Bose-Einstein condensation in a minimal inhomogeneous system

We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem . By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.We study the effects of repulsive interaction and disorder on bosons in a two-site Bose–Hubbard system, which provides a simple model of the dirty boson problem . By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture. It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system. While these corrections to a simple meanfield Bogoliubov theory are usually small in extended systems, we show that care has to be taken when modeling small inhomogeneous Bose systems.

arXiv:1305.4120Journal of Physics A Mathematical and TheoreticalDec 16, 20132 citations

Disordered bosons: Condensate and excitations

Kanwal G. Singh, Daniel S. Rokhsar

The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schr\"odinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with $^{4}\mathrm{He}$ adsorbed in porous media.The disordered Bose-Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wave function in the presence of disorder is found by solving a nonlinear Schr\"odinger equation. Using the Bogoliubov approximation to find the excitations above this condensate, we calculate the condensate fraction, superfluid density, and density of states for a two-dimensional disordered system. These results are compared with experiments done with $^{4}\mathrm{He}$ adsorbed in porous media.

arXiv:cond-mat/9307039Physical review. B, Condensed matterApr 1, 199449 citations

Condensate deformation and quantum depletion of Bose–Einstein condensates in external potentials

Cord Axel Müller, Christopher Gaul

The one-body density matrix of weakly interacting condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials at the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically and finally, the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas–Fermi limit of very smooth potentials.The one-body density matrix of weakly interacting condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials at the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically and finally, the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas–Fermi limit of very smooth potentials.

arXiv:1202.3489New Journal of PhysicsJul 27, 201241 citations

Exact versus mean-field description of the Bose-Einstein condensate: a model study

Magdalena A. Załuska–Kotur, Mariusz Gajda, Arkadiusz Orłowski +1 more

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactl y soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactl y soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives quite accurate description of the system in the limit of weak interactions.

arXiv:cond-mat/0004469Apr 27, 20004 citations

The effects of disorder in dimerized quantum magnets in mean field approximations

Abdulla Rakhimov, Shuhrat Mardonov, E Ya Sherman +1 more

We study theoretically the effects of disorder on Bose–Einstein condensates (BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The condensation occurs in a magnetic field, where the concentration of bosons in the random potential is sufficient to form the condensate. The effect of doping is partly modeled by a δ -correlated distribution of impurities, which (i) leads to a uniform renormalization of the system parameters and (ii) produces disorder in the system with renormalized parameters. This approach can explain qualitatively the available magnetization data on the Tl 1− x K x CuCl 3 compound taken as an example. In addition to the magnetization, we found that the speed of the Bogoliubov mode has a maximum as a function of x . No evidence of the pure Bose glass phase has been found in the BEC regime.We study theoretically the effects of disorder on Bose–Einstein condensates (BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The condensation occurs in a magnetic field, where the concentration of bosons in the random potential is sufficient to form the condensate. The effect of doping is partly modeled by a δ -correlated distribution of impurities, which (i) leads to a uniform renormalization of the system parameters and (ii) produces disorder in the system with renormalized parameters. This approach can explain qualitatively the available magnetization data on the Tl 1− x K x CuCl 3 compound taken as an example. In addition to the magnetization, we found that the speed of the Bogoliubov mode has a maximum as a function of x . No evidence of the pure Bose glass phase has been found in the BEC regime.

arXiv:1206.4143New Journal of PhysicsNov 7, 20128 citations

The effects of disorder in dimerized quantum magnets in mean field approximations

Abdulla Rakhimov, Mardonov, Shuhrat, Eugene Ya. Sherman +1 more

We study theoretically the effects of disorder on Bose–Einstein condensates (BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The condensation occurs in a magnetic field, where the concentration of bosons in the random potential is sufficient to form the condensate. The effect of doping is partly modeled by a δ-correlated distribution of impurities, which (i) leads to a uniform renormalization of the system parameters and (ii) produces disorder in the system with renormalized parameters. This approach can explain qualitatively the available magnetization data on the Tl1−xKxCuCl3 compound taken as an example. In addition to the magnetization, we found that the speed of the Bogoliubov mode has a maximum as a function of x. No evidence of the pure Bose glass phase has been found in the BEC regime.We study theoretically the effects of disorder on Bose–Einstein condensates (BEC) of bosonic triplon quasiparticles in doped dimerized quantum magnets. The condensation occurs in a magnetic field, where the concentration of bosons in the random potential is sufficient to form the condensate. The effect of doping is partly modeled by a δ-correlated distribution of impurities, which (i) leads to a uniform renormalization of the system parameters and (ii) produces disorder in the system with renormalized parameters. This approach can explain qualitatively the available magnetization data on the Tl1−xKxCuCl3 compound taken as an example. In addition to the magnetization, we found that the speed of the Bogoliubov mode has a maximum as a function of x. No evidence of the pure Bose glass phase has been found in the BEC regime.

Jan 1, 20129 citations

^{4}\mathrm{He}

adsorbed in porous media.