Classical and quantum dynamics of pulsating instability in a Bose-Einstein condensate in an optical lattice

TL;DR

This paper investigates the classical and quantum dynamics of a Bose-Einstein condensate in an optical lattice, revealing pulsating instabilities and the effects of quantum fluctuations modeled via the Truncated Wigner Approximation.

Contribution

It introduces a detailed analysis of pulsating instabilities in BECs within optical lattices and extends classical results by incorporating quantum effects using TWA.

Findings

Classical mean field theory predicts undamped pulsating instability.

Quantum effects cause damping of the pulsations when averaged over stochastic realizations.

A qualitative analogy with a double-well system explains the quasi-periodic behavior.

Abstract

We study the dynamics of a Bose-Einstein condensate (BEC) in a one dimensional optical lattice in the limit of weak atom-atom interactions. Numerically we find that a BEC may develop a pulsating instability in which atoms nearly periodically collect themselves into a pulse and subsequently disperse back into the initial homogeneous state. A qualitative explanation of the quasi-periodic behavior is given by drawing an analogy with a double-well system. In an extension we introduce quantum effects approximately within Truncated Wigner Approximation (TWA). In pure classical mean field theory the condensate shows an undamped pulsating instability, whereas we have observed a damping in the oscillation when we average over many stochastic realizations.