Physics of Low-Dimensional Ultracold Bose Gases

TL;DR

This paper explores the unique properties of ultracold Bose gases in low dimensions, demonstrating the BKT transition in 2D via simulations and deriving effective equations for 1D gases at zero temperature.

Contribution

It provides the first simulation-based confirmation of the BKT transition in 2D Bose gases and derives an effective 1D model using a Gaussian ansatz and Lagrangian approach.

Findings

Confirmation of BKT phase via correlation functions and vortex behavior

Derivation of effective 1D equations for Bose gases at zero temperature

Insights into superfluidity and phase transitions in low-dimensional systems

Abstract

In this work we investigate the unique properties of ultracold Bose gases in one and two dimensions. In two dimensions, we present simulations of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition using the projected Gross-Pitaevskii equation formalism. We confirm the presence of the BKT phase by observing algebraic decay in the first-order correlation function, unbinding of vortex pairs, and behaviour of the superfluid fraction. In one dimension we use a transverse Gaussian ansatz and the Lagrangian approach to derive an effective equation of motion for the one dimensional Bose gas at zero temperature.