The unitary gas in an isotropic harmonic trap: symmetry properties and applications

We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, and relations between the moments of the trapping potential energy and the moments of the total energy

Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential

A unitary quantum gas is a gas of quantum particles with a binary interaction of infinite scattering length and negligible range. It has been produced in recent experiments with gases of fermionic atoms by means of a Feshbach resonance. Using the Fermi pseudo-potential model for the atomic interaction, we show that the time evolution of such a gas in an isotropic three-dimensional time dependent harmonic trap is exactly given by a gauge and scaling transform.Comment: submitted 23 March 200

Creation and detection of a mesoscopic gas in a non-local quantum superposition

We investigate the scattering of a quantum matter wave soliton on a barrier in a one dimensional geometry and we show that it can lead to mesoscopic Schr\"odinger cat states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition and we discuss in details the experimental feasibility.Comment: 4 pages, 1 figur

Energy, decay rate, and effective masses for a moving polaron in a Fermi sea: Explicit results in the weakly attractive limit

We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $g\to0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy \Delta E(\KK) of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses m_\parallel^*(\KK), m_\perp^*(\KK), as functions of the impurity wave vector \KK. Depending on the modulus of \KK and on the impurity-to-fermion mass ratio $M/m$ we identify four regions separated by singularities in derivatives with respect to \KK of the second-order term of \Delta E(\KK), and we discuss the physical origin of these regions. Remarkably, the second-order term of m_\parallel^*(\KK) presents points of non-differentiability, replaced by a logarithmic divergence for $M=m$, when \KK is on the Fermi surface of the fermions. We also discuss the third-order contribution and relevance for cold atom experiments.Comment: 6 pages, 4 figures; final version, including a finite temperature calculatio

One particle in a box: the simplest model for a Fermigas in the unitary limit

We consider a single quantum particle in a spherical box interacting with a fixed scatterer at the center, to construct a model of a degenerate atomic Fermi gas close to a Feshbach resonance. One of the key predictions of the model is the existence of two branches for the macroscopic state of the gas, as a function of the magnetic field controlling the value of the scattering length.This model is able to draw a qualitative picture of all the different features recently observed in a degenerate atomic Fermi gas close to the resonance, even in the unitary limit