Novel quantum systems are an emerging technology that promises significant advancement and understanding in the fields of quantum computing, quantum information science, and fundamental quantum optics research. A quantum system of significant interest is the optical cavity polariton, which are formed from interactions between electronic states in matter systems and the quantized radiation field in a cavity. Properties of such optical cavity polaritons have been exploited to realize phenomena such as polariton lasing, Bose-Einstein condensation, making integrated circuit elements that can be optically switched, and achieving long-range polariton transport. In particular, forming polaritons with molecules or nanoparticles has garnered much attention recently, and the resulting hybridized states are known as molecular polaritons. Like polaritons formed from an atom's electronic states, these molecular polaritons exhibit properties that are derived from both the matter excitations and the photonic components inside a cavity. However, these molecular polaritons possess additional vibrational states from their matter excitations that affect transduction between the matter and photonic degrees of freedom (DOF). These additional states offer new opportunities in the fields of quantum chemistry and quantum materials, as the physical properties of the constituent molecules can be tuned via strong light-matter interactions. For instance, the potential energy surfaces of molecules coupled to a cavity photon can be modified by changing its light-matter coupling strength or the frequency of the cavity mode, hence, providing new pathways for chemical reactions to occur.