Universal correlations and coherence in quasi-two-dimensional trapped Bose gases

TL;DR

This paper investigates the correlations and coherence properties of quasi-two-dimensional trapped Bose gases above the Kosterlitz-Thouless transition, revealing universal behaviors and the conditions for Bose-Einstein condensation.

Contribution

It demonstrates that mean-field theory effectively captures dominant interactions and introduces a universal expression for correlation density applicable across various parameters.

Findings

Correlation density is universally described by classical-field calculations.

Deviations from universality are minimal in current experiments.

Finite-size effects reveal the crossover from Kosterlitz-Thouless to Bose-Einstein condensation.

Abstract

We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with Quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allows us to characterize the cross-over from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.