Mechanical oscillators inside an optical cavity: interplay with atoms and fields

Abstract

The objective of this thesis is to explore different aspects of quantum phenomena in a mesoscopic systems in cavity optomechanical setups. In such a system, the optical and the mechanical degrees of freedom, the fundamental frequencies of which are quite different from each other in order of magnitude, couple together through the radiation pressure force and give rise to a rich platform to experience the quantum mechanical behaviour in a mesoscopic mechanical oscillator. Such a system becomes even more interesting from the perspective of quantum technology, quantum control or quantum state engineering, when we couple it with additional degree of freedom of heterogeneous nature, such as atom(s), ion(s) or atomic ensemble(s) and this configuration is known as a hybrid cavity optomechanical system. This auxiliary system can be controlled easily by external coherent sources. Hence, the effective coupling can be manipulated with the help of this externally-driven physical system. This leads to a possibility of quantum control of the mechanical motion and its read out by the auxiliary system, and vice versa. Thus the hybrid optomechnanical systems pose as a promising platform for the quantum information processing and quantum communication. The present thesis focusses on the hybrid optomechanical system where the mechanical oscillator in the form of a thin membrane is trapped inside an optical cavity [commonly known as the membrane in the middle (MIM) setup]. We have explored various optomechanical effects by introducing a single atom, two atoms as well as a pair of atomic ensembles. We have investigated the possibility of quadrature squeezing of the mechanical oscillator assisted by an atom and of two-atom quantum gate, driven by the mechanical motion. We further derived conditions for achieving enhanced Rabi coupling between identical atomic ensembles. In a multiple cavity (multiple membrane) setup, we have also shown how to transfer the average fluctuation from one membrane to the other adiabatically, in a STIRAP(Stimulated Raman adiabatic passage)-way. All the results presented in this thesis are supported by detailed analytical and numerical study.