Vortices in Superfluid Fermi Gases through the BEC to BCS Crossover

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: $k_{F}^{-1}$ and the coherence length $\xi$, while only variation on the scale of $\xi$ is seen away from the BCS limit. The circulating current has a peak value $j_{max}$ which is a non-monotonic function of $1/k_F a_s$ implying a maximum critical velocity $\sim v_F$ at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.Comment: 4 Pages, 4 Figure

BCS-BEC crossover on the two-dimensional honeycomb lattice

The attractive Hubbard model on the honeycomb lattice exhibits, at half-filling, a quantum critical point (QCP) between a semimetal with massless Dirac fermions and an s-wave superconductor (SC). We study the BCS-BEC crossover in this model away from half-filling at zero temperature and show that the appropriately defined crossover line (in the interaction-density plane) passes through the QCP at half-filling. For a range of densities around half-filling, the ``underlying Fermi surface'' of the SC, defined as the momentum space locus of minimum energy quasiparticle excitations, encloses an area which evolves nonmonotonically with interactions. We also study fluctuations in the SC and the semimetal, and show the emergence of an undamped Leggett mode deep in the SC. We consider possible implications for experiments on ultracold atoms and high temperature SCs.Comment: Revised - added section on the Fermi surface evolution, corrected error in superfluid density, added possible implications for cuprate

Shear viscosity and damping for a Fermi gas in the unitarity limit

The shear viscosity of a two-component Fermi gas in the normal phase is calculated as a function of temperature in the unitarity limit, taking into account strong-coupling effects that give rise to a pseudogap in the spectral density for single-particle excitations. The results indicate that recent measurements of the damping of collective modes in trapped atomic clouds can be understood in terms of hydrodynamics, with a decay rate given by the viscosity integrated over an effective volume of the cloud.Comment: 7 pages, 3 figures. Discussion significantly extended. Appendix added. To appear in PR

Electron Self-Energy of High Temperature Superconductors as Revealed by Angle Resolved Photoemission

In this paper, we review some of the work our group has done in the past few years to obtain the electron self-energy of high temperature superconductors by analysis of angle-resolved photoemission data. We focus on three examples which have revealed: (1) a d-wave superconducting gap, (2) a collective mode in the superconducting state, and (3) pairing correlations in the pseudogap phase. In each case, although a novel result is obtained which captures the essense of the data, the conventional physics used leads to an incomplete picture. This indicates that new physics needs to be developed to obtain a proper understanding of these materials.Comment: 5 pages, revtex, 3 encapsulated postscript figures, SNS97 proceeding

Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling

We study the short-range correlation strength of three dimensional spin half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high temperature limit, we derive the expression for the second order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second order virial expansion in the limit that the spin-orbit coupling constants are small, and find that the correlation strength between the fermions increases as the forth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.Comment: 7 pages, 4 figure

Collective oscillations of a trapped Fermi gas near a Feshbach resonance

The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.Comment: 3 pages, including 1 figur

Collective modes of trapped gases at the BEC-BCS crossover

The collective mode frequencies in isotropic and deformed traps are calculated for general polytropic equation of states, $P\propto n^{\gamma+1}$, and expressed in terms of $\gamma$ and the trap geometry. For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the effective power $\gamma\simeq0.5-1.3$ is calculated from Jastrow type wave-function ans\"atze, and from the crossover model of Leggett. The resulting mode frequencies are calculated for these phases around the BCS-BEC crossover.Comment: Revised version to be published in PR

Size-shrinking of deuterons in very dilute superfluid nuclear matter

It is shown within the strong-coupling BCS approach that, starting from the zero-density limit of superfluid nuclear matter, with increasing density deuterons first shrink before they start expanding.Comment: 2 pages, Latex, 1 figure included, submitted to Phys. Rev.

Quantum phase transitions in the Fermi-Bose Hubbard model

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram.Comment: 4 pages, 3 figure