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arXiv:1702.04735 · Physical Review A

Fulde-Ferrell-Larkin-Ovchinnikov state to topological superfluidity transition in bilayer spin-orbit-coupled degenerate Fermi gases

Liang‐Liang Wang, Qing Sun, W.-M. Liu, Gediminas Juzeliūnas, An-Chun Ji

Published May 24, 2017• 12 citations
arXivHTMLPDF

Abstract

Recently a scheme has been proposed for generating the two-dimensional Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al., Phys. Rev. A 93, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the Bogoliubov---de Gennes simulations with a weak harmonic trap added.

DOI
10.1103/physreva.95.053628

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Recently a scheme has been proposed for generating the two-dimensional Rashba-type spin-orbit coupling (SOC) for ultracold atomic bosons in a bilayer geometry [S.-W. Su et al., Phys. Rev. A 93, 053630 (2016)]. Here we investigate the superfluidity properties of a degenerate Fermi gas affected by the SOC in such a bilayer system. We demonstrate that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state appears in the regime of small to moderate atom-light coupling. In contrast to the ordinary SOC, the FFLO state emerges in the bilayer system without adding any external fields or spin polarization. As the atom-light coupling increases, the system can transit from the FFLO state to a topological superfluid state. These findings are also confirmed by the Bogoliubov---de Gennes simulations with a weak harmonic trap added.
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases under a Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well known that the system is either a Bardeen-Cooper-Schrieffer superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zero-energy Majorana modes. However, in the weakly interacting regime the topological superfluid prefers to stay at the trap edge, in contrast to a FFLO superfluid, which occurs near the trap center. As a result, it is unlikely to experimentally observe an inhomogeneous FFLO superfluid with topo-logical order without specifically tailoring the geometry or other parameters of the Fermi cloud.
Inspired by a recent observation of the supersolidity for bosonic atoms in a laser-assisted superlattice potential [J. Li, et. al., Nature 543, 91 (2017)], we consider an attractive two-component degenerate Fermi gas in a bilayer structure with two atomic hyperfine ground states involved. We find that the synthetic spin-orbit coupling (SOC) induced by the laser-assisted interlayer tunneling has a dramatical effect both on the two-body and many-body physics for atomic fermions. A bound molecular state appears, and the molecular dispersion can contain two minima at finite momenta even for vanishing intra- and inter-layer detunings. This is responsible for the pairing instability of the underlying attractive Fermi gas. As a result, the ground state of the system is found to be a Fulde-Ferrell-Larkin-Ovchinikov (FFLO) superfluid with a spontaneous density-modulation of the order parameter. Due to the specific pairing mechanism in this system, the FFLO state is robust and appears in a wide parameter regime with the characteristic pairing momentum on the order of the SOC strength. The unique features of the two-body and many-body state can be observed in current experiments with ultracold atoms.
The realization of spin-orbit coupling (SOC) in ultracold atoms has triggered an intensive exploring of topological superfluids in the degenerate Fermi gases based on mean-field theory, which has not yet been reported in experiments. Here, we demonstrate the topological phase transitions in the system via the numerically exact quantum Monte Carlo method. Without prior assumptions, our unbiased real-space calculation shows that spin-orbit coupling can stabilize an unconventional pairing in the weak SOC regime, in which the Fulde-Ferrell-Larkin-Ovchinnikov pairing coexists with the Bardeen-Cooper-Schrieffer pairing. Furthermore, we use the jumps in the spin polarization at the time-reversal invariant momenta to qualify the topological phase transition, where we find the critical exponent deviated from the mean-field theory. Our results pave the way for the searching of unconventional pairing and topological superfluids with degenerate Fermi gases.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in two-dimensional superconductors about 50 years ago, but so far unambiguous experimental evidence is still lacking. The recently experimentally realized spin-imbalanced Fermi gases may potentially unveil this elusive state, but they require very stringent experimental conditions. In this Rapid Communication, we show that FFLO phases may be observed even in a three-dimensional (3D) degenerate Fermi gas with spin-orbit coupling and an in-plane Zeeman field. The FFLO phase is driven by the interplay between the asymmetry of the Fermi surface and the superfluid order, instead of the interplay between magnetic and superconducting order in solid materials. The predicted FFLO phase exists in a giant parameter region, possesses a stable long-range superfluid order due to the 3D geometry, and can be observed with an experimentally already achieved temperature ($T\ensuremath{\sim}0.05{E}_{F}$), thus opening a fascinating avenue for exploring FFLO physics.
We show that the combination of spin-orbit coupling and in-plane Zeeman field in a two-dimensional degenerate Fermi gas can lead to a larger parameter region for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases than that using spin-imbalanced Fermi gases. The resulting FFLO superfluids are also more stable due to the enhanced energy difference between FFLO and conventional Bardeen-Cooper-Schrieffer (BCS) excited states. We clarify the crucial role of the symmetry of Fermi surface on the formation of finite momentum pairing. The phase diagram for FFLO superfluids is obtained in the BCS-BEC crossover region and possible experimental observations of FFLO phases are discussed.
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to (i) Fulde-Ferrell-like superfluidity and (ii) skyrmionlike polarization textures near the edges of the system. We also discuss the effects of interaction, temperature, SOC anisotropy, and Zeeman field anisotropy on the superfluid ground-state and polarization textures.