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arXiv:1504.05047 · Physical Review A

Three-component Fulde-Ferrell superfluids in a two-dimensional Fermi gas with spin-orbit coupling

Fang Qin, Fan Wu, Wei Zhang, Wei Yi, Guang‐Can Guo

Published Aug 4, 2015• 8 citations
arXivHTMLPDF

Abstract

We investigate the pairing physics of a three-component spin-orbit coupled Fermi gas in two spatial dimensions. The three atomic hyperfine states of the system are coupled by the recently realized synthetic spin-orbit coupling (SOC), which mixes different hyperfine states into helicity branches in a momentum-dependent manner. As a consequence, the interplay of spin-orbit coupling and the hyperfine-state-dependent interactions leads to the emergence of Fulde-Ferrell (FF) pairing states with finite center-of-mass momenta even in the absence of the Fermi-surface asymmetry that is usually mandatory to stabilize an SOC-induced FF state. We show that, for different combinations of spin-dependent interactions, the ground state of the system can either be the conventional Bardeen-Cooper-Schrieffer pairing state with zero center-of-mass momentum or be the FF pairing states. Of particular interest here is the existence of a three-component FF pairing state in which every two out of the three components form FF pairing. We map out the phase diagram of the system and characterize the properties of the three-component FF state, such as the order parameters, the gapless contours, and the momentum distributions. Based on these results, we discuss possible experimental detection schemes for the interesting pairing states in the system.

DOI
10.1103/physreva.92.023604

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We investigate the pairing physics of a three-component spin-orbit coupled Fermi gas in two spatial dimensions. The three atomic hyperfine states of the system are coupled by the recently realized synthetic spin-orbit coupling (SOC), which mixes different hyperfine states into helicity branches in a momentum-dependent manner. As a consequence, the interplay of spin-orbit coupling and the hyperfine-state-dependent interactions leads to the emergence of Fulde-Ferrell (FF) pairing states with finite center-of-mass momenta even in the absence of the Fermi-surface asymmetry that is usually mandatory to stabilize an SOC-induced FF state. We show that, for different combinations of spin-dependent interactions, the ground state of the system can either be the conventional Bardeen-Cooper-Schrieffer pairing state with zero center-of-mass momentum or be the FF pairing states. Of particular interest here is the existence of a three-component FF pairing state in which every two out of the three components form FF pairing. We map out the phase diagram of the system and characterize the properties of the three-component FF state, such as the order parameters, the gapless contours, and the momentum distributions. Based on these results, we discuss possible experimental detection schemes for the interesting pairing states in the system.
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 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.
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.
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.
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 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.