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

Collective mode evidence of high-spin bosonization in a trapped one-dimensional atomic Fermi gas with tunable spin

We calculate the frequency of collective modes of a one-dimensional repulsively interacting Fermi gas with high-spin symmetry confined in harmonic traps at zero temperature. This is a system realizable with fermionic alkaline-earth-metal atoms such as $^{173}$Yb, which displays an exact SU($\kappa$) spin symmetry with $\kappa\geqslant2$ and behaves like a spinless interacting Bose gas in the limit of infinite spin components $\kappa\rightarrow\infty$, namely high-spin bosonization. We solve the homogeneous equation of state of the high-spin Fermi system by using Bethe ansatz technique and obtain the density distribution in harmonic traps based on local density approximation. The frequency of collective modes is calculated by exactly solving the zero-temperature hydrodynamic equation. In the limit of large number of spin-components, we show that the mode frequency of the system approaches to that of a one-dimensional spinless interacting Bose gas, as a result of high-spin bosonization. Our prediction of collective modes is in excellent agreement with a very recent measurement for a Fermi gas of $^{173}$Yb atoms with tunable spin confined in a two-dimensional tight optical lattice.Comment: 11 pages, 8 figure

First and second sound in a two-dimensional dilute Bose gas across the Berezinskii-Kosterlitz-Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau's two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii-Kosterlitz-Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. Our predictions can be readily examined in current experimental setups for 2D dilute Bose gases.Comment: 5 pages, 4 figure