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arXiv:1302.0553 · Physical Review A

Inhomogeneous Fulde-Ferrell superfluidity in spin-orbit-coupled atomic Fermi gases

Xia-Ji Liu, Hui Hu

Published May 28, 2013• 42 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.051608

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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 theoretically predict a topological matter---topological inhomogeneous Fulde-Ferrell superfluid---in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near sss-wave Feshbach resonances. The realization of such a spin-orbit-coupled Fermi system has already been demonstrated recently by using a two-photon Raman process and the extra one-dimensional confinement is easy to achieve using a tight two-dimensional optical lattice. The topological Fulde-Ferrell superfluid phase is characterized by a nonzero center-of-mass momentum and a nontrivial Berry phase. By tuning the Rabi frequency and the detuning of Raman laser beams, we show that such an exotic topological phase occupies a significant part of parameter space and therefore it could be easily observed experimentally, by using, for example, momentum-resolved and spatially resolved radio-frequency spectroscopy.
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 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.
The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.
We theoretically investigate the inhomogeneous Fulde–Ferrell (FF) superfluidity in a three-dimensional atomic Fermi gas with Rashba spin–orbit coupling near a broad Feshbach resonance. We show that within mean-field theory the FF superfluid state is always more favorable than the standard Bardeen–Cooper–Schrieffer superfluid state when an in-plane Zeeman field is applied. We present a qualitative finite-temperature phase diagram near resonance and argue that the predicted FF superfluid is observable with experimentally attainable temperatures (i.e. T ∼ 0.2 T F , where T F is the characteristic Fermi degenerate temperature).
The recent experimental realization of spin-orbit (SO) coupling for ultracold atoms opens a completely new avenue for exploring new quantum matters. In experiments, the SO coupling is implemented simultaneously with a Zeeman field. Such SO-coupled Fermi gases are predicted to support Majorana fermions with non-Abelian exchange statistics in one dimension (1D). However, as shown in recent theory and experiments for 1D spin-imbalanced Fermi gases, the Zeeman field can lead to the long-sought Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids with nonzero center-of-mass momentum Cooper pairings, in contrast to the zero center-of-mass momentum pairings in Majorana superfluids. Therefore a natural question to ask is which phase, FFLO or Majorana superfluids, will survive in SO-coupled Fermi gases in the presence of a large out-of-plane Zeeman field. In this paper, we address this question by studying the mean-field quantum phases of 1D (quasi-1D) SO-coupled fermionic cold-atom optical lattices.