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

Physical Review A

Zero-temperature properties of a trapped Bose-condensed gas: Beyond the Thomas-Fermi approximation

Emil Lundh, C. J. Pethick, H. Smith

Published Mar 1, 1997• 152 citations
Publisher

Abstract

We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud. For large clouds, our results are in excellent agreement with available numerical calculations.

DOI
10.1103/physreva.55.2126

Related papers

Ground-State Properties of Magnetically Trapped Bose-Condensed Rubidium Gas

Gordon Baym, C. J. Pethick

In light of the recent experimental observation of Bose-Einstein condensation in dilute ${}^{87}\mathrm{Rb}$ gas cooled to nanokelvin-scale temperatures, we give a quantitative account of the ground-state properties of magnetically trapped Bose gases. Using simple scaling arguments, we show that at large particle number the kinetic energy is a small perturbation, and find a spatial structure of the cloud of atoms and its momentum distribution dependent in an essential way on particle interactions. We also estimate the superfluid coherence length and the critical angular velocity at which vortex lines become energetically favorable.

arXiv:cond-mat/9508040•Physical Review Letters•Jan 1, 1996•696 citations

The condensate wave function of a trapped atomic gas

F. Dalfovo, Лев П. Питаевский, S. Stringari

We discuss various properties of the ground state of a Bose-condensed dilute gas confined by an external potential. We devote particular attention to the role played by the interaction in determining the kinetic energy of the system and the aspect ratio of the velocity distribution. The structure of the wave function near the classical turning point is discussed and the drawback of the Thomas-Fermi approximation is explicitly pointed out. We consider also states with quantized vorticity and calculate the critical angular velocity for the production of vortices. The presence of vortex states is found to increases the stability of the condensate in the case of attractive interactions.

Journal of Research of the National Institute of Standards and Technology•Jul 1, 1996•28 citations

Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms

Antonio Muñoz Mateo, V. Delgado

By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary number of atoms in the mean-field regime. Specifically, we obtain approximate analytical expressions for the ground-state properties of spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct analytical formulas in both the TF and the perturbative regimes, and remain valid and accurate in between these two limiting cases. Mean-field quasi-one-dimensional (quasi-1D) and -2D condensates appear as simple particular cases of our formulation. The validity of our results is corroborated by an independent numerical computation based on the 3D Gross-Pitaevskii equation.

arXiv:cond-mat/0701695•Physical Review A•Dec 20, 2006•27 citations

Static Properties of Trapped Bose Gases at Finite Temperature: I. Thomas- Fermi Limit

Mohamed Benarous, Samet, H. Chachou

We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.

arXiv:cond-mat/0611490•Nov 18, 2006•0 citations

Analytical estimate of the critical velocity for vortex pair creation in trapped Bose condensates

Michael Crescimanno, C. G. Koay, R. Peterson +1 more

We use a Thomas-Fermi approximation that includes the leading kinetic terms due to fluid motion to estimate analytically the critical velocity for the formation of vortex pairs in harmonically trapped Bose-Einstein condensates. We find rough agreement between this analytical estimate and recent experiments on trapped sodium gas condensates.

arXiv:cond-mat/0001163•Physical Review A•Nov 15, 2000•28 citations

Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas

Alexander L. Fetter, David L. Feder

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order ${R}^{\ensuremath{-}4}\mathrm{ln}R$ and ${R}^{\ensuremath{-}4},$ where R is the number-dependent dimensionless condensate radius in units of the oscillator length $\sqrt{\ensuremath{\Elzxh}/m{\ensuremath{\omega}}_{0}}.$ The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order ${R}^{\ensuremath{-}4}.$

arXiv:cond-mat/9704173•Physical Review A•Oct 1, 1998•61 citations
We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud. For large clouds, our results are in excellent agreement with available numerical calculations.
In light of the recent experimental observation of Bose-Einstein condensation in dilute 87Rb{}^{87}\mathrm{Rb}87Rb gas cooled to nanokelvin-scale temperatures, we give a quantitative account of the ground-state properties of magnetically trapped Bose gases. Using simple scaling arguments, we show that at large particle number the kinetic energy is a small perturbation, and find a spatial structure of the cloud of atoms and its momentum distribution dependent in an essential way on particle interactions. We also estimate the superfluid coherence length and the critical angular velocity at which vortex lines become energetically favorable.
We discuss various properties of the ground state of a Bose-condensed dilute gas confined by an external potential. We devote particular attention to the role played by the interaction in determining the kinetic energy of the system and the aspect ratio of the velocity distribution. The structure of the wave function near the classical turning point is discussed and the drawback of the Thomas-Fermi approximation is explicitly pointed out. We consider also states with quantized vorticity and calculate the critical angular velocity for the production of vortices. The presence of vortex states is found to increases the stability of the condensate in the case of attractive interactions.
By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary number of atoms in the mean-field regime. Specifically, we obtain approximate analytical expressions for the ground-state properties of spherical, cigar-shaped, and disk-shaped condensates that reduce to the correct analytical formulas in both the TF and the perturbative regimes, and remain valid and accurate in between these two limiting cases. Mean-field quasi-one-dimensional (quasi-1D) and -2D condensates appear as simple particular cases of our formulation. The validity of our results is corroborated by an independent numerical computation based on the 3D Gross-Pitaevskii equation.
We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit. We derive simple analytic expressions for the condensate properties at finite temperature. The noncondensate and anomalous density profiles are also analyzed in terms of the condensate fraction. The results are quite encouraging owing to the simplicity of the formalism.
Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order ${R}^{\ensuremath{-}4}\mathrm{ln}R$ and ${R}^{\ensuremath{-}4},$ where R is the number-dependent dimensionless condensate radius in units of the oscillator length $\sqrt{\ensuremath{\Elzxh}/m{\ensuremath{\omega}}_{0}}.$ The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order ${R}^{\ensuremath{-}4}.$