Condensation and quasicondensation in an elongated three-dimensional Bose gas

TL;DR

This paper investigates the transition from normal gas to quasicondensate and true Bose-Einstein condensate in an elongated 3D Bose gas, analyzing density fluctuations and phase coherence across temperatures using classical-field simulations.

Contribution

It provides a detailed analysis of the crossover from quasicondensate to true condensate in an elongated 3D Bose gas, including identification of the transition point and coherence properties.

Findings

Second-order transition near ideal Bose gas critical temperature

Persistent phase fluctuations until lower temperatures

Qualitative change in coherence function during crossover

Abstract

We study the equilibrium correlations of a Bose gas in an elongated three-dimensional harmonic trap using a grand-canonical classical-field method. We focus in particular on the progressive transformation of the gas from the normal phase, through a phase-fluctuating quasicondensate regime to the so-called true-condensate regime, with decreasing temperature. Choosing realistic experimental parameters, we quantify the density fluctuations and phase coherence of the atomic field as functions of the system temperature. We identify the onset of Bose condensation through analysis of both the generalized Binder cumulant appropriate to the inhomogeneous system, and the suppression of the effective many-body T matrix that characterizes interactions between condensate atoms in the finite-temperature field. We find that the system undergoes a second-order transition to condensation near the critical temperature for an ideal Bose gas in the strongly anisotropic three-dimensional geometry, but remains in a strongly phase-fluctuating quasicondensate regime until significantly lower temperatures. We characterize the crossover from a quasicondensate to a true condensate by a qualitative change in the form of the non-local first-order coherence function of the field, and compare our results to those of previous works employing a density-phase Bogoliubov-de Gennes analysis.