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

On the renormalization of quasi parton distribution

Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasi parton distributions. Like a light-cone parton distribution, a quasi parton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of non-local operators in general is not well understood. However, in the case of quasi quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizable by the quark wave function renormalization in the axial gauge. We first show that the renormalization of the self energy correction to the quasi quark distribution is equivalent to that of the heavy-light quark vector current in heavy quark effective theory at one-loop order. Assuming this equivalence at two-loop order, we then show that the multiplicative renormalizability of the quasi quark distribution is true at two-loop order.Comment: 14 pages, 4 figure

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