Abstract

The experimental realization of ultracold quantum gases triggered a new theoretical interest in basic many body systems, which have not been realized in nature previously. One example of a fundamental many body problem that is now experimentally accessible for the first time is the so called BCS -BEC crossover from weakly bound Cooper pairs to a Bose-Einstein condensate of strongly bound molecules in attractively interacting, two-component Fermi gases. In this talk I will give a brief introduction to the BCS -BEC crossover, show recent theoretical results on single particle spectral functions and discuss the controversial issue of a possible pseudogap behavior in the strongly interacting system above Tc. Moreover, I will show how a slight generalization of this model to a situation with a population imbalance between the two Fermionic species gives rise to a rich phase diagram that is poorly understood from a theoretical point of view. In particular I’m going to discuss the seemingly simple limit of a single “down-spin” interacting with a Fermi-sea of “up-spins”.