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 three-dimensional (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 T2 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 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.
Highlights
The dirty boson problem has become a central and fascinating subject in condensed matter physics starting from the first theoretical investigations more than 20 years ago [1, 2, 3]
In this work we report on a path-integral Monte Carlo (PIMC) study of an interacting Bose gas in the presence of correlated disorder produced by 3D optical speckles
We find that in a quantum degenerate bosonic gas a random potential is most efficient in suppressing superfluidity if it is correlated over length scales comparable with the mean interparticle distance
Summary
The dirty boson problem has become a central and fascinating subject in condensed matter physics starting from the first theoretical investigations more than 20 years ago [1, 2, 3]. Theoretical investigations, including quantum Monte Carlo simulations, have mainly addressed the problem of bosons on a lattice with on site bound disorder, the so-called disordered Bose-Hubbard model In this case commensurability, i.e. the integer ratio of the number of particles to the number of lattice sites, plays a major role allowing for a superfluid/insulator (of the Mott type) transition in the absence of disorder that is purely driven by interaction effects. The results of the GP equation for the ground-state energy and the spatial distribution of particles are accurate even in the regime of strong disorder with short-range correlations This conclusion might be useful in view of investigating the structural properties of the Bose glass phase.
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