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Title: Effective size of a trapped atomic Bose gas

Abstract

We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang et al. [Chin. Phys. Lett. 20, 799 (2003)], is shown to be a good indication for Bose-Einstein condensation. Our study also supports the use of the average width of a trapped Bose gas for a nondestructive calibration of its temperature.

Authors:
 [1];  [2];  [1];  [3]
  1. School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
  2. Center for Advanced Study, Tsinghua University, Beijing 100084 (China)
  3. (China)
Publication Date:
OSTI Identifier:
20786573
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.053627; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; CALIBRATION; MEAN-FIELD THEORY; RADIATION PRESSURE; TEMPERATURE DEPENDENCE; TRAPPING

Citation Formats

Zhang Wenxian, Xu, Z., You, L., and Center for Advanced Study, Tsinghua University, Beijing 100084. Effective size of a trapped atomic Bose gas. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Zhang Wenxian, Xu, Z., You, L., & Center for Advanced Study, Tsinghua University, Beijing 100084. Effective size of a trapped atomic Bose gas. United States. doi:10.1103/PHYSREVA.72.0.
Zhang Wenxian, Xu, Z., You, L., and Center for Advanced Study, Tsinghua University, Beijing 100084. Tue . "Effective size of a trapped atomic Bose gas". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786573,
title = {Effective size of a trapped atomic Bose gas},
author = {Zhang Wenxian and Xu, Z. and You, L. and Center for Advanced Study, Tsinghua University, Beijing 100084},
abstractNote = {We investigate the temperature-dependent effective size of a trapped interacting atomic Bose gas within a mean field theory approximation. The sudden shrinking of the average length, as observed in an earlier experiment by Wang et al. [Chin. Phys. Lett. 20, 799 (2003)], is shown to be a good indication for Bose-Einstein condensation. Our study also supports the use of the average width of a trapped Bose gas for a nondestructive calibration of its temperature.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 5,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • We discuss the transition from a fully decoherent to a (quasi)condensate regime in a harmonically trapped weakly interacting one-dimensional (1D) Bose gas. By using analytic approaches and verifying them against exact numerical solutions, we find a characteristic crossover temperature and crossover atom number that depend on the interaction strength and the trap frequency. We then identify the conditions for observing either an interaction-induced crossover scenario or else a finite-size Bose-Einstein condensation phenomenon characteristic of an ideal trapped 1D gas.
  • We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at T=0 within the Thomas-Fermi approximation. Results are also given for themore » monopole {open_quotes}breathing{close_quote}{close_quote} mode as well as for the m=0 excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well. {copyright} {ital 1997} {ital The American Physical Society}« less
  • We calculate the critical temperature of a trapped interacting Bose-Fermi gas mixture by means of a first-order perturbation method in a local-density approximation. An explicit analytical expression is derived for the dependence of the critical temperature on the numbers of bosons and fermions, the strengths of boson-boson and boson-fermion interactions, and the trapping frequencies.
  • We adopt an effective-field-theory view to describe the low-energy excitations of trapped Bose gases, which allows a direct and systematic way to investigate the consequences of spontaneous symmetry breaking. The derivation of the effective Lagrangian can incorporate various approximations and can reproduce the results obtained by the standard hydrodynamic approach. Based on the effective Lagrangian, we calculate the energy spectrum and Matsubara Green's function of trapped one-dimensional Bose gases with {delta}-function repulsive interaction allowing the comparison of various results obtained by different approaches. We also analytically calculate the finite-temperature correlation function of trapped two-dimensional (2D) Bose gases. The calculation schememore » can be easily extended to higher dimensions. We find that particle interactions will always decrease the coherence length of the condensate in 2D, confirming recent numerical results. The validation of various asymptotic expressions are given.« less
  • We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length {ital a} and the ratio {eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function {psi}{sub 0}. We find that for {ital a}{lt}0 and {eta}{lt}1 it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For {eta}{gt}1 a negative scattering length prevents the formation of the condensate. If {ital a}{approx_gt}0, then an increase of densitymore » is accompanied by the evolution of {psi}{sub 0} to a comparatively wide quasihomogeneous distribution. {copyright} {ital 1996 The American Physical Society.}« less