Scientific Report - BEC

Fermionic superfluidity and BCS-BEC crossover 14FERMIONIC SUPERFLUIDITY AND BCS-BECCROSSOVERAn impressive amount of experimental and theoretical work has characterized theinvestigation of ultra cold Fermi gases in the last few years. The Trento team hascontributed significantly to the field. In particular a significant effort has been devotedto writing a long review paper [1], published in the journal Reviews of Modern Physics.In this section we report a selection of significant achievements concerning the study ofthe elementary excitations along the crossover and of the single-particle excitations bystimulated Raman spectroscopy [2]. Other contributions of the Trento team concern ofthe study trapped Fermi gases with unequal masses [3], the study of the fluctuations ofthe number of particle both in Bose and Fermi gases [4] and the study of the Josephsonrelations along the crossover [5]. The following sections will be instead devoted to theeffects of polarization on fermionic superfluidity and to the problem of rotating Fermigases and to the implementation of Monte Carlo approaches.Collective oscillations and Landau critical velocityIn [6] we have investigated the behaviour of the collective excitations of a superfluidFermi gas along the BEC-BCS crossover and their interplay with the single-particleexcitations in the determination of Landau’s critical velocity. The calculation wascarried out using a natural generalization of the Bogoliubov de-Gennes equations whichaccounts for the self consistent treatment of the collective oscillations. Actually theBdG equations, in their traditional form, account for the description of the singleparticleexcitations (including the pairing gap), but not for the phonon mode (theso called Bogoliubov-Anderson mode). The description of this latter mode requiresthe development of a kinetic theory which was implemented in our work along thewhole BEC-BCS crossover. Special attention has been devoted in this paper to thecalculation of the Landau’s critical velocity whose behaviour is very different in thevarious regimes. In the molecular BEC regime the phonon mode provides the propermechanism for Landau’s instability in the presence of a moving frame, while singleparticle excitations are not important, being located at very high energies. In the BECregime the sound velocity vanishes with the square root of the scattering length, andhence gives rise to small values of the critical velocity. In the opposite BCS regime ofnegative scattering lengths the relevant excitations are instead of single-particle natureand are characterized by the pairing gap whose value becomes smaller and smaller asthe scattering length tends to zero. One then expects that the critical velocity will take