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Critical temperature of Bose-Einstein condensation in trapped atomic Bose-Fermi mixtures

A. P. Albus, S. Giorgini, F. Illuminati, L. Viverit

Published Jan 1, 2002• 2 citations
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Abstract

We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential, to lowest order in both the Bose-Bose and Bose-Fermi coupling constans. The relativ importance of the effect on the critical temperature of the boson-fermion interactions is investigated as a function of the parameters of mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.

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We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential, to lowest order in both the Bose-Bose and Bose-Fermi coupling constans. The relativ importance of the effect on the critical temperature of the boson-fermion interactions is investigated as a function of the parameters of mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.
We calculate the shift in the critical temperature of Bose–Einstein condensation for a dilute Bose–Fermi mixture confined by a harmonic potential, to lowest order in both the Bose–Bose and Bose–Fermi coupling constants. The relative importance of the effect on the critical temperature of the boson–boson and boson–fermion interactions is investigated as a function of the parameters of the mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose–Fermi mixtures is discussed.
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.
The effects of impurity and Bose-Fermi interactions on the transition temperature of a dipolar Bose–Einstein condensation in trapped Bose-Fermi mixture, by using the two-fluid model, are investigated. The shift of the transition temperature consists of four contributions due to contact, Bose-Fermi, dipole-dipole, and impurity interactions. We will show that in the presence of an anisotropic trap, the Bose-Fermi correction to the shift of transition temperature due to the excitation spectra of the thermal part is independent of anisotropy factor. Applying our results to trapped Bose-Fermi mixtures shows that, by knowing the impurity effect, the shift of the transition temperature due to Bose-Fermi interaction could be measured for isotropic trap (dipole-dipole contributions is zero) and Feshbach resonance technique (contact potential contribution is negligible).
The dependence of the critical temperature shift in the Bose component of a degenerate Bose-Fermi gas mixture in a harmonic trap on the number of bosons and fermions has been obtained on the basis of the effective Hamiltonian of the Bose subsystem. The presence of the Fermi component leads to a qualitatively new behavior of the shift, as compared to the case of a single interacting Bose gas in the trap. Namely, the T c(N) dependence has a different curvature in the presence of the Fermi component.
One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.