Tripartite coupled hybrid cavity optomechanics

This thesis theoretically studies a full coupling quantum system which is a mixing of quantum electrodynamics and optomechanics. To this end, we consider a generic cavity optomechanics scheme involving a tripartite system consisting of a Fabry-Perot cavity, a qubit, and a mechanical resonator where the three components are mutually interacting. The first three chapters provide the necessary theoretical tools for the understanding of the models and concepts as are used throughout this work. The last three chapters present the main results obtained during this Ph.D. project. In this study, the coupling between a cavity mode and an atom has been explored within the field of QED, while for the optomechanical part, the interaction between the cavity and the mechanical resonator has been described in terms of usual radiation-pressure coupling. However, the dispersive, radiation–pressure interaction between the mechanical and the electromagnetic modes is typically very weak, harnessing up to now the demonstration of interesting nonlinear dynamics and quantum control at the single-photon level. It has been shown both theoretically and experimentally that if the interaction is mediated by a nonlinear element (such as qubit), one can have effective dynamics corresponding to a huge enhancement of the single-photon optomechanical coupling. We first study the Hamiltonian for the closed system considering that its Hamiltonian is in Rabi form, and we investigate its spectrum as a function of the coupling strength. We analyzed the eigenvalues using various mathematical techniques. We particularly exploit the Bloch-Siegert approach to rewrite the Hamiltonian in the form of the quantum Rabi model, which has analytical solutions. In comparison with rotating wave approximation, the Bloch-Siegert approach leads to an effective Hamiltonian for non-zero detuning; moreover, this method leads to relatively accurate solutions even for the large coupling strength. Next, we investigate the dynamics of the tripartite system when the cavity mode and the mechanical mode interact via an off-resonant qubit in the presence of damping and losses. We determine the condition under which the qubit can be adiabatically eliminated, and the system dynamics can be considered as an effective optomechanical system operating in the strong coupling regime, where the effective optomechanical coupling rate is of the order of the frequency. We use the Schrieffer–Wolff treatment to construct an effective optomechanical Hamiltonian. Finally, we verify the results by investigating the stationary cavity photon number and the stationary mean phonon number in the low excitation regime