Exact treatment of trapped imbalanced fermions in the BEC limit

We 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 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 is 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 are presented for the density profiles of composite bosons and excess fermions. Results for the formation of vortex patterns in the presence of density imbalance are also presented.