Influence of Induced Interactions on the Superfluid Transition in Dilute Fermi Gases

We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with 2 species having equal densities, the transition temperature is suppressed by a factor $(4e)^{1/3}\approx 2.2$, and for $\nu$ fermion species, the transition temperature is increased by a factor $(4e)^{\nu /3-1} \approx 2.2^{\nu-3}$. For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an effective interaction, and we estimate the increase of the transition temperature due to this effect.Comment: 4 pages, 3 figure

Signatures of macroscopic quantum coherence in ultracold dilute Fermi gases

We propose a double-well configuration for optical trapping of ultracold two-species Fermi-Bose atomic mixtures. Two signatures of macroscopic quantum coherence attributable to a superfluid phase transition for the Fermi gas are analyzed. The first signature is based upon tunneling of Fermi pairs when the power of the deconfining laser beam is significantly reduced. The second relies on the observation of interference fringes in a regime where the fermions are trapped in two sharply separated minima of the potential. Both signatures rely on small decoherence times for the Fermi samples, which should be possible by reaching low temperatures using a Bose gas as a refrigerator, and a bichromatic optical dipole trap for confinement, with optimal heat-capacity matching between the two species

Boson induced s-wave pairing in dilute boson-fermion mixtures

We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give an analytical method to derive the associated $T_c$ in the limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a $T_c$ of the same order as for a pure Fermi gas with bare attraction.Comment: 12 pages, no figure

Ground-state properties of trapped Bose-Fermi mixtures: role of exchange-correlation

We introduce Density Functional Theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local density approximation. We solve numerically the Kohn-Sham system and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange--correlation is discussed by comparison with current experiments; in particular, we investigate the effect of of the repulsive potential energy contribution due to exchange--correlation on the stability of the mixture against collapse.Comment: 6 pages, 4 figures (final version as published in Physical Review

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

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.Comment: 15 pages, 2 figures, submitted to J. Phys.