Allan Griffin

BCS-BEC crossover in a gas of Fermi atoms with a Feshbach resonance

We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.

Conserving and gapless approximations for an inhomogeneous Bose gas at finite temperatures

We derive and discuss the equations of motion for the condensate and its fluctuations for a dilute, weakly interacting Bose gas in an external potential within the self-consistent Hartree-Fock-Bogoliubov (HFB) approximation. Account is taken of the depletion of the condensate and the anomalous Bose correlations, which are important at finite temperatures. We give a critical analysis of the self-consistent HFB approximation in terms of the Hohenberg-Martin classification of approximations (conserving vs gapless) and point out that the Popov approximation to the full HFB gives a gapless single-particle spectrum at all temperatures. The Beliaev second-order approximation is discussed as the spectrum generated by functional differentiation of the HFB single-particle Green{close_quote}s function. We emphasize that the problem of determining the excitation spectrum of a Bose-condensed gas (homogeneous or inhomogeneous) is difficult because of the need to satisfy several different constraints. {copyright} {ital 1996 The American Physical Society.}

Dynamics of Trapped Bose Gases at Finite Temperatures

Starting from an approximate microscopic model of a trapped Bose-condensed gas at finite temperatures, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. The kinetic equation is a generalization of our earlier work in that collisions between the condensate and non-condensate (C12) are now included, in addition to collisions between the excited atoms as described by the Uehling–Uhlenbeck (C22) collision integral. The continuity equation for the local condensate density contains a source term Γ12which is related to the C12collision term. If we assume that the C22collision rate is sufficiently rapid to ensure that the non-condensate distribution function can be approximated by a local equilibrium Bose distribution, the kinetic equation can be used to derive hydrodynamic equations for the non-condensate. The Γ12source terms appearing in these equations play a key role in describing the equilibration of the local chemical potentials associated with the condensate and non-condensate components. We give a detailed study of these hydrodynamic equations and show how the Landau two-fluid equations emerge in the frequency domain ωτμ ≪ τμis a characteristic relaxation time associated with C12collisions. More generally, the lack of complete local equilibrium between the condensate and non-condensate is shown to give rise to a new relaxational mode which is associated with the exchange of atoms between the two components. This new mode provides an additional source of damping in the hydrodynamic regime. Our equations are consistent with the generalized Kohn theorem for the center of mass motion of the trapped gas even in the presence of collisions. Finally, we formulate a variational solution of the equations which provides a very convenient and physical way of estimating normal mode frequencies. In particular, we use relatively simple trial functions within this approach to work out some of the monopole, dipole and quadrupole oscillations for an isotropic trap.

Finite-temperature excitations in a dilute Bose-condensed gas

Abstract We present a systematic account of several approximations for the Beliaev self-energies for a uniform dilute Bose gas at finite temperature. We discuss the first-order Popov approximation, which gives a phonon velocity which vanishes as n 0 (T) , where n0(T) is the Bose condensate density. We generalize this Popov approximation using a t-matrix calculated with self-consistent ladder diagrams. This analysis shows that this t-matrix becomes very temperature-dependent and vanishes at Tc, in agreement with Bijlsma and Stoof (1995). Finally, we make a detailed study of the Beliaev–Popov (B–P) approximation for the self-energies which are second order in the t-matrix. We work out the contribution from each individual diagram and give formal expressions for the self-energies and the excitation energy spectrum valid at arbitrary temperature. Careful attention is given to all infrared-divergent contributions. We rederive the well-known T=0 result of Beliaev (1958) for long-wavelength excitations. The analogous evaluation of the finite-temperature B–P self-energies is given in the low-frequency and long-wavelength limit. The corrections to the chemical potential, excitation energy and damping are all found to be proportional to the temperature near Tc. All infrared divergent terms are shown to cancel out in physical quantities in the long-wavelength limit at arbitrary temperatures.

Finite Temperature Excitations of a Trapped Bose Gas

We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantities are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a relatively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting trapped gas in the high temperature limit. {copyright} {ital 1997} {ital The American Physical Society}

Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance

We investigate strong-coupling superfluidity in a uniform two-component gas of ultracold Fermi atoms attractively interacting via quasimolecular bosons associated with a Feshbach resonance. This interaction is tunable by the threshold energy

Dynamical Instability of a Condensate Induced by a Rotating Thermal Gas

2\ensuremath{\nu}

Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas

of the Feshbach resonance, becoming large as

Quasiparticle Kinetic Equation in a Trapped Bose Gas at Low Temperatures

2\ensuremath{\nu}

TWO-FLUID HYDRODYNAMICS FOR A TRAPPED WEAKLY INTERACTING BOSE GAS

is decreased (relative to