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Phase diagram of trapped degenerate Fermi gases including effective s- and p-wave interactions

R. Roth, H. Feldmeier

Published Jan 1, 2001• 10 citations
OpenAlex

Abstract

Abstract. The inuence of s- and p-wave interactions on trapped degenerate one and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation including the s- and p-wave terms of an eective contact interaction. On this basis the stability of the dilute gas against mean-eld induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The ndings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has signicant inuence on the phase diagram of the degenerate Fermi gas and causes new phenomena like absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases. PACS numbers: 03.75.Fi, 34.20.Cf, 32.80.Pj 1.

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Phase diagram of trapped degenerate Fermi gases including effective s- and p-wave interactions

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The influence of s- and p-wave interactions on trapped degenerate one- and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation, including the s- and p-wave terms of an effective contact interaction. On this basis the stability of the dilute gas against mean-field induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore, the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The findings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has a significant influence on the phase diagram of the degenerate Fermi gas and causes new phenomena such as absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases.

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We consider a mixture of two-component Fermi gases at low temperature. The density profile of this degenerate Fermi gas is calculated under the semiclassical approximation. The results show that the fermion-fermion interactions make a large correction to the density profile at low temperature. The phase separation of such a mixture is also discussed for both attractive and repulsive interatomic interactions, and the numerical calculations demonstrate the existance of a stable temperature region T c1 < T < T c2 for the mixture. In addition, we give the critical temperature of the BCS-type transition in this system beyond the semiclassical approximation.

arXiv:quant-ph/0305133•Physica Scripta•Jan 1, 2002•0 citations
Abstract. The inuence of s- and p-wave interactions on trapped degenerate one and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation including the s- and p-wave terms of an eective contact interaction. On this basis the stability of the dilute gas against mean-eld induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The ndings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has signicant inuence on the phase diagram of the degenerate Fermi gas and causes new phenomena like absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases. PACS numbers: 03.75.Fi, 34.20.Cf, 32.80.Pj 1.
The influence of s- and p-wave interactions on trapped degenerate one- and two-component Fermi gases is investigated. The energy functional of a multicomponent Fermi gas is derived within the Thomas-Fermi approximation, including the s- and p-wave terms of an effective contact interaction. On this basis the stability of the dilute gas against mean-field induced collapse due to attractive interactions is investigated and explicit stability conditions in terms of Fermi momentum and s- and p-wave scattering lengths are derived. Furthermore, the spatial separation in a two-component Fermi gas is discussed, explicit conditions for the onset of component demixing are given, and the density distributions in the separated phase are calculated. The findings are summarized in a zero-temperature phase diagram for the degenerate two-component Fermi gas. It is shown that the p-wave interaction has a significant influence on the phase diagram of the degenerate Fermi gas and causes new phenomena such as absolute stabilization against collapse and component separation. It may therefore be useful in the context of the envisioned BCS transition in trapped atomic Fermi gases.
The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an effective contact interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multicomponent Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.
The stability of trapped dilute Fermi gases against collapse towards large densities is studied. A Hermitian effective contact interaction for all partial waves is derived, which is particularly suited for a mean-field description of these systems. Including the s- and p-wave parts, explicit stability conditions and critical particle numbers are given as a function of the scattering lengths. The p-wave contribution determines the stability of a single-component gas and can substantially modify the stability of a two-component gas. Moreover it may give rise to a novel p-wave stabilized high-density phase.
The stability of two-component degenerate Fermi gases with attractive interactions in a harminic trap with a quartic distortion in the mean-field is studied.The influences of anharmonicity and p-wave interaction on the stability of Fermi gas are discussed,respectively.It is shown that the anharmonicity of harminic trap and the p-wave interaction have important effect on the stability of Fermi gas,and have an effect on the particle numberal density distributing.Using variational approaches,the stability condition of the system in a harminic trap with a quartic distortion under the effective s-and p-wave interactions are derived.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.
We consider a mixture of two-component Fermi gases at low temperature. The density profile of this degenerate Fermi gas is calculated under the semiclassical approximation. The results show that the fermion-fermion interactions make a large correction to the density profile at low temperature. The phase separation of such a mixture is also discussed for both attractive and repulsive interatomic interactions, and the numerical calculations demonstrate the existance of a stable temperature region T c1 < T < T c2 for the mixture. In addition, we give the critical temperature of the BCS-type transition in this system beyond the semiclassical approximation.