The trapped two-dimensional Bose gas: from Bose-Einstein condensation to Berezinskii-Kosterlitz-Thouless physics

TL;DR

This paper investigates the phase transition in a quasi-two-dimensional Bose gas, demonstrating that the observed transition aligns with Berezinskii-Kosterlitz-Thouless physics rather than traditional Bose-Einstein condensation, and combines theoretical models with experimental data.

Contribution

It combines mean-field theory with BKT transition predictions and quantum Monte Carlo results to accurately describe the experimental observations of a 2D Bose gas.

Findings

The transition cannot be explained by ideal Bose-Einstein condensation.

Including residual thermal excitation improves agreement between mean-field and QMC results.

Predicted critical atom number significantly exceeds ideal gas predictions, matching experimental data.

Abstract

We analyze the results of a recent experiment with bosonic rubidium atoms harmonically confined in a quasi-two-dimensional geometry. In this experiment a well defined critical point was identified, which separates the high-temperature normal state characterized by a single component density distribution, and the low-temperature state characterized by a bimodal density distribution and the emergence of high-contrast interference between independent two-dimensional clouds. We first show that this transition cannot be explained in terms of conventional Bose-Einstein condensation of the trapped ideal Bose gas. Using the local density approximation, we then combine the mean-field (MF) Hartree-Fock theory with the prediction for the Berezinskii-Kosterlitz-Thouless transition in an infinite uniform system. If the gas is treated as a strictly 2D system, the MF predictions for the spatial density profiles significantly deviate from those of a recent Quantum Monte-Carlo (QMC) analysis. However when the residual thermal excitation of the strongly confined degree of freedom is taken into account, an excellent agreement is reached between the MF and the QMC approaches. For the interaction strength corresponding to the experiment, we predict a strong correction to the critical atom number with respect to the ideal gas theory (factor $\sim 2$). A quantitative agreement between theory and experiment is reached concerning the critical atom number if the predicted density profiles are used for temperature calibration.