Three-fluid description of the sympathetic cooling of a boson-fermion mixture

We present a model for sympathetic cooling of a mixture of fermionic and bosonic atomic gases in harmonic traps, based on a three-fluid description. The model confirms the experimentally observed cooling limit of about 0.2T(F) when only bosons are pumped. We propose sequential cooling-pumping first of bosons and afterward fermions-as a way to obtain lower temperatures. For this scheme, our model predicts that temperatures less than 0.1T(F) can be reached.