Equation of state of a polarized Fermi gas in the Bose-Einstein-condensate limit

We present a theoretical study of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime in the case of an unequal number of fermions of two species. We take full account of the composite nature of the dimers made of fermions. In the limit of low densities, we calculate the ground-state energy of the system, or equivalently the chemical potentials of each species, as well as the one-particle gap and the energy of an impurity immersed in a Fermi sea. For the chemical potentials we go up to order (density)(4/3). The results found involve the exact atom-dimer a(AD) and dimer-dimer a(DD) scattering lengths and therefore include the three-and four-body problems in the many-body problem. We briefly comment on the importance of the different mean-field corrections for recent experiments.