Nonequilibrium Dynamics of Optical Lattice-Loaded BEC Atoms: Beyond HFB Approximation

TL;DR

This paper investigates the nonequilibrium behavior of a Bose-Einstein condensate in an optical lattice using advanced 2PI effective action methods, revealing the importance of multi-particle scattering effects beyond mean-field approximations.

Contribution

It introduces a systematic comparison of HFB, 1/N expansion, and perturbative approaches for BEC dynamics, highlighting the advantages of second order 2PI approximations.

Findings

Second order 2PI approximations capture damping effects missed by mean-field.

These approximations improve over HFB but are less accurate at late times.

Multi-particle scattering is crucial for realistic nonequilibrium dynamics.

Abstract

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system at National Institute of Standards and Technology (NIST) where the placement of atoms in an optical lattice is controlled by using an intermediate superlattice. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: a) the Hartree-Fock-Bogoliubov (HFB) approximation, b) the next-to-leading order 1/$\mathcal{N}$ expansion of the 2PI effective action up to second order in the interaction strength and c) a second order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many body solution for a moderate number of atoms and wells. As a general feature we observe that because the second order 2PI approximations include multi-particle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution that a mean field collisionless approach fails to produce. While the second order approximations show a clear improvement over the HFB approximation our numerical result shows that they do not work so well at late times, when interaction effects are significant.