Exact treatment of trapped imbalanced fermionsin the BEC limit

In the present contribution we shall analyze the effects of imbalancing the populations of two-component trapped fermions in the BEC (strong-coupling) limit of the attractive interaction between fermions of different components. In particular, we shall derive a set of coupled equations which describe composite bosons and excess fermions in this limit, starting from the gap equation with two different fermionic chemical potentials. Care will be used to include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths, which require us to consider beyond-mean-field effects. Numerical results will be presented for the density profiles of composite bosons and excess fermions, which are relevant to the recent experiments with trapped Fermi atoms. Results for the formation of vortex patterns in the presence of density imbalance will also be presented.