Sympathetic cooling route to Bose-Einstein condensate and Fermi-liquid mixtures

We discuss a sympathetic cooling strategy that can successfully mitigate fermion-hole heating in a dilute atomic Fermi-Bose mixture and access the temperature regime in which the fermions behave as a Fermi liquid. We introduce an energy-based formalism to describe the temperature dynamics with which we study a specific and promising mixture, composed of Li-6 and Rb-87. Analyzing the harmonically trapped mixture, we find that the favorable features of this mixture are further enhanced by using different trapping frequencies for the two species.