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

Topological Fulde-Ferrell superfluid in spin-orbit coupled atomic Fermi gases

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.Comment: 5 pages, 4 figure

Critical temperature of a Rashba spin-orbit coupled Bose gas in harmonic traps

We investigate theoretically Bose-Einstein condensation of an ideal, trapped Bose gas in the presence of Rashba spin-orbit coupling. Analytic results for the critical temperature and condensate fraction are derived, based on a semi-classical approximation to the single-particle energy spectrum and density of states, and are compared with exact results obtained by explicitly summing discrete energy levels for small number of particles. We find a significant decrease of the critical temperature and of the condensate fraction due to a finite spin-orbit coupling. For large coupling strength and finite number of particles $N$, the critical temperature scales as $N^{2/5}$ and $N^{2/3}$ in three and two dimensions, respectively, contrasted to the predictions of $N^{1/3}$ and $N^{1/2}$ in the absence of spin-orbit coupling. Finite size corrections in three dimensions are also discussed.Comment: 9 pages and 8 figures; published version in Physical Review

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

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 centre-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 (i.e., $0.05T_{F}$, where $T_{F}$ is the Fermi temperature), the FF superfluid state dominates the phase diagram, in sharp contrast to the conventional case without spin-orbit coupling. We show that the finite centre-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.Comment: 5 pages and 4 figures; Please see also arXiv:1211.1831 by V. B. Shenoy for relevant discussion