Dilute Bose gas with correlated disorder: A Path Integral Monte Carlo study

TL;DR

This study uses path integral Monte Carlo simulations to analyze how correlated disorder affects the thermodynamics, superfluid transition, and localization phenomena in a dilute Bose gas, revealing the interplay between disorder correlation length and quantum phases.

Contribution

It provides the first detailed Monte Carlo analysis of a Bose gas with correlated disorder, connecting disorder effects with superfluidity, localization, and mean-field theories.

Findings

Disorder shifts the superfluid transition temperature.

Energy exhibits a T^2 dependence in the Bose glass phase.

Low-temperature properties align with Gross-Pitaevskii theory even under strong disorder.

Abstract

We investigate the thermodynamic properties of a dilute Bose gas in a correlated random potential using exact path integral Monte Carlo methods. The study is carried out in continuous space and disorder is produced in the simulations by a 3D speckle pattern with tunable intensity and correlation length. We calculate the shift of the superfluid transition temperature due to disorder and we highlight the role of quantum localization by comparing the critical chemical potential with the classical percolation threshold. The equation of state of the gas is determined in the regime of strong disorder, where superfluidity is suppressed and the normal phase exists down to very low temperatures. We find a $T^2$ dependence of the energy in agreement with the expected behavior in the Bose glass phase. We also discuss the major role played by the disorder correlation length and we make contact with a Hartree-Fock mean-field approach that holds valid if the correlation length is very large. The density profiles are analyzed as a function of temperature and interaction strength. Effects of localization and the depletion of the order parameter are emphasized in the comparison between local condensate and total density. At very low temperature we find that the energy and the particle distribution of the gas are very well described by the T=0 Gross-Pitaevskii theory even in the regime of very strong disorder.