Cavity quantum electrodynamics in the weak coupling regime is one of the most well-studied areas of quantum optics. On the other hand, dynamics of ultrastrongly coupled light and matter – when the coupling rate becomes comparable to the main transition frequency in the system – must be derived from the full interaction Hamiltonian as the rotating wave approximation fails. This regime is expected to exhibit fascinating quantum effects, such as virtual photon excitations in the cavity field or dissipative phase transitions where highly entangled states are created. It is difficult to achieve ultrastrong coupling in cavity optomechanics as it requires a strong laser drive, which typically results in unstable experimental conditions. However, optically levitated particles couple to the electric field of the cavity mode (via coherent scattering), which leaves the cavity mode unpopulated and thus allows for stable operation at any coupling rate. Coupling rate of 30% of the mechanical frequency has recently been demonstrated, which is at the very onset of ultrastrong coupling regime. This project will explore ultrastrong and deep-strong cavity optomechanical interaction in cavities with small mode volume and demonstrate coupling rates as high as 1000 times the mechanical frequency.