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arXiv:1212.0420 · Physical Review A

Normal-state properties of spin-orbit-coupled Fermi gases in the upper branch of the energy spectrum

Xiao-Lu Yu, Shang-Shun Zhang, Wu‐Ming Liu

Published Apr 29, 2013• 3 citations
arXivHTMLPDF

Abstract

We investigate normal-state properties of spin-orbit-coupled Fermi gases with repulsive $s$-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 ${m}_{s}^{*}$, and the Green's function renormalization factor ${Z}_{s}$ 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 $s$ 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.

DOI
10.1103/physreva.87.043633

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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 \ensuremathτs{\ensuremath{\tau}}_{s}\ensuremathτs​, 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 derive analytical expressions for the quasiparticle lifetime $\ensuremath{\tau}$, the effective mass m∗{m}^{*}m∗, and the Green's function renormalization factor ZZZ for a two-dimensional Fermi liquid with electron-electron interaction in the presence of the Rashba spin-orbit interaction. We find that the modifications are independent of the Rashba band index $\ensuremath{\rho}$, and occur in second order of the spin-orbit coupling $\ensuremath{\alpha}$. In the derivation of these results, we also discuss the screening of the Coulomb interaction, as well as the susceptibility and the self-energy in small $\ensuremath{\alpha}$.
We investigate the collective modes in the spin-orbit-coupled Fermi gas with repulsive sss-wave interaction. The interplay between spin-orbit coupling and atom-atom interactions plays the crucial role in the collective behaviors of Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit-coupled Fermi gas has strongly correlated spin and density excitations. Within the scheme of random-phase approximation, we classify collective modes based on the symmetry group and determine their properties via the poles of corresponding correlation functions. Besides, the particle-hole continuum is obtained, where the imaginary part of these correlation functions becomes nonvanishing. We also propose an experimental protocol for detecting these collective modes and discuss corresponding experimental signatures in the ultracold Fermi gases experiment.
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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.
We briefly review recent progress on ultracold atomic Fermi gases with different types of synthetic spin-orbit coupling, including the one-dimensional (1D) equal weight Rashba-Dresselhaus and two-dimensional (2D) Rasbha spin-orbit couplings. Theoretically, we show how the single-body, two-body and many-body properties of Fermi gases are dramatically changed by spin-orbit coupling. In particular, the interplay between spin-orbit coupling and interatomic interaction may lead to several long-sought exotic superfluid phases at low temperatures, such as anisotropic superfluid, topological superfluid and inhomogeneous superfluid. Experimentally, only the first type - equal weight combination of Rasbha and Dresselhaus spin-orbit couplings - has been realized very recently using a two-photon Raman process. We show how to characterize a normal spin-orbit coupled atomic Fermi gas in both non-interacting and strongly-interacting limits, using particularly momentum-resolved radio-frequency spectroscopy. The experimental demonstration of a strongly-interacting spin-orbit coupled Fermi gas opens a promising way to observe various exotic superfluid phases in the near future.
Motivated by the remarkable experimental control of synthetic gauge fields in ultracold atomic systems, we investigate the effect of an artificial Rashba spin-orbit coupling on the spin polarization of a two-dimensional repulsive Fermi gas. By using a variational many-body wave function, based on a suitable spinorial structure, we find that the polarization properties of the system are indeed controlled by the interplay between spin-orbit coupling and repulsive interaction. In particular, two main effects are found: (1) The Rashba coupling determines a gradual increase of the degree of polarization beyond the critical repulsive interaction strength, at variance with conventional two-dimensional Stoner instability. (2) The critical interaction strength, above which finite polarization is developed, shows a dependence on the Rashba coupling, i.e., it is enhanced in case the Rashba coupling exceeds a critical value. A simple analytic expression for the critical interaction strength is further derived in the context of our variational formulation, which allows for a straightforward and insightful analysis of the present problem.