Three-component topological superfluid in one-dimensional Fermi gases with spin-orbit coupling (original) (raw)
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Topological superfluid in one-dimensional spin-orbit-coupled atomic Fermi gases
Physical Review A, 2012
We investigate theoretically the prospect of realizing a topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases under Zeeman field in harmonic traps. In the absence of spin-orbit coupling, it is well-known that the system is either a Bardeen-Cooper-Schrieffer (BCS) superfluid or an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. Here we show that with spin-orbit coupling it could be driven into a topological superfluid, which supports zeroenergy Majorana modes. However, in the weakly interacting regime the spin-orbit coupling does not favor the spatially oscillating FFLO order parameter. As a result, it seems difficult to create an inhomogeneous topological superfluid in current cold-atom experiments.
Chinese Physics B, 2015
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 phases with an imperfect Rashba spin-orbit coupling are also studied.
Physical Review A, 2013
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel onedimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin orbit coupling (SOC), and an s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T = 0) Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes, and show that the T = 0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with non-zero center of mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center of mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the 3D and the 1D system and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one-dimensional. We also find evidence of the existence of a Zeeman tuned topological quantum phase transition (TQPT) within the FFLO phase itself and for large values of the Zeeman field and small SOC the TQPT gives rise to a topologically distinct FFLO phase.
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel onedimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field, Rashba type spin orbit coupling (SOC), and an s-wave attractive interaction, while the radial motion is tightly confined. We solve the zero-temperature (T = 0) Bogoliubov-de Gennes (BdG) equations for the quasi-1D Fermi gas with the dispersion modified by tunneling between the tubes, and show that the T = 0 phase diagram hosts the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase with non-zero center of mass momentum Cooper pairs for small values of the SOC while for larger values of the SOC and high Zeeman fields the uniform superfluid phase with zero center of mass momentum Cooper pairs has an instability towards the topological uniform superfluid phase with Majorana fermions at the tube ends. Also, we show that tuning the two-dimensional optical lattice strength in this model allows one to explore the crossover behaviors of the phases during the transition between the 3D and the 1D system and in general the FFLO (for small SOC) and the topological uniform superfluid phase (for large SOC) are favored as the system becomes more one-dimensional. We also find evidence of the existence of a Zeeman tuned topological quantum phase transition (TQPT) within the FFLO phase itself and for large values of the Zeeman field and small SOC the TQPT gives rise to a topologically distinct FFLO phase.
Topological Fulde-Ferrell superfluid in spin-orbit-coupled atomic Fermi gases
Physical Review a, 2013
We theoretically predict a new topological matter -topological inhomogeneous Fulde-Ferrell superfluid -in one-dimensional atomic Fermi gases with equal Rashba and Dresselhaus spin-orbit coupling near s-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 non-trivial 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.
Gapless Topological Fulde-Ferrell Superfluidity in Spin-Orbit Coupled Fermi Gases
Physical Review Letters, 2014
Topological superfluids usually refer to a superfluid state which is gapped in the bulk but metallic at the boundary. Here we report that a gapless, topologically non-trivial superfluid with inhomogeneous Fulde-Ferrell pairing order parameter can emerge in a two-dimensional spin-orbit coupled Fermi gas, in the presence of both in-plane and out-of-plane Zeeman fields. The Fulde-Ferrell pairing -induced by the spin-orbit coupling and in-plane Zeeman field -is responsible for this gapless feature. The existence of such an exotic superfluid is not restricted to the pure Rashba or Dresselhaus spin-orbit coupling. However, its phase space becomes extremely narrow when the spin-orbit coupling is tuned towards having an equal weight in Rashba and Dresselhaus components.
This paper explores the dynamic of a 2D topological superfluid Fermi (TSF) gas with spin orbit coupling (SOC) in nonadiabatic scenario. By examining the system's energy spectrum in linear time dependent magnetic field, we established a connection between the multi-level Landau-Zener-Majorana-Stückelberg (LZMS) model of couple qubits and the 2D-TSF. The LZMS transition probabilities are derived using the density-matrix formalism (DMF) and the LZMS survival probabilities are determined using the Brundobler-Elser (B-E) formula. The presence of SOC introduces interesting phenomena such as the emergence of topological Fermi-arcs in the system, allowing the creation and manipulation of exotic quantum states (Majorana fermions) to
BCS-BEC Crossover and Topological Phase Transition in 3D Spin-Orbit Coupled Degenerate Fermi Gases
Physical Review Letters, 2011
We investigate the BCS-BEC crossover in three dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a non-topological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two topologically protected Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum resolved photoemission spectroscopy.
Physical Review A, 2013
We discuss the thermodynamic signatures for the topological phase transitions into Majorana and Weyl superfluid phases in ultracold Fermi gases in two and three dimensions in the presence of Rashba spin-orbit coupling and a Zeeman field. We analyze the thermodynamic properties exhibiting the distinct nature of the topological phase transitions linked with the Majorana fermions (2D Fermi gas) and Weyl fermions (3D Fermi gas) which can be observed experimentally, including pressure, chemical potential, isothermal compressibility, entropy, and specific heat, as a function of the interaction and the Zeeman field at both zero and finite temperatures. We conclude that among the various thermodynamic quantities, the isothermal compressibility and the chemical potential as a function of the artificial Zeeman field have the strongest signatures of the topological transitions in both two and three dimensions.
Topological States in a one-dimensional fermi gas with attractive interaction
Physical review letters, 2015
We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field, and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons are all doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero. The effect is expected to...