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Title: 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 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.

Authors:
 [1];  [2];  [1]
  1. Fachbereich Physik, Universitaet Duisburg-Essen, 47048 Duisburg (Germany)
  2. (Russian Federation)
Publication Date:
OSTI Identifier:
20982170
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.023619; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; BOSE-EINSTEIN CONDENSATION; COMPRESSIBILITY; CONDENSATES; DENSITY; GROUND STATES; INTERACTIONS; MEAN-FIELD THEORY; PHASE TRANSFORMATIONS; POTENTIALS; RANDOMNESS; SOUND WAVES; STABILITY; STOCHASTIC PROCESSES; STRUCTURE FACTORS; SUPERFLUIDITY; VELOCITY

Citation Formats

Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, and Graham, R. Bose-Einstein-condensed systems in random potentials. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.023619.
Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, & Graham, R. Bose-Einstein-condensed systems in random potentials. United States. doi:10.1103/PHYSREVA.75.023619.
Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, and Graham, R. Thu . "Bose-Einstein-condensed systems in random potentials". United States. doi:10.1103/PHYSREVA.75.023619.
@article{osti_20982170,
title = {Bose-Einstein-condensed systems in random potentials},
author = {Yukalov, V. I. and Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 and Graham, R.},
abstractNote = {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.},
doi = {10.1103/PHYSREVA.75.023619},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • 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 anymore » 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.« less
  • We show that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length {sigma}{sub R}. For speckle potentials the Fourier transform of the correlation function vanishes for momenta k>2/{sigma}{sub R} so that the Lyapunov exponent vanishes in the Born approximation for k>1/{sigma}{sub R}. Then, for the initial healing length of the condensate {xi}{sub in}>{sigma}{sub R} the localization is exponential, and for {xi}{sub in}<{sigma}{sub R} it changes to algebraic.
  • We theoretically investigate the physics of interacting Bose-Einstein condensates at equilibrium in a weak (possibly random) potential. We develop a perturbation approach to derive the condensate wave function for an amplitude of the potential smaller than the chemical potential of the condensate and for an arbitrary spatial variation scale of the potential. Applying this theory to disordered potentials, we find in particular that, if the healing length is smaller than the correlation length of the disorder, the condensate assumes a delocalized Thomas-Fermi profile. In the opposite situation where the correlation length is smaller than the healing length, we show thatmore » the random potential can be significantly smoothed and, in the mean-field regime, the condensate wave function can remain delocalized, even for very small correlation lengths of the disorder.« less
  • A perfect Bose gas can condensate in one dimension in the presence of a random potential due to the presence of Lifshitz tails in the one-particle density of states. Here, we show that scale-free correlations in the random potential suppress the disorder induced Bose-Einstein condensation (BEC). Within a tight-binding approach, we consider free Bosons moving in a scale-free correlated random potential with spectral density decaying as 1/k{sup {alpha}}. The critical temperature for BEC is shown to vanish in chains with a binary nonstationary potential ({alpha}>1). On the other hand, a weaker suppression of BEC takes place in nonbinarized scale-free potentials.more » After a slightly increase in the stationary regime, the BEC transition temperature continuously decays as the spectral exponent {alpha}{yields}{infinity}.« less
  • No abstract prepared.