Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

TL;DR

This paper presents a quantum kinetic theory model for Bose-Einstein condensate growth, incorporating detailed occupation dynamics and stimulated transfer, aligning well with experiments at higher temperatures and offering insights into the condensate's spatial evolution.

Contribution

It introduces a comprehensive quantum kinetic model that accounts for occupation changes and stimulated transfer, providing an alternative to phenomenological fitting methods for condensate growth.

Findings

Good agreement with experimental data at higher temperatures

Growth rate is faster at lower temperatures in experiments

Model offers a new approach to analyze condensate spatial shape

Abstract

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.