Wright, Kenneth E.Trapped ions have been a staple resource of quantum simulation for the past decade. By taking advantage of the spin motion coupling provided by the Coulomb interaction, trapped ions have been used to study quantum phase transitions of highly frustrated spins, many body localization, as well as discrete time crystals. However, all of these simulations involve decoupling the ion motion from spin at the end of the experimental procedure. Here we present progress towards driving bosonic interference between occupied phonon modes. This thesis details a tool box for manipulating the motional states of a chain of trapped ions. Taking advantage of spin motion interaction of tightly trapped chains of 171Yb+ ions with two photon Raman transition, we show how to prepare a specic number state of a given normal mode of motion. This is achieved without traditional individual addressing but instead by using composite pulse sequences and ion transport. This involves a stage of quantum state distillation, and we also show preservation of phonon and spin coherence after this distillation step. This Fock state preparation sets the stage to observe bosonic interference of different phonon modes. We use stimulated Raman transitions to create a parametric drive; this drive will couple different normal modes of motion. To observe the bosonic nature of the phonons, we preform a Hong-Ou-Mandel (HOM) interference experiment on two singly occupied normal modes. We use the same spin motion coupling to read out the spin states of individual ions as a witness for this interaction. We also describe a process to use stimulated rapid adiabatic passage (STIRAP) to read out normal mode occupation. The toolbox presented here will be useful for future experiments towards boson sampling using trapped ions.enDissertationQuantum physicsAtomic physicsHong Ou MandelPhononTrapped Ion