Weakly interacting Bose gas in a random environment

TL;DR

This paper investigates the zero-temperature behavior of a dilute weakly interacting Bose gas in a random environment, identifying localized and superfluid regimes, and providing theoretical predictions for experimental verification.

Contribution

It introduces a comprehensive analysis of localization and superfluid transition in disordered Bose gases across different dimensions, with explicit calculations of critical density and regime distinctions.

Findings

Localized states form in deep potential wells with negligible tunneling

A critical density $n_c$ marks the transition from localized to superfluid states

Four regimes are identified in trapped gases, including a superfluid phase

Abstract

Zero temperature properties of a dilute weakly interacting $d$-dimensional Bose gas in a random potential are studied. We calculate geometrical and energetic characteristics of the localized state of a gas confined in a large box or in a harmonic trap. Different regimes of the localized state are found depending on the ratio of two characteristic length scales of the disorder, the Larkin length and the disorder correlation length. Repulsing bosons confined in a large box with average density $n$ well below a critical value $n_c$ are trapped in deep potential wells of extension much smaller than distance between them. Tunneling between these wells is exponentially small. The ground state of such a gas is a random singlet with no long-range phase correlation For $n>n_c$ repulsion between particles overcomes the disorder and the gas transits from the localized to a coherent superfluid state. The critical density $n_c$ is calculated in terms of the disorder parameters and the interaction strength. For atoms in traps four different regimes are found, only one of it is superfluid. The theory is extended to lower (1 and 2) dimensions. Its quantitative predictions can be checked in experiments with ultracold atomic gases and other Bose-systems.