The Stochastic Gross-Pitaevskii Methodology

TL;DR

The paper reviews the stochastic Gross-Pitaevskii method for modeling non-equilibrium finite temperature Bose gases, emphasizing its ability to unify condensed and thermal atom descriptions and its application to recent atom chip experiments.

Contribution

It provides a comprehensive review of the stochastic Gross-Pitaevskii approach, including simplifications for numerical implementation and interpretation of simulation results.

Findings

Successful ab initio modeling of atom chip experiments

Analysis of dark soliton decay in phase-fluctuating condensates

Demonstration of the method's power in describing critical fluctuations

Abstract

We review the stochastic Gross-Pitaevskii approach for non-equilibrium finite temperature Bose gases, focussing on the formulation of Stoof; this method provides a unified description of condensed and thermal atoms, and can thus describe the physics of the critical fluctuation regime. We discuss simplifications of the full theory, which facilitate straightforward numerical implementation, and how the results of such stochastic simulations can be interpreted, including the procedure for extracting phase-coherent (`condensate') and density-coherent (`quasi-condensate') fractions. The power of this methodology is demonstrated by successful ab initio modelling of several recent atom chip experiments, with the important information contained in each individual realisation highlighted by analysing dark soliton decay within a phase-fluctuating condensate.