Momentum-resolved radio-frequency spectroscopy of ultracold atomic Fermi gases in a spin-orbit coupled lattice

We investigate theoretically momentum-resolved radio-frequency (rf) spectroscopy of a noninteracting atomic Fermi gas in a spin-orbit coupled lattice. This lattice configuration has been recently created at MIT [Cheuk et al., arXiv:1205.3483] for 6Li atoms, by coupling the two hyperfine spin-states with a pair of Raman laser beams and additional rf coupling. Here, we show that momentum-resolved rf spectroscopy can measure single-particle energies and eigenstates and therefore resolve the band structure of the spin-orbit coupled lattice. In our calculations, we take into account the effects of temperatures and harmonic traps. Our predictions are to be confronted with future experiments on spin-orbit coupled Fermi gases of 40K atoms in a lattice potential.Comment: 9 pages, 8 figure

Impurity probe of topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases

We investigate theoretically non-magnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps, by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to topologically trivial Bardeen-Cooper-Schrieffer \textit{s}-wave superfluid, topological superfluid can host a mid-gap state that is bound to localized non-magnetic impurity. For strong impurity scattering, the bound state becomes universal, with nearly zero energy and a wave-function that closely follows the symmetry of that of Majorana fermions. We propose that the observation of such a universal bound state could be a useful evidence for characterizing the topolgoical nature of topological superfluids. Our prediction is applicable to an ultracold resonantly-interacting Fermi gas of $^{40}$K atoms with spin-orbit coupling confined in a two-dimensional optical lattice.Comment: 9 pages, 8 figure

Fulde-Ferrell pairing instability of a Rashba spin-orbit coupled Fermi gas

We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean-field, particularly in the strong-coupling unitary limit. We also investigate the pairing instability with increasing Rashba spin-orbit coupling, along the crossover from a Bardeen-Cooper-Schrieffer superfluid to a Bose-Einstein condensate of Rashbons (i.e., the tightly bound state of two fermions formed by strong Rashba spin-orbit couplingComment: 8 pages, 9 figure

A self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

A self-consistent theory is derived to describe the BCS-BEC crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper-pairs and ``bare'' Feshbach molecules, has been included within a self-consistent $T$-matrix approximation, beyond the Nozi\`{e}res and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature $T_c$ increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor $Z_m$ of the molecule's Green function and a complex effective mass have been determined, to characterize the fraction and lifetime of Feshbach molecules at $T_c$. Our many-body calculations of $Z_m$ agree qualitatively well with the recent measurments on the gas of $^6$Li atoms near the broad resonance at 834 Gauss. The crossover from narrow to broad resonances has also been studied.Comment: 6 papes, 6 figure

Topological superfluid in one-dimensional spin-orbit coupled atomic Fermi gases

ARC Centre of Excellence for Quantum-Atom Optics, Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122, AustraliaComment: 7 pages, 8 figures; submitted to Physical Review