Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2602.21380 · New Journal of Physics

Finite-temperature superfluid depletion of disordered Bose gases

Cord Axel Müller

Published Sep 9, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined effects of which are rather intriguing, and difficult to describe quantitatively. By inhomogeneous Bogoliubov theory, applicable to weakly interacting condensed Bose gases in static external potentials with arbitrary spatial correlations, we calculate the normal fluid density via the transverse current–current correlation. We obtain finite-temperature disorder corrections to the normal fraction known since Laudau’s seminal two-fluid theory, using diagrammatic perturbation theory for systems of any dimensionality, with closed analytical expressions to leading, quadratic order in disorder strength.

DOI
10.1088/1367-2630/aea4e9

Related papers

Bose-Bose mixtures in a weak-disorder potential: Fluctuations and superfluidity

Abdelâali Boudjemâa, Karima Abbas

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.

arXiv:2008.11156•Physical Review A•Aug 25, 2020•10 citations

Behavior of the anomalous correlation function in a uniform two-dimensional Bose gas

Abdelâali Boudjemâa

We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature. The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature.

arXiv:1110.0123•Physical Review A•Oct 9, 2012•30 citations

Non-equilibrium disordered Bose gases: condensation, superfluidity and dynamical Bose glass

Lei Chen, Zhaoxin Liang, Ying Hu +1 more

Abstract In an equilibrium three-dimensional (3D) disordered condensate, it is well established that disorder can generate an amount of normal fluid ρ n equaling to of ρ ex , where ρ ex is a sum of interaction-induced quantum depletion and disorder-induced condensate deformation. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of the Bose glass phase. In this work, we show that, by bringing a weakly disordered 3D condensate to non-equilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state of Hamiltonian H f in which the ρ n far exceeds of the ρ ex . This suggests the possibility of engineering Bose glass in the dynamic regime. Here, we refer to the dynamical Bose glass as the case where in the steady state of quenched condensate , the superfluid density goes to zero while the condensate density remains finite. As both the ρ n and ρ ex are measurable quantities, our results allow an experimental demonstration of the dramatized interplay between the disorder and interaction in the non-equilibrium scenario.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 21, 2015•9 citations

Bogoliubov Theory of Disordered Bose-Einstein Condensates

Christopher Gaul, Cord Axel Müller

We describe interacting bosons at low temperature in spatially correlated random potentials. By a Bogoliubov expansion around the deformed mean-field condensate, the fundamental Hamiltonian for elementary excitations is derived, achieving an analytical formulation in the case of weak disorder. From this, we calculate the sound velocity and true zero-temperature condensate depletion in correlated disorder and all dimensions.

arXiv:1009.5448•Sep 28, 2010•0 citations

Quantum phase transitions in low-dimensional weakly interacting disordered Bose gases

Joseph Saliba

In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.

•Jan 1, 2016•0 citations

Collective excitations of a dilute Bose gas at finite temperature: time dependent Hartree–Fock–Bogoliubov theory

Abdelâali Boudjemâa, Nadia Guebli

Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.

arXiv:1710.04003•Journal of Physics A Mathematical and Theoretical•Sep 4, 2017•8 citations
Abstract At zero temperature, homogeneous interacting Bose-condensed fluids are entirely superfluid, with remarkable transport properties. A non-superfluid, normal component is induced by finite temperatures and spatial inhomogeneity, the combined effects of which are rather intriguing, and difficult to describe quantitatively. By inhomogeneous Bogoliubov theory, applicable to weakly interacting condensed Bose gases in static external potentials with arbitrary spatial correlations, we calculate the normal fluid density via the transverse current–current correlation. We obtain finite-temperature disorder corrections to the normal fraction known since Laudau’s seminal two-fluid theory, using diagrammatic perturbation theory for systems of any dimensionality, with closed analytical expressions to leading, quadratic order in disorder strength.
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.
We investigate the behavior of the anomalous correlation function in two-dimensional Bose gas. In the local case, we find that this quantity has a finite value in the limit of weak interactions at zero temperature. The effects of the anomalous density on some thermodynamic quantities are also considered. These effects can modify, in particular, the chemical potential, the ground-state energy, the depletion, and the superfluid fraction. Our predictions are in good agreement with recent analytical and numerical calculations. We show also that the anomalous density presents a significant importance compared to the noncondensed one at zero temperature. The single-particle anomalous correlation function is expressed in two-dimensional homogenous Bose gases by using the density-phase fluctuation. We then confirm that the anomalous average accompanies in analogous manner the true condensate at zero temperature, while it does not exist at finite temperature.
Abstract In an equilibrium three-dimensional (3D) disordered condensate, it is well established that disorder can generate an amount of normal fluid ρ n equaling to of ρ ex , where ρ ex is a sum of interaction-induced quantum depletion and disorder-induced condensate deformation. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of the Bose glass phase. In this work, we show that, by bringing a weakly disordered 3D condensate to non-equilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state of Hamiltonian H f in which the ρ n far exceeds of the ρ ex . This suggests the possibility of engineering Bose glass in the dynamic regime. Here, we refer to the dynamical Bose glass as the case where in the steady state of quenched condensate , the superfluid density goes to zero while the condensate density remains finite. As both the ρ n and ρ ex are measurable quantities, our results allow an experimental demonstration of the dramatized interplay between the disorder and interaction in the non-equilibrium scenario.
In this thesis, we study the quantum phase transition triggered by an external random po- tential in ultra-cold low-dimensional weakly-interacting Bose gases at zero temperature. In one-dimensional systems, the quantum phases are characterized by the decay at long-range of the one-body density matrix. This decay exhibits an algebraic behaviour in the superfluid quasi-condensed phase while in the insulating Bose glass phase this it becomes exponen- tial, signaling the complete loss of coherence in the system. In two-dimensional systems, a characterization based on the long-range behaviour of the one-body density matrix appears to be highly demanding from a computational point of view. We therefore characterized the superfluid-insulator transition in two-dimensional systems by the low-energy behaviour of the cumulative density of states of the Bogoliubov excitations. While in the superfluid condensed phase this quantity grows as the square of the excitation energy in agreement with the existence of a finite velocity of sound, in the insulating Bose glass phase this power law is less than quadratic. This study is performed in the framework of an extended Bogoliubov approach properly adapted to treat low-dimensional Bose gases. Using a systematic numerical study, we draw the interaction-disorder phase diagrams of the superfluid-insulator transition in 1D and 2D. The phase boundary follows two different power- laws depending on the length scales characterizing the spatial correlations of the disorder and the strength of interactions. The power-law exponents were found to be in agreement with the ones predicted by scaling arguments, both in the white noise and the Thomas-Fermi regimes. In the two-dimensional system, the classical percolation threshold in the Thomas-Fermi limit was found to overestimate the critical disorder below which the onset of superfluidity should be observed for a given interaction strength.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.