The thesis reports on the design and implementation of a novel experimental apparatus for the realization and investigation of ultracold Fermi-Fermi mixtures of Cr-53 and Li-6 atoms. After a brief introduction to the physics of ultracold Fermi gases with tunable interactions, the manuscript also reports on the exceptional peculiarities and unprecedented potentiality of the Cr-Li mixture. The thesis describes the first realization and investigation of magneto-optically trapped cold clouds of Cr and Li atoms worldwide. Furthermore, the thesis also reports on the study of normal and superfluid fermionic currents of Li-6 atoms through a thin Josephson junction across the BEC-BCS crossover. The study led to the extraction of the critical values of particle imbalance across the junction beyond which dissipative dynamics is established.
We realize simultaneous quantum degeneracy in mixtures consisting of the alkali and alkaline-earth-like atoms Li and Yb. This is accomplished within an optical trap by sympathetic cooling of the fermionic isotope
6Li with evaporatively cooled bosonic
174Yb and, separately, fermionic
173Yb. Using cross-thermalization studies, we also measure the elastic
s-wave scattering lengths of both Li-Yb combinations, $|{a}_{^{6}\mathrm{Li}\ensuremath{-}^{174}\mathrm{Yb}}|=1.0\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{nm}$ and $|{a}_{^{6}\mathrm{Li}\ensuremath{-}^{173}\mathrm{Yb}}|=0.9\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{nm}$. The equality of these lengths is found to be consistent with mass-scaling analysis. The quantum degenerate mixtures of Li and Yb, as realized here, can be the basis for creation of ultracold molecules with electron spin degrees of freedom, studies of novel Efimov trimers, and impurity probes of superfluid systems.