Quantitative test of thermal field theory for Bose-Einstein condensates II

TL;DR

This paper presents a detailed numerical analysis of a gapless finite-temperature theory for Bose-Einstein condensates, successfully matching experimental measurements and introducing a novel summation method to improve computational convergence.

Contribution

It provides a comprehensive numerical implementation of a gapless response theory for Bose-Einstein condensates, including a new asymmetric summation technique for better convergence.

Findings

Accurate reproduction of dipole mode frequencies and phases.

Development of a novel asymmetric summation method.

Quantitative agreement with JILA experimental data.

Abstract

We have recently derived a gapless theory of the linear response of a Bose-condensed gas to external perturbations at finite temperature and used it to explain quantitatively the measurements of condensate excitations and decay rates made at JILA [D. S. Jin et.al., Phys. Rev. Lett. 78, 764 (1997)]. The theory describes the dynamic coupling between the condensate and non-condensate via a full quasiparticle description of the time-dependent normal and anomalous averages and includes all Beliaev and Landau processes. In this paper we provide a full discussion of the numerical calculations and a detailed analysis of the theoretical results in the context of the JILA experiment. We provide unambiguous proof that the dipole modes are obtained accurately within our calculations and present quantitative results for the relative phase of the oscillations of the condensed and uncondensed atom clouds. One of the main difficulties in the implementation of the theory is obtaining results which are not sensitive to basis cutoff effects and we have therefore developed a novel asymmetric summation method which solves this problem and dramatically improves the numerical convergence. This new technique should make the implementation of the theory and its possible future extensions feasible for a wide range of condensate populations and trap geometries.