Threshold of molecular bound state and BCS transition in dense ultracold Fermi gases with Feshbach resonance

We consider the normal state of a dense ultracold atomic Fermi gas in the presence of a Feshbach resonance. We study the BCS and the molecular instabilities and their interplay, within the framework of a recent many-body approach. We find surprisingly that, in the temperature domain where the BCS phase is present, there is a non zero lower bound for the binding energy of molecules at rest. This could give an experimental mean to show the existence of the BCS phase without observing it directly.Comment: 5 pages, revtex, 1 figur

The 3-body Coulomb problem

We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived from the consideration of the scattering properties of the system. In particular this makes full use of the solution of the two-body problem, the interaction appearing only through the corresponding known T-matrix. In the case of the Coulomb potential we make use of a very convenient expression for the T-matrix obtained by Schwinger. As a check we apply this approach to the well-known problem of the Helium atom ground state and obtain a perfect numerical agreement with the known result for the ground state energy. The wave function is directly obtained from the corresponding solution. We expect our method to be in particular quite useful for the trion problem in semiconductors.Comment: 19 pages, 8 figure

Optical signatures of a fully dark exciton condensate

We propose optical means to reveal the presence of a dark exciton condensate that does not yield any photoluminescence at all. We show that (i) the dark exciton density can be obtained from the blueshift of the excitonic absorption line induced by dark excitons; (ii) the polarization of the dark condensate can be deduced from the blueshift dependence on probe photon polarization and also from Faraday effect, linearly polarized dark excitons leaving unaffected the polarization plane of an unabsorbed photon beam. These effects result from carrier exchanges between dark and bright excitons.Comment: 5 pages, 4 figure

Effects of fermion exchanges on the polarization of exciton condensates

Exchange processes are responsible for the stability of elementary boson condensates with respect to their possible fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom are ignored. We here show that their inclusion can produce a "spin-fragmentation" of a condensate of dark excitons, i.e., an unpolarized condensate with equal amount of dark excitons with spins (+2) and (-2). Quite surprisingly, for spatially indirect excitons of semiconductor bilayers, we predict that the condensate polarization can switch from unpolarized to fully polarized, depending on the distance between the layers confining electrons and holes. Remarkably, the threshold distance associated to this switching lies in the regime where experiments are nowadays carried out.Comment: 5 pages, 1 figur

Comment on "Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons [Phys. Rev. A 79, 033610 (2009)]"

Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they deal with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial step is erroneous, contradicting both physical intuition and known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.Comment: Submitted to Phys. Rev. A on 30 April 200