lattice bosons when the lattice depth is rapidly reduced. We find a simple closed form expression for the static structure factor in the limit of vanishing interactions. The corresponding real-space density correlation function shows multiple spatial oscillations which linearly disperse as a function of time. By perturbatively including the effects of the interactions we calculate how the boson quasi-momentum evolves following the quench.