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
