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 6Li and 87Rb. Analyzing the harmonically trapped mixture, we find that the favourable features of this mixture are further enhanced by using different trapping frequencies for the two species.