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arXiv:1408.5824 · Physical Review A

Floquet Fulde-Ferrell-Larkin-Ovchinnikov superfluids and Majorana fermions in a shaken fermionic optical lattice

Zhen Zheng, Chunlei Qu, Xu‐Bo Zou, Chuanwei Zhang

Published Jun 22, 2015• 17 citations
arXivHTMLPDF

Abstract

Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids, Cooper pairings with finite momentum, and Majorana fermions (MFs), quasiparticles with non-Abelian exchange statistics, are two topics under intensive investigation in the past several decades, but unambiguous experimental evidence for them has not been found yet. Here we show that the recent experimentally realized shaken optical lattice provides a pathway to realize FFLO superfluids and MFs. By tuning the shaking frequency and amplitude, various couplings between the $s$ and $p$ orbitals of the lattice (called the pseudospins) can be generated. We show that the combination of the $s$- and $p$-band dispersion inversion, the engineered pseudospin coupling, and the on-site attractive interaction naturally allows the observation of FFLO superfluids as well as MFs in different parameter regions.

DOI
10.1103/physreva.91.063626

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Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluids, Cooper pairings with finite momentum, and Majorana fermions (MFs), quasiparticles with non-Abelian exchange statistics, are two topics under intensive investigation in the past several decades, but unambiguous experimental evidence for them has not been found yet. Here we show that the recent experimentally realized shaken optical lattice provides a pathway to realize FFLO superfluids and MFs. By tuning the shaking frequency and amplitude, various couplings between the sss and ppp orbitals of the lattice (called the pseudospins) can be generated. We show that the combination of the sss- and ppp-band dispersion inversion, the engineered pseudospin coupling, and the on-site attractive interaction naturally allows the observation of FFLO superfluids as well as MFs in different parameter regions.
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.
Fulde-Ferrell-Larkin-Ovchinnikov Superfluids with PPP-wave Symmetry in Spinless Fermionic Optical Lattices
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose Cooper pairing hosts a non-zero center-of-mass momentum, is predicted and well studied in spin-singlet superfluids in past decades. Different from previous works that engineer FFLO superfluids in spinful cold atoms, we show that the FFLO superfluids, with ppp-wave symmetry, can emerge in a spinless environment associated with nearest-neighbor-site interactions. The novel mechanism of the FFLO superfluids lies on the split Fermi surfaces at low filling factor, which naturally gives rise to Cooper pairings with finite momentum. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. The exotic topological transition can be explained by the spontaneously-broken translational invariance of order parameters. Finally, we investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of the FFLO state, and show its possibility to be observed at finite temperature.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state with nonzero total momentum Cooper pairs in a large magnetic field, was first predicted about 50 years ago and has since become an important concept in many branches of physics. Despite an intensive search in various materials, unambiguous experimental evidence for the FFLO phase is still lacking in experiments. In this paper we show that both Fulde-Ferrell (FF) (a uniform order parameter with a plane-wave phase) and Larkin-Ovchinnikov (LO) phases (a spatially varying order parameter amplitude) can be observed using fermionic cold atoms in spin-orbit-coupled optical lattices. The increasing spin-orbit coupling enhances the FF phase over the LO phase. The coexistence of superfluid and magnetic orders is also found in the normal BCS phase. The pairing mechanism for different phases is understood by visualizing superfluid pairing densities in different spin-orbit bands. The possibility of observing similar physics using spin-orbit-coupled superconducting ultrathin films is also discussed.
Abstract : Majorana fermions (MFs) are quantum particles that are their own anti-particles, and satisfy non-Abelian exchange statistics. The latter is the key for their potential use in fault-tolerant topological quantum computation. In this project, we proposed to investigate the possibility of realizing MFs in much more physically robust s-wave superfluids by utilizing two additional components: spin-orbit coupling and Zeeman fields. In the last year grant period, we have made the following important achievements: 1)We found a large BKT transition temperature due to large effective superfluid densities in a spin-orbit coupled Fulde-Ferrell superfluid, making it possible to observe 2D Fulde-Ferrell superfluids at finite temperature;2) Collaborated with Ian Speilmans group, we demonstrated the tunable spin-orbit coupling through the modulation of the Raman coupling strength in experiments; 3)We found that the spin-orbit coupled Fulde-Ferrell superfluids can support Weyl points or rings with nontrivial topological structures; 4)We proposed and experimentally realized a new type of tunable spin-orbit coupling using optical lattice band pseudospins. The research leads to 23 peer-reviewed publications, including 4 in Physical Review Letters and 1 in Nature Communications.
We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.
Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around [ π , π ] evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.