Path-integral Monte Carlo and the squeezed trapped Bose-Einstein gas

TL;DR

This paper uses path-integral Monte Carlo simulations to study Bose-Einstein condensation in trapped gases, confirming the transition to effective two-dimensional behavior as confinement anisotropy increases, and compares results with theoretical predictions.

Contribution

It demonstrates the effectiveness of PIMC simulations in accurately modeling anisotropic trapped Bose gases and validates theoretical predictions for density profiles and condensate fractions in 2D regimes.

Findings

PIMC simulations match exact solutions for ideal gases.

Density profiles agree with 2D Hartree-Fock predictions.

Condensate fraction estimates bracket the exact value.

Abstract

Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.