Quasi-particle properties of trapped Fermi gases

Luca Giorgetti, Luciano Viverit, G. Gori, E. Vigezzi, Ricardo A. Broglia

Published Jan 1, 2004• 1 citation

Abstract

Abstract. We develop a consistent formalism in order to explore the effects of density and spin fluctuations on the quasi-particle properties and on the pairing critical temperature of a trapped Fermi gas on the attractive side of a Feshbach resonance. We first analyze the quasi-particle properties of a gas due to interactions far from resonance (effective mass and lifetime, quasi-particle strength and effective interaction) for the two cases of a spherically symmetric harmonic trap and of a spherically symmetric infinite potential well. We then explore the effect of each of these quantities on Tc and point out the important role played by the discrete level structure. PACS numbers: 03.75.Ss, 21.10.-k, 21.60.JzQuasi-particle properties of trapped Fermi gases 2 1.

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OpenAlex

Abstract

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arXiv:0706.3360Reviews of Modern PhysicsOct 2, 20081,997 citations

T_c

and point out the important role played by the discrete level structure.

\sim

1000 particles. The calculation provides insight on the many-body physics of finite Fermi gases and is closely related to similar problems recently considered in the case of atomic nuclei and neutron stars.

In view of ongoing experiments to trap ultracold spin-polarized

{}^{6}\mathrm{Li},

we study various properties of an interacting Fermi gas in a harmonic trap, taking the discrete nature of the unperturbed harmonic trap levels into account exactly. As

{}^{6}\mathrm{Li}

has a rather large and negative scattering length, we focus on the effects of the attractive atom-atom interaction on several thermodynamic properties, and on the momentum and density distributions. The dependence of the chemical potential, the specific heat, and the density and momentum distributions on the number of particles in the trap is obtained. We also calculate the energy of the gas. Comparison is made with results of a semiclassical calculation and with the properties of a noninteracting gas. We find that the effect of the interactions is rather large for realistic trap frequencies. Hence it is important to include these interactions in any quantitative predictions relevant for experiments.

{T}_{\mathrm{c}},

reflecting the change of the dominant particles going from Fermi atoms to composite bosons. In the BEC regime, these composite bosons are shown to first appear well above

{T}_{\mathrm{c}}.

We also discuss the ``phase diagram'' above

{T}_{\mathrm{c}}

as a function of the tunable threshold energy $2\ensuremath{\nu}.$ We introduce a characteristic temperature ${T}^{*}(2\ensuremath{\nu})$ describing the effective crossover in the normal phase from a Fermi gas of atoms to a gas of stable molecules.

s

-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.