Limits to $T/T_{\mathrm F }$ and progress towards ultracold $^{6}$Li-$^{87}$Rb mixtures

Ultracold dilute atomic gases are providing a new window into quantum physics, with particular regard to the first-principle study of superfluid phenomena. Fermionic degeneracy (measured by $T/T_{\mathrm F }$) achieved with current apparata using sympathetic cooling techniques seems to be limited by the heat capacity matching between the Fermi and Bose species and by Fermi-hole heating. We will discuss these factors and report on the development of an apparatus for simultaneous trapping and cooling of $^{6}$Li and $^{87}$Rb, using a light-assisted magnetic trap.\footnote{M. Brown-Hayes and R. Onofrio, Phys. Rev. A \textbf{70}, 063614 (2004).} The $^{6}$Li and $^{87}$Rb species combination, in conjunction with the improvement in heat capacity matching, should allow for an improved lower limit to attainable temperatures in Fermi-Bose mixtures.\footnote{R. C\^{o}t\'{e}, R. Onofrio, E. Timmermans, Phys. Rev. A \textbf{72}, 041605(R) (2005).} We also report on seemingly opposite approaches to reaching a lower $T/T_{F}$ and suggest the differences are due to two distinct measures of cooling efficiency.