The Projected Gross-Pitaevskii Equation for harmonically confined Bose gases

TL;DR

This paper extends the Projected Gross-Pitaevskii equation to harmonic traps, providing a numerical method to simulate finite-temperature Bose gases and their condensation dynamics.

Contribution

It introduces a robust numerical scheme for the PGP equation in harmonic potentials and demonstrates its application to equilibrium and evaporative cooling processes.

Findings

Accurate simulation of condensate properties at finite temperature

Observation of condensate growth during evaporative cooling

Inference of condensate fraction in non-equilibrium dynamics

Abstract

We extend the Projected Gross Pitaevskii equation formalism of Davis et al. [Phys. Rev. Lett. \bf{87}, 160402 (2001)] to the experimentally relevant case of harmonic potentials. We outline a robust and accurate numerical scheme that can efficiently simulate this system. We apply this method to investigate the equilibrium properties of a harmonically trapped three-dimensional Bose gas at finite temperature, and consider the dependence of condensate fraction, position and momentum distributions, and density fluctuations on temperature. We apply the scheme to simulate an evaporative cooling process in which the preferential removal of high energy particles leads to the growth of a Bose-Einstein condensate. We show that a condensate fraction can be inferred during the dynamics even in this non-equilibrium situation.