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

The study of quantum many-body systems remains a topic at the forefront of both theoretical and experimental physics research. These systems can exhibit a wealth of interesting phenomena and phases, and their understanding is important for progress towards new quantum technologies. Ultracold atomic gases are a powerful experimental platform for studying quantum many-body physics due to the flexibility and control that they afford. From the perspective of quantum simulation, mixtures of bosonic and fermionic neutral atoms offer a unique experimental system which permits tunable interactions between both types of fundamental particles. In solid-state materials, the interplay between the bosonic and fermionic components can be very important, with the most famous example being phonon-induced electron pairing in conventional superconductors. This thesis describes experiments on quantum degenerate mixtures of bosonic $^{133}$Cs and fermionic $^6$Li with tunable interspecies interactions. We have created the first degenerate mixtures of Li and Cs atoms and performed several experiments studying the role of interactions in their ground state and dynamics. The central question investigated is this: ``What happens to a Bose-Einstein condensate when it is immersed in a degenerate Fermi gas?" Throughout the work presented in this thesis, we have discovered several answers: the fermionic environment changes the effective confinement, the effective 2- and 3- body interactions, the phase diagram, and the excitations of the condensate. Our work represents significant progress in understanding the quantum behavior of Bose-Fermi mixtures, establishing the Li-Cs system as a valuable experimental platform in this direction. We lay groundwork for future studies of strongly interacting bosons and fermions, for which there are numerous fascinating theoretical proposals suggesting new quantum phases and phenomena.