Bose-Einstein-condensed systems in random potentials

Abstract

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic meanfield approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state. But the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

Hartree–Fock mean-field theory for trapped dirty bosons

“…Inserting (42), (43) into (36), (37) and using the Schwinger integral (46), [53, (3.471.9)], and [53, (8.469.3)], as well as performing the replica limit N → 0 yields:…”

“…A major result is that increase in the disorder strength at zero temperature yields a first-order quantum phase transition from a superfluid to a Bose-glass phase, where in the latter all particles reside in the respective minima of the random potential. This prediction is achieved for three dimensions by solving the underlying Gross-Pitaevskii equation with a random phase approximation [36], as well as by a stochastic self-consistent mean-field approach using two chemical potentials, one for the condensate and one for the excited particles [37,38]. Dual to that, the non-perturbative approach of Refs.…”

Dirty bosons in a three-dimensional harmonic trap

“…In addition, increasing the disorder strength at small temperatures yields a first-order quantum phase transition from a superfluid to a Bose-glass phase, where in the latter case all particles reside in the respective minima of the random potential. This prediction is achieved at zero temperature by solving the underlying Gross-Pitaevskii equation with a random phase approximation [36], as well as at finite temperature by a stochastic self-consistent meanfield approach using two chemical potentials, one for the condensate and one for the excited particles [37]. Numerically, Monte-Carlo (MC) simulations have been applied to study the homogeneous dirty boson problem.…”

Effect of random on-site energies on the critical temperature of a lattice Bose gas

“…In presence of random on-site energies, T c increases for large filling, but much less than for for bond-disordered lattices, resulting in very small shift of T c for small disorder. These results should be compared with the findings for a continuous (i.e., without optical lattice) Bose gas in presence of a disordering potential [32,33,34,35,36]: without any confining potential, it has been shown that the critical temperature decreases with disorder [32]. In Refs.…”