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arXiv:1105.0995 · Europhysics Letters (EPL)

Spontaneous separation of two-component Fermi gases in a double-well trap

Junjun Xu, Qiang Gu

Published Jun 1, 2011• 4 citations
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Abstract

The two-component Fermi gas in a double-well trap is studied using the density functional theory and the density profile of each component is calculated within the Thomas-Fermi approximation. We show that the two components are spatially separate in the two wells once the repulsive interaction exceeds the Stoner point, signaling the occurrence of the ferromagnetic transition. Therefore, the double-well trap helps to explore itinerant ferromagnetism in atomic Fermi gases, since the spontaneous separation can be examined by measuring component populations in one well.

DOI
10.1209/0295-5075/94/60001

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The two-component Fermi gas in a double-well trap is studied using the density functional theory and the density profile of each component is calculated within the Thomas-Fermi approximation. We show that the two components are spatially separate in the two wells once the repulsive interaction exceeds the Stoner point, signaling the occurrence of the ferromagnetic transition. Therefore, the double-well trap helps to explore itinerant ferromagnetism in atomic Fermi gases, since the spontaneous separation can be examined by measuring component populations in one well.
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.
We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean-field release energy, its separate kinetic and interaction contributions, as well as the potential energy all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation and derive an energy functional that includes a term that depends on the local magnetization gradient and acts as a ``surface tension.'' Using this energy functional, we numerically study the energetics of some candidate spin textures that may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an ``in-out'' domain-wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K gases.
The component separation of the trapped large-spin Fermi gas is studied within density functional theory. The ground state and ferromagnetic transition in the gas, with and without the spin mixing collision, are calculated. In the absence of spin mixing, two patterns of separation are observed as the interaction between atoms increases, whereas only one of them corresponds to a ferromagnetic transition. The phase diagram suggests that the pattern which the system chooses depends on the interaction strength in the collision channels. With the presence of spin mixing, the distribution of phase region changes because of the interplay between different collision channels. Specifically, the spin exchange benefits the FM transition, while it suppresses the component separation of CS-II pattern.
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the most well-characterized phases of correlated Fermi systems. A recent experiment has reported the first evidence for novel phase behavior on the repulsive side of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting recent theoretical studies to the atomic trap geometry, we show that an adiabatic ferromagnetic transition would take place at a weaker interaction strength than is observed in experiment. This discrepancy motivates a simple nonequilibrium theory that takes account of the dynamics of magnetic defects and three-body losses. The formalism developed displays good quantitative agreement with experiment.
Spin asymmetry of ground states is studied in trapped spin-degenerate (two-component) gases of fermionic atoms with repulsive interaction between different components; and, for a large particle number, the asymmetric (collective ferromagnetic) states are shown to be stable because it can be energetically favorable to increase the Fermi energy of one component rather than increase the interaction energy between up-down components. We formulate the Thomas-Fermi equations and give algebraic methods to solve them. From the Thomas-Fermi solutions, we find three kinds of ground states in the finite system: (1) paramagnetic (spin-symmetric), (2) ferromagnetic (equilibrium), and (3) ferromagnetic (nonequilibrium) states. We present the density profiles and the critical atom numbers for these states obtained analytically, and, in ferromagnetic states, the spin asymmetries are shown to occur in the central region of the trapped gas, and increase with increasing particle number. Based on the obtained results, we discuss the experimental conditions and current difficulties in realizing the ferromagnetic states of the trapped atom gas, which should be overcome.
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.