Phase transition dimensionality crossover from two to three dimensions in a trapped ultracold atomic Bose gas

TL;DR

This study investigates how a trapped ultracold atomic Bose gas transitions from two to three dimensions, revealing a continuous change from BKT to BEC phase transition and a monotonic increase in critical temperature.

Contribution

It demonstrates the dimensionality crossover in a Bose gas using a hybrid trap and stochastic Gross-Pitaevskii simulations, highlighting the transition from BKT to BEC.

Findings

Continuous shift from BKT to BEC phase transition.

Critical temperature increases monotonically with dimensionality.

Strongest variation occurs at small chemical potentials.

Abstract

The equilibrium properties of a weakly interacting atomic Bose gas across the Berezinskii-Kosterlitz-Thouless (BKT) and Bose-Einstein condensation (BEC) phase transitions are numerically investigated through a dimensionality crossover from two to three dimensions. The crossover is realised by confining the gas in an experimentally feasible hybridised trap which provides homogeneity along the planar xy-directions through a box potential in tandem with a harmonic transverse potential along the transverse z-direction. The dimensionality is modified by varying the frequency of the harmonic trap from tight to loose transverse trapping. Our findings, based on a stochastic (projected) Gross-Pitaevskii equation, showcase a continuous shift in the character of the phase transition from BKT to BEC, and a monotonic increase of the identified critical temperature as a function of dimensionality, with the strongest variation exhibited for small chemical potential values up to approximately twice the transverse confining potential