Excitation spectrum of two-dimensional cold fermionic gases in the dilute limit

Two-dimensional gases of fermionic atoms have been recently realized, and cooled down to temperatures a few tenths of the Fermi temperature. Such ultracold atom systems are ideal tools to investigate the fundamental properties of Fermi ensembles subject to short-range interactions. One of the key questions is whether the interaction changes the ground state and excitation spectrum in a non-perturbative way, or whether the weak-coupling perturbation theory and Fermi-liquid idea remain valid in two dimensions. In contrast to condensed-matter systems, in atomic gases the perturbation theory must be carried out at finite temperature and far from the Fermi surface for a meaningful comparison with experiment. We have calculated the electronic self-energy of dilute two-dimensional Fermi gases at arbitrary temperature and momentum, using the ladder approximation. This scheme is expected to become exact (in a perturbative sense) in the low-density limit. For short-range attractive interaction, we study the evolution of the excitation spectrum as a function of temperature and interaction strength, and we compare our results with recent experiments.