Thermodynamical approaches to efficient sympathetic cooling in ultracold Fermi-Bose atomic mixtures

We discuss the cooling efficiency of ultracold Fermi-Bose mixtures in species-selective traps using a thermodynamical approach. The dynamics of evaporative cooling trajectories is analyzed in the specific case of bichromatic optical dipole traps also taking into account the effect of partial spatial overlap between the Fermi gas and the thermal component of the Bose gas. We show that large trapping frequency ratios between the Fermi and the Bose species allow for the achievement of a deeper Fermi degeneracy, consolidating in a thermodynamic setting earlier arguments based on more restrictive assumptions. In particular, we confirm that the minimum temperature of the mixture is obtained at the crossover between boson and fermion heat capacities, and that below such a temperature sympathetic cooling vanishes. When the effect of partial overlap is taken into account, optimal sympathetic cooling of the Fermi species may be achieved by properly tuning the relative trapping strength of the two species in a time-dependent fashion. Alternatively, the dimensionality of the trap in the final stage of cooling can be changed by increasing the confinement strength, which also results in a crossover of the heat capacities at deeper Fermi degeneracies. This technique may be extended to Fermi-Bose degenerate mixtures in optical lattices.