Fermi Gas in the Harmonic Trap

Лев П. Питаевский, S. Stringari

Published Jan 1, 2016• 0 citations

Abstract

Abstract This chapter deals with Fermi gases confined in harmonic traps. After offering a reminder of the properties of the harmonically trapped ideal Fermi gas, the chapter focuses on the effect of interactions, employing the local density approximation to calculate the density profiles and the momentum along the BCS–BEC crossover and comparing theoretical predictions with experiments.

DOI: 10.1093/acprof:oso/9780198758884.003.0017

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Publisher

Abstract

DOI: 10.1093/acprof:oso/9780198758884.003.0017

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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.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.

arXiv:physics/9807027Physical Review ASep 1, 199876 citations

We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined

T

-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature

{T}_{\mathrm{c}}

, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures

{T}^{*}

and

{T}^{**}

at which the pseudogap structures in these quantities completely disappear. Determining

{T}^{*}

and

{T}^{**}

over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.

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.