Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice

TL;DR

This paper develops a mean-field theoretical approach using time-dependent Hartree-Fock-Bogoliubov calculations to explain the large damping of oscillations in 1D Bose gases in optical lattices, aligning well with experimental data.

Contribution

It introduces a fluctuation-dissipation formula for damping based on a new physical picture and compares HFB and Gutzwiller methods for different lattice depths.

Findings

HFB calculations qualitatively match observed damping.

Derived a fluctuation-dissipation damping formula.

Good agreement with experiments for shallow lattices.

Abstract

We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.