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arXiv:cond-mat/0011049 · Conference on Theoretical Nuclear Physics in Italy

SHELL EFFECTS AND PHASE SEPARATION IN A TRAPPED MULTI-COMPONENT FERMI SYSTEM

Luca Salasnich, L. Reatto, Alberto Parola

Published Jun 1, 2001• 1 citation
arXivHTMLPDF

Abstract

Shell effects in the coordinate space can be seen with degenerate Fermi vapors in non-uniform trapping potentials. In particular, below the Fermi temperature, the density profile of a Fermi gas in a confining harmonic potential is characterized by several local maxima. This effect is enhanced for "magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In the case of a multi-component Fermi vapor, the separation of Fermi components in different spatial shells (phase-separation) depends on temperature, number of particles and scattering length. We derive analytical formulas, based on bifurcation theory, for the critical density of Fermions and the critical chemical potential, which give rise to the phase-separation.

DOI
10.1142/9789812811356_0016

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Shell effects in the coordinate space can be seen with degenerate Fermi vapors in non-uniform trapping potentials. In particular, below the Fermi temperature, the density profile of a Fermi gas in a confining harmonic potential is characterized by several local maxima. This effect is enhanced for "magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In the case of a multi-component Fermi vapor, the separation of Fermi components in different spatial shells (phase-separation) depends on temperature, number of particles and scattering length. We derive analytical formulas, based on bifurcation theory, for the critical density of Fermions and the critical chemical potential, which give rise to the phase-separation.
We study the thermodynamical properties of Fermi vapours confined in a harmonic external potential. In the case of the ideal Fermi gas, we compare exact density profiles with their semiclassical approximation in the conditions of recent experiments. Then, we consider the phase separation of a multi-component Fermi vapour. In particular, we analyse the phase separation as a function of temperature, number of particles and scattering length. Finally, we discuss the effect of rotation on the stability and thermodynamics of the trapped vapours.
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.
On the basis of the phase diagram of the uniform system, we calculate the density profiles of a trapped polarized Fermi gas at zero temperature using the local density approximation. By varying the overall polarization and the interaction strength, we analyze the appearance of a discontinuity in the profile, signaling a first-order phase transition from a superfluid inner core to a normal outer shell. The local population imbalance between the two components and the size of the various regions of the cloud corresponding to different phases are also discussed. The calculated profiles are quantitatively compared with the ones recently measured by Shin et al. [Phys. Rev. Lett. 101, 070404 (2008)].
Closed-form analytic expressions are derived for the density profile of a harmonically trapped noninteracting Fermi gas in ddd dimensions. Shell structure effects are included to leading order in 1/N1/N1/N, where NNN is the number of particles. These corrections to the local density approximation scale as $\ensuremath{\delta}n/n\ensuremath{\sim}{N}^{\ensuremath{-}\ensuremath{\alpha}}$, where $\ensuremath{\alpha}=(1+1/d)/2$.
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.
We study the two-component repulsive Fermi gas with imbalanced populations in one dimension. Starting from the Bethe ansatz solution we calculate analytically the phase diagram for the homogeneous system. We show that three phases appear: the balanced phase, the fully polarized phase, and the partially polarized phase. By means of the local density approximation and the equation of state for the homogeneous system we calculate the density profile for the harmonically confined case. We show that a two-shell structure appears: at the center of the cloud we find the partially polarized phase and at the edges the fully polarized one. The radii of the inner and outer shells are calculated for different values of the polarization and the coupling strength. We calculate the dependence of the magnetization on the polarization for different values of the coupling strength and we show that the susceptibility is always finite.