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 regime (BEC), 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 equivalentely 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 3 and 4-body problems in the manybody problem. We briefly comment on the importance of the different mean-field corrections for recent experiments.