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arXiv:1106.0960 · Physical Review Letters

Nature and Properties of a Repulsive Fermi Gas in the Upper Branch of the Energy Spectrum

Vijay B. Shenoy, Tin-Lun Ho

Published Nov 14, 2011• 36 citations
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Abstract

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.

DOI
10.1103/physrevlett.107.210401

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We investigate normal-state properties of spin-orbit-coupled Fermi gases with repulsive sss-wave interaction, in the absence of molecule formation, i.e., in the so-called ``upper branch.'' Within the framework of random-phase approximation, we derive analytical expressions for the quasiparticle lifetime ${\ensuremath{\tau}}_{s}$, the effective mass ms∗{m}_{s}^{*}ms∗​, and the Green's function renormalization factor Zs{Z}_{s}Zs​ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit-coupled electron gas with Coulomb interaction, we show that the modifications are dependent on the Rashba band index sss and occur in the first order of the spin-orbit-coupling strength. We also calculate experimental observables such as spectral weight, density of state, and specific heat, which exhibit significant differences from their counterparts without spin-orbit coupling. We expect our microscopic calculations of these Fermi-liquid parameters would have immediate applications to the spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum.
We present highly accurate energy spectra and eigenfunctions of small 1D harmonically trapped two-component Fermi gases with interspecies δ-function interactions, and analyze the correlations of the so-called upper branch (i.e., the branch that describes a repulsive Fermi gas consisting of atoms but no molecules) for positive and negative coupling constants. Changes of the two-body correlations as a function of the interspecies coupling strength reflect the competition of the interspecies interaction and the effective repulsion due to the Pauli exclusion principle, and are interpreted as a few-body analog of a transition from a nonmagnetic to a magnetic phase. Moreover, we show that the eigenstate ψadia of the infinitely strongly interacting system with |n1+n2|>2 and |n1-n2|<n (n1 and n2 denote the number of fermions of components 1 and 2, respectively), which is reached experimentally by adiabatically changing the system parameters, does not, as previously proposed, coincide with the wave function ψG obtained by applying a generalized Fermi-Fermi mapping function to the eigenfunction of the noninteracting single-component Fermi gas.
In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (α n +4ε F /3) ( n and ε F denote the particle-number density and the Fermi energy respectively, α = 4π a ℏ 2 / m , and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (α n +4ε F /3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.
We study the attractive and repulsive two-component Fermi gas with spin imbalance in two dimensions. Using a generalized TTT-matrix approximation, we examine the thermodynamic properties of both attractive and repulsive contact interacting Fermi gases. The interaction strength, which is characterized by the bound state energy Eb=ℏ2/ma2d2E_b=\hbar^2/m a_{2d}^2Eb​=ℏ2/ma2d2​ in vacuum, can be adjusted through a Feshbach resonance. We calculate the interaction energy, compressibility and spin susceptibility of the two branches of the Fermi gas. For the repulsive branch, we also find a critical strength of interaction a2d(c)a_{2d}^{(c)}a2d(c)​ above which this metastable thermodynamic state becomes unstable. This critical value depends on the temperature and the spin imbalance (the "magnetization") of the system.
We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozi\`eres and Schmitt-Rink, the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold 133Cs^{133}\text{C}\text{s}133Cs atoms where recent measurements indicate that the gas may be sufficiently long lived to explore the many-body physics around a Feshbach resonance.