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arXiv:1106.0473 · Physical Review Letters

Stability of Spin-Orbit Coupled Fermi Gases with Population Imbalance

M. Iskin, A. Levent Subaşı

Published Jul 28, 2011• 107 citations
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Abstract

We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-Bose-Einstein condensate evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum-space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.

DOI
10.1103/physrevlett.107.050402

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We use the self-consistent mean-field theory to analyze the effects of Rashba-type spin-orbit coupling (SOC) on the ground-state phase diagram of population-imbalanced Fermi gases throughout the BCS-Bose-Einstein condensate evolution. We find that the SOC and population imbalance are counteracting, and that this competition tends to stabilize the uniform superfluid phase against the phase separation. However, we also show that the SOC stabilizes (destabilizes) the uniform superfluid phase against the normal phase for low (high) population imbalances. In addition, we find topological quantum phase transitions associated with the appearance of momentum-space regions with zero quasiparticle energies, and study their signatures in the momentum distribution.
We use the mean-field theory to analyze the ground-state phase diagrams of spin-orbit-coupled mass-imbalanced Fermi gases throughout the BCS-BEC evolution, including both the population-balanced and -imbalanced systems. Our calculations show that the competition between the mass and population imbalance and the Rashba-type spin-orbit coupling gives rise to very rich phase diagrams, involving normal, superfluid, and phase-separated regions. In addition, we find quantum phase transitions between the topologically trivial gapped superfluid and the nontrivial gapless superfluid phases, opening the way for the experimental observation of exotic phenomena with cold atom systems.
We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC increases.
We analyze the effects of in- and out-of-plane Zeeman fields on the BCS--Bose-Einstein condensation (BEC) evolution of a Fermi gas with equal Rashba-Dresselhaus (ERD) spin-orbit coupling (SOC). We show that the ground state of the system involves gapless superfluid phases that can be distinguished with respect to the topology of the momentum-space regions with zero excitation energy. For the BCS-like uniform superfluid phases with zero center-of-mass momentum, the zeros may correspond to one or two doubly degenerate spheres, two or four spheres, two or four concave spheroids, or one or two doubly degenerate circles, depending on the combination of Zeeman fields and SOC. Such changes in the topology signal a quantum phase transition between distinct superfluid phases and leave their signatures on some thermodynamic quantities. We also analyze the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)--like nonuniform superfluid phases with finite center-of-mass momentum and obtain an even richer phase diagram.
We investigate the ground state of a uniform two-dimensional polarized Fermi gas with Rashba spin-orbit coupling at zero temperature. We construct the phase diagram by comparing the thermodynamic potential of superfluid and phase-separated states in detail. Due to the competition between polarization and spin-orbit coupling, we find that phase-separated states in the phase diagram can be topologically trivial and nontrivial. These two topologically distinct phase-separated states can not be connected without topological phase transition. The spin-orbit coupling reduces the effect of the population imbalance. Therefore, the phase-separated states are unstable to the superfluid phases for a large spin-orbit coupling.
Here we consider both balanced and imbalanced Fermi gases throughout the BCS-BEC evolution, and we study the effects of spin-orbit coupling (SOC) on the spontaneously induced countercirculating mass currents and the associated intrinsic angular momentum via the Bogoliubov--de Gennes (BdG) formalism. In particular, we find that even a small SOC destabilizes Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) type spatially modulated superfluid phases and phase-separated states against the polarized superfluid phase. We also show that the continuum of the quasiparticle and quasihole excitation spectrum can be connected by zero, one, or two discrete branches of interface modes, depending on the number of interfaces between a topologically trivial phase and a nontrivial phase.
Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary. How to obtain the topological superfluid state by using spin–orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic. In this paper, we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin–orbit coupling at zero temperature. We find that due to the competition among mass imbalance, pairing interaction and spin–orbit coupling, there is a double-well structure in the thermodynamic potential, which affects the properties of the ground state of the system. We comprehensively give the phase diagrams of the system on the plane of spin–orbit coupling and chemical potential, and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy. This study not only points out the stable region of topological superfluid state of mass-imbalanced Fermi gas, but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.