Comment on "Collective excitations of a degenerate gas at the BEC-BCS crossover"

Very recent experiments have studied for the first time collective excitations of an ultracold $^6$Li gas covering in particular the BEC-BCS crossover domain. We point out that the results for the axial mode, through hydrodynamics, give direct access to the (3D) equation of state of the strongly interacting gas, mostly near the unitarity limit. On the other hand the surprising results found for the radial mode are actually not necessarily in contradiction with the expectations from superfluid hydrodynamics.Comment: 2 pages, 1 figur

Analytical theory of the dressed bound state in highly polarized Fermi gases

We present an analytical treatment of a single \down atom within a Fermi sea of \up atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte-Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results when \up and \down atoms have different masses, which is of interest for experiments in progress.Comment: 5 pages, 3 figure

Few vs many-body physics of an impurity immersed in a superfluid of spin 1/2 attractive fermions

In this article we investigate the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions. For resonant interactions, we first relate the stability diagram of dimer and trimer states to the three-body problem for an impurity interacting with a pair of fermions. Then we calculate the beyond-mean-field corrections to the energy of a weakly interacting impurity. We show that these corrections are divergent and have to be regularized by properly accounting for three-body physics in the problem

Momentum distribution of a dilute unitary Bose gas with three-body losses

Using Boltzmann's equation, we study the effect of three-body losses on the momentum distribution of a homogeneous unitary Bose gas in the dilute limit where quantum correlations are negligible. We calculate the momentum distribution of the gas and show that inelastic collisions are quantitatively as important as a second order virial correction.Comment: 4 pages + supplemental materia

Collective modes of a trapped Lieb-Liniger gas: a hydrodynamic approach

We consider a trapped repulsive one-dimensional (1D) Bose gas at very low temperature. In order to study the collective modes of this strongly interacting system, we use a hydrodynamic approach, where the gas is locally described by the Lieb-Liniger model of bosons interacting via a repulsive delta potential. Solving the corresponding linearized hydrodynamic equations, we obtain the collective modes and concentrate more specifically on the lowest compressional mode. This is done by finding models, approaching very closely the exact equation of stae of the gas, for which the linearized hydrodynamic equations are exactly solvable. Results are in excellent agreement with those of the sum rule approach of Menotti and Stringari.Comment: Proceedings of the Laser Physics Workshop held in Hamburg (August 2003), Seminar on the Physics of Cold Trapped Atom

Hydrodynamic spectrum of a superfluid in an elongated trap

--In this article we study the hydrodynamic spectrum of a superfluid confined in a cylindrical trap. We show that the dispersion relation $\omega$(q) of the phonon branch scales like \sqrt q at large q, leading to a vanishingly small superfluid critical velocity. In practice the critical velocity is set by the breakdown of the hydrodynamic approximation. For a broad class of superfluids, this entails a reduction of the critical velocity by a factor ($\omega$ $\perp$ /\"i1/2c) 1/3 with respect to the free-space prediction (here $\omega$ $\perp$ is the trapping frequency and \"i1/2c the chemical potential of the cloud)