Thermodynamics of a trapped Bose-condensed gas

Abstract

We investigate the thermodynamic behaviour of a Bose gas interacting with repulsive forces and confined in a harmonic anisotropic trap. We develop the formalism of mean field theory for non uniform systems at finite temperature, based on the generalization of Bogoliubov theory for uniform gases. By employing the WKB semiclassical approximation for the excited states we derive systematic results for the temperature dependence of various thermodynamic quantities: condensate fraction, density profiles, thermal energy, specific heat and moment of inertia. Our analysis points out important differences with respect to the thermodynamic behaviour of uniform Bose gases. This is mainly the consequence of a major role played by single particle states at the boundary of the condensate. We find that the thermal depletion of the condensate is strongly enhanced by the presence of repulsive interactions and that the critical temperature is decreased with respect to the predictions of the non-interacting model. Our work points out an important scaling behaviour exhinited by the system in large $N$ limit. Scaling permits to express all the relevant thermodynamic quantities in terms of only two parameters: the reduced temperature $t=T/T_c^0$ and the ratio between the $T=0$ value of the chemical potential and the critical temperature $T_c^0$ for Bose-Einstein condensation. Comparisons with first experimental results and ab-initio calculations are presented.

47 pages, RevTeX, figures are available on request, please write to [email protected]

References in corpus (3)

• Quantum Monte Carlo Calculations for a large number of bosons in a harmonic trap
• Scaling and thermodynamics of a trapped Bose-condensed gas
• Internal energy and condensate fraction of a trapped interacting Bose gas

Cited by in corpus (8)

• Beyond Mean-Field Low-Lying Excitations of Dipolar Bose Gases
• Observation of Atom Number Fluctuations in a Bose-Einstein Condensate
• Condensation and quasicondensation in an elongated three-dimensional Bose gas
• Scale invariance and universality in a cold gas of indirect excitons
• Dark Matter as a Non-Relativistic Bose-Einstein Condensate with Massive Gravitons
• Measurement of the order parameter and its spatial fluctuations across Bose-Einstein condensation
• A local exchange theory for trapped dipolar gases
• Critical temperature of trapped interacting bosons from large-N based theories