Fermion Mediated Interactions in Quantum Degenerate $^{133}$Cs-$^6$Li Bose-Fermi Mixtures

Quantum simulation with ultracold quantum gases is one of the important building blocks of modern Atomic, Molecule and Optics physics (AMO physics). Benefiting from the clean and versatile experimental platforms, quantum simulation emphasizes building connections with other physics systems. In recent years, it has remained at the very frontier of modern physics research. Among topics of quantum simulation, Bose-Fermi mixtures present unique scientific interests. From the theoretical point of view, a majority of important physics mechanisms involves both bosons and fermions. In the meantime, harder challenges arising from experimenting with two or more species encourage experimentalists to develop more advanced platforms. Mediated interaction is a fundamental and widely observed phenomenon in many physical systems ranging from conventional superconductivity, Coulomb interaction, giant magnetoresistance to Yukawa interaction. Mediated interaction is no exception, being a vital concept in Bose-Fermi mixtures. This thesis presents experiments with quantum degenerate $^{6}\text{Li}$-$^{133}\text{Cs}$ Bose-Fermi mixtures, with its focus on fermion mediated interaction. We have created the first quantum degenerate fermionic $^{6}\text{Li}$ bosonic $^{133}\text{Cs}$ mixtures and found the first experimental observation of fermion mediated interaction with a Bose-Einstein condensate(BEC) in mixture system. Encouraged by this observation, we study sound propagation in BECs with fermion mediated interactions. A significant dependence of BEC sound speed on the Bose-Fermi interaction strength $a_{BF}$ is observed, which indicates the fundamental impact of mediated interactions on Bose-Fermi mixtures. Eventually, we extend our study towards challenging strong interaction regime where Bose-Fermi interaction scattering length $|a_{\text{BF}}|$ is comparable to Fermi wavelength $1/k_\text{F}$. With advancement in observation toolbox, we made the first observation of a new resonance in the strong interaction regime, which indicates a possible boson-boson pairing mechanism originating from mediated interaction. This newly observed resonance would help reveal the fundamental underlying connection between many body aspect of mediated interaction induced pairing and few body aspect of Efimov physics. Our investigation represents significant progress in understanding of fermion mediated interaction mechanism in Bose-Fermi mixtures. It offers a more complete physics picture of Bose-Fermi mixtures in a different parameter regime. The observation of possible boson-boson pairing induced by fermions, sheds light on strongly interacting Bose-Fermi quantum gases research and will hopefully encourage new ideas and theories for strong interacting Bose-Fermi mixture.