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arXiv:quant-ph/0305133 · Physica Scripta

Two-component Fermi Gas in a Harmonic Trap

X. X. Yi, H J Wang, H. T. Cui, C M Zhang

Published Jan 1, 2002• 0 citations
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Abstract

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.

DOI
10.1238/physica.regular.066a00284

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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.
We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger equation in three dimensions, rather than from the cumbersome variational equations of the underlying energy density functional. With the employed hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic trap. We present transitions from identical density profiles of the two fermion species towards isotropic and anisotropic separations for various confinements, including harmonic and double-well-type traps. Our proposed method is suited for arbitrary trap geometries and can be straightforwardly extended to study dynamics in the light of ongoing experiments on degenerate Fermi gases.
We use a semiclassical approximation to investigate density variations and dipole oscillations of an interacting three-component normal Fermi gas in a harmonic trap. We consider both attractive and repulsive interactions between different pairs of fermions and study the effect of population imbalance on densities. We find that the density profiles significantly deviate from those of non-interacting profiles and extremely sensitive to interactions and population imbalance. Unlike for a two-component Fermi system, we find density imbalance even for balanced populations. For some range of parameters, one component completely repels from the trap center giving rise a donut shape density profile. Further, we find that the in-phase dipole oscillation frequency is consistent with Kohn's theorem and other two dipole mode frequencies are strongly effected by the interactions and the number of atoms in the harmonic trap.
We present a numerical study of mixed boson-fermion systems at zero temperature in isotropic and anisotropic harmonic traps. We investigate the phenomenon of component separation as a function of the strength of the interparticle interaction. While solving a Gross-Pitaevskii mean-field equation for the boson distribution in the trap, we utilize two different methods to extract the density profile of the fermion component; a semiclassical Thomas-Fermi approximation and a quantum-mechanical Slater determinant Schr\"odinger equation.
We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions toward ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree–Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the bare contact interaction energy and especially to the Thomas–Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a plethora of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general.
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 investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.