We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean field, particularly in the strong-coupling unitary limit. We also investigate the pairing instability with increasing Rashba spin-orbit coupling, along the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate of rashbons (i.e., the tightly bound state of two fermions formed by strong Rashba spin-orbit coupling).
We theoretically investigate a three-dimensional Fermi gas with Rashba spin–orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde–Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space (i.e., massless Dirac fermions). The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin–orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin–orbit coupling is also studied.
We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit-coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF, and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the
x direction, the tensor component along the
y direction
ns,yy is generally larger than
ns,xx in most parameter space. At zero temperature, there is always a discontinuity jump in
ns,xx as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit-coupling strength, interatomic interaction strength, and in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of
0.1TF, where
TF is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.
Inhomogeneous superfluidity lies at the heart of many intriguing phenomena in quantum physics. It is believed to play a central role in unconventional organic or heavy-fermion superconductors, chiral quark matter, and neutron star glitches. However, so far even the simplest form of inhomogeneous superfluidity, the Fulde-Ferrell (FF) pairing state with a single center-of-mass momentum, is not conclusively observed due to the intrinsic complexibility of any realistic Fermi systems in nature. Here we theoretically predict that the controlled setting of ultracold fermionic atoms with synthetic spin-orbit coupling induced by a two-photon Raman process, demonstrated recently in cold-atom laboratories, provides a promising route to realize the long-sought FF superfluidity. At experimentally accessible low temperatures, the FF superfluid state dominates the phase diagram, in sharp contrast to the conventional case without spin-orbit coupling. We show that the finite center-of-mass momentum carried by Cooper pairs is directly measurable via momentum-resolved radio-frequency spectroscopy. Our work opens the way to direct observation and characterization of inhomogeneous superfluidity.
Topological Fermi superfluids have played the central role in various fields of physics. However, all previous studies focus on the cases where Cooper pairs have zero center-of-mass momenta (i.e., normal superfluids). The topology of Fulde–Ferrell (FF) superfluids with nonzero momentum pairings have never been explored until recent findings that FF superfluids in a spin–orbit (SO) coupled Fermi gas can accommodate Majorana fermions in real space in low dimensions and Weyl fermions in momentum space in three dimension. In this review, we first discuss the mechanism of pairings in SO coupled Fermi gases in optical lattices subject to Zeeman fields, showing that SO coupling as well as Zeeman fields enhance FF states while suppress Larkin–Ovchinnikov states. We then present the low temperature phase diagram including both FF superfluids and topological FF superfluids phases in both two dimension and three dimension. In one dimension, Majorana fermions as well as phase dependent order parameter are visualized. In three dimension, we show the properties of Weyl fermions in momentum space such as anisotropic linear dispersion, Fermi arch, and gaplessness away from k⊥ = 0. Finally, we discuss some possible methods to probe FF superfluids and topological FF superfluids in cold atom systems.
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.