Two-dimensional attractive fermi gas : balanced and highly polarized regimes at zero temperature

We study a two dimensional two species Fermi gas with attractive short-range interactions at zero temperature, both in the unpolarized regime, which shows a BCS-BEC crossover type of superfluid ground state, and in the highly polarized regime, corresponding to an impurity immersed in a Fermi sea, which exhibits a transition from a polaronic to a molecular ground state. We use Diffusion Monte Carlo with Fixed Node approximation in order to calculate the energy per particle and extract the effective interactions among composite particles in the strongly interacting regime, where beyond mean field effects are crucial. In the impurity regime we calculate the evolution of the quasiparticle weight in the attractive polaronic branch as a function of the coupling. We also discuss the relevance of these results to ongoing experiments.