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:cond-mat/0106410 · Journal of Physics B Atomic Molecular and Optical Physics

Dilute bose gas in a quasi two-dimensional trap

Brandon P. van Zyl, R. K. Bhaduri, Justin Sigetich

Published Jun 20, 2001• 11 citations
arXivHTMLPDF

Abstract

We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature $T^{\star}$ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.

DOI
10.48550/arxiv.cond-mat/0106410

Related papers

Scaling and Thermodynamics of a Trapped Bose-Condensed Gas

S. Giorgini, Лев П. Питаевский, S. Stringari

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number $N$ of atoms, harmonic oscillator length, deformation of the trap, $s$-wave scattering length) fix its thermodynamic behavior in the large $N$ limit through two dimensionless scaling parameters. These are the reduced temperature $t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}$ and the ratio $\ensuremath{\eta}$ between the $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature ${T}_{c}^{0}$ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.

arXiv:cond-mat/9612192•Physical Review Letters•May 26, 1997•86 citations

The effect of interactions on Bose-Einstein condensation in a quasi two-dimensional harmonic trap

R. K. Bhaduri, S. M. Reimann, S. Viefers +2 more

A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed phase as the temperature is lowered. Its density profile and energy are identical to that of an ideal gas obeying the fractional exclusion statistics of Haldane.

arXiv:cond-mat/9908210•Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2000•43 citations

Critical global thermodynamics of the BEC transition of a harmonically confined weakly interacting Bose gas

I. Reyes-Ayala, Freddy Jackson Poveda-Cuevas, Jorge Amin Seman +1 more

The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are analyzed using a proposed model for the equation of state of the underlying homogenous Bose fluid. The equation of state is given in terms of the homogenous particle density as a function of the chemical potential and temperature of the gas. On the normal side of the fluid it is assumed to be an ideal Bose gas while in the superfluid state we propose a function that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the {\it global} thermodynamics of the harmonically confined gas which shows that, at the critical transition of the confined gas, the thermodynamic susceptibilities, such as the isothermal compressibility, do not diverge, in contrast to the behavior of the uniform gas. The singularity of the critical transition in the confined system appears now at the derivatives of the susceptibilities. We discuss how these properties can be experimentally tested.

•Jul 8, 2016•0 citations

Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

I. Reyes-Ayala, Freddy Jackson Poveda-Cuevas, Jorge Amin Seman +1 more

Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.

arXiv:1607.02389•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2017•5 citations

Thermodynamics of a trapped Bose-Fermi mixture

Hui Hu, Xia-Ji Liu

By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction, we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped ${}^{87}\mathrm{Rb}{\ensuremath{-}}^{40}\mathrm{K}$ mixtures is discussed.

arXiv:cond-mat/0302570•Physical Review A•Aug 26, 2003•22 citations

Finite-Temperature Disordered Bosons in Two Dimensions

Giulio Bertoli, V. P. Michal, B. L. Altshuler +1 more

We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.

arXiv:1708.03628•Physical Review Letters•Jul 18, 2018•17 citations
We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature T⋆T^{\star}T⋆. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature T⋆T^{\star}T⋆ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.
We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number NNN of atoms, harmonic oscillator length, deformation of the trap, sss-wave scattering length) fix its thermodynamic behavior in the large NNN limit through two dimensionless scaling parameters. These are the reduced temperature t=T/Tc0t\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T/{T}_{c}^{0}t=T/Tc0​ and the ratio $\ensuremath{\eta}$ between the T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature Tc0{T}_{c}^{0}Tc0​ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.
The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are analyzed using a proposed model for the equation of state of the underlying homogenous Bose fluid. The equation of state is given in terms of the homogenous particle density as a function of the chemical potential and temperature of the gas. On the normal side of the fluid it is assumed to be an ideal Bose gas while in the superfluid state we propose a function that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the {\it global} thermodynamics of the harmonically confined gas which shows that, at the critical transition of the confined gas, the thermodynamic susceptibilities, such as the isothermal compressibility, do not diverge, in contrast to the behavior of the uniform gas. The singularity of the critical transition in the confined system appears now at the derivatives of the susceptibilities. We discuss how these properties can be experimentally tested.
Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.
By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction, we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped ${}^{87}\mathrm{Rb}{\ensuremath{-}}^{40}\mathrm{K}$ mixtures is discussed.
We study phase transitions in a two dimensional weakly interacting Bose gas in a random potential at finite temperatures. We identify superfluid, normal fluid, and insulator phases and construct the phase diagram. At T=0 one has a tricritical point where the three phases coexist. The truncation of the energy distribution at the trap barrier, which is a generic phenomenon in cold atom systems, limits the growth of the localization length and in contrast to the thermodynamic limit the insulator phase is present at any temperature.