We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.
We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for an arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological superfluid state and the normal state for a highly polarized Fermi gas in the thermodynamic limit. As polarization in a Fermi gas with SOC is induced by the effective Zeeman field, we also discuss the influences of the effective Zeeman field on the ground state of the system. Our findings may be tested directly in future experiments.
We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few fermionic impurities are immersed in a noninteracting two-component Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Because of the interplay of SOC and the spin-selective interaction, the molecular state intrinsically acquires a nonzero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular states with different center-of-mass momenta, which corresponds to a first-order transition between FF phases in the thermodynamic limit. As the interaction strength is tuned, a polaron-molecule transition occurs in the highly imbalanced system, where the boundary varies nonmonotonically with SOC parameters and gives rise to the reentrance of polaron states. The rich physics in this system can be probed using existing experimental techniques.
We study the phase diagram of a two-dimensional ultracold Fermi gas with the synthetic spin-orbit coupling (SOC) that has recently been realized at the National Institute of Standards and Technology (NIST). Because of the coexistence of anisotropic SOC and effective Zeeman fields in the NIST scheme, the system shows a rich structure of phase separation involving exotic gapless superfluid states and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states with different center-of-mass momenta. In particular, we characterize the stability region of FFLO states and demonstrate their unique features under SOC. We then show that the effective transverse Zeeman field in the NIST scheme can qualitatively change the landscape of the thermodynamic potential which leads to intriguing effects such as the disappearance of pairing instability, the competition between different FFLO states, and the stabilization of a fully gapped FFLO state. These interesting features may be probed, for example, by measuring the in situ density profiles or by the momentum-resolved radio-frequency spectroscopy.
We investigate properties of exotic pairing states in a three-dimensional Fermi gas with three-dimensional spin-orbit coupling and an effective Zeeman field. The interplay of spin-orbit coupling, effective Zeeman field, and pairing can lead to first-order phase transitions between different phases, and to interesting nodal superfluid states with gapless surfaces in the momentum space. We then demonstrate that pairing states with zero center-of-mass momentum are unstable against Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, with a finite center-of-mass momentum opposite to the direction of the effective Zeeman field. Unlike conventional FFLO states, these FFLO states are induced by the coexistence of spin-orbit coupling and Fermi surface deformation, and have intriguing features like first-order transitions between different FFLO states, nodal FFLO states with gapless surfaces in momentum space, and exotic fully gapped FFLO states. With the recent theoretical proposals for realizing three-dimensional spin-orbit coupling in ultracold atomic gases, our work is helpful for future experimental studies and provides valuable information for the general understanding of pairing physics in spin-orbit-coupled fermionic systems.
We investigate the highly polarized limit of a two-dimensional Fermi gas, where we effectively have a single spin-down impurity atom immersed in a spin-up Fermi sea. By constructing variational wave functions for the impurity, we map out the ground state phase diagram as a function of mass ratio ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ and interaction strength. In particular, we determine when it is favorable for the dressed impurity (polaron) to bind particles from the Fermi sea to form a dimer, trimer, or even larger clusters. Similarly to three dimensions, we find that the Fermi sea favors the trimer state so that it exists for ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ less than the critical mass ratio for trimer formation in the vacuum. We also find a region where dimers have finite momentum in the ground state, a scenario that corresponds to the Fulde-Ferrell-Larkin-Ovchinnikov superfluid state in the limit of large spin imbalance. For equal masses (${m}_{\ensuremath{\uparrow}}={m}_{\ensuremath{\downarrow}}$), we compute rigorous bounds on the polaron-dimer transition, and we show that the polaron energy and residue is well captured by the variational approach, with the former quantity being in good agreement with experiment. When there is a finite density of impurities, we find that this polaron-dimer transition is preempted by a first-order superfluid-normal transition at zero temperature, but it remains an open question what happens at finite temperature.
We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling (SOC) coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spin-selected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass (c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.
We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.