We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the diffusion Monte Carlo method, we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.
We investigate the phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas at zero temperature with disorder. By using the diffusion Monte Carlo method, we calculate the superfluid and the condensate fraction of the system as a function of density and strength of disorder. In the regime of weak disorder we find agreement with the analytical results obtained within the Bogoliubov model. For strong disorder the system enters an unusual regime where the superfluid fraction is smaller than the condensate fraction.
The phenomenon of Bose-Einstein condensation and superfluidity in a Bose gas with disorder is investigated. Diffusion Monte Carlo (DMC) method is used to calculate superfluid and condensate fraction of the system as a function of density and strength of disorder at zero temperature. The algorithm and implementation of the Diffusion Monte Carlo method is explained in details. Bogoliubov theory is developed for the analytical description of the problem. Ground state energy, superfluid fraction and condensate fraction are calculated. It is shown that same results for the superfluid fraction can be obtained in a perturbative manner from Gross-Pitaevskii equation. Ground state energy, obtained from DMC calculations, is compared to predictions of Bogoliubov theory, which are found to be valid in the regime, when the strength of disorder is small. It is shown that "unusual" situation, when the superfluid fraction is smaller than the condensate fraction, can be realized in this system.
Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.
We study the properties of a homogeneous dilute Bose-Bose gas in a weak-disorder potential at zero temperature. By using the perturbation theory, we calculate the disorder corrections to the condensate density, the equation of state, the compressibility, and the superfluid density as a function of density, strength of disorder, and miscibility parameter. It is found that the disorder potential may lead to modifying the miscibility-immiscibility condition and a full miscible phase turns out to be impossible in the presence of the disorder. We show that the intriguing interplay of the disorder and intra- and interspecies interactions may strongly influence the localization of each component, the quantum fluctuations, and the compressibility, as well as the superfluidity of the system.
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field 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.
We investigate the properties of a homogeneous dipolar Bose gas in a weak three-dimensional isotropic speckle disorder at finite temperatures. By using the Bogoliubov theory (beyond the mean field), we calculate the condensate and the superfluid fractions as a function of density and strengths of disorder and interaction. The disorder impact on the anomalous density, the chemical potential, and the ground-state energy is also analyzed. We show that the peculiar interplay of the dipole-dipole interaction and weak disorder makes the superfluid fraction and sound velocity anisotropic.
The superfluid transition of a three-dimensional gas of hard-sphere bosons in a disordered medium is studied using quantum Monte Carlo methods. Simulations are performed in continuous space both in the canonical and in the grand-canonical ensemble. At fixed density we calculate the shift of the transition temperature as a function of the disorder strength, while at fixed temperature we determine both the critical chemical potential and the critical density separating normal and superfluid phases. In the regime of strong disorder the normal phase extends up to large values of the degeneracy parameter, and the critical chemical potential exhibits a linear dependence in the intensity of the random potential. The role of interactions and disorder correlations is also discussed.