Coherent coupling of fluctuations in optomechanical systems

Abstract

Cavity optomechanics explores the e ect of radiation pressure of the cavity eld on the mechanical system. There is a change in the length of the cavity due to the radiation pressure on the mechanical mirror. Consequently, the resonance mode of the cavity is changed, and furthermore the radiation pressure on the mechanical system changes. Cavity optomechanics technique can be implemented for light to manipulate and measure small mechanical movements relevant to quantum physics. Cavity optomechanical system has been used for squeezing, non demolition detection of light, bistability, non classical states and Entanglement. Cavity optomechanical systems are characterised by a high frequency of optical eld, so thermal uctuations have a minimal impact on optical mode. Thermal uctuations, however, cannot be ignored in mechanical systems. Thus, to observe the quantum behavior of the mechanical oscillators, they need to be cooled down to near ground state. Multiple oscillators, trapped ions, as well as an ensemble of atoms have been studied in cavity optomechanical systems. In this thesis, we propose a scheme to transfer uctuations between the oscillators and the trapped ion. We use the dark state to transfer the phonons uctuation's from one membrane to another membrane. Entanglement of the trapped ion's vibrational mode with the mechanical oscillator is observed. We show the Sympathetic cooling of the mechanical oscillator with the help of the trapped ion. We also study the bistability in the trapped ion optomechanical system. In the the last section of the thesis, we discussed the e ects of linear and quadratic coupling on the entanglement and synchronization between the mechanical oscillators. This quadratic coupling is found to help preserve entanglement and synchronisation simultaneously