Theoretical Study On Dynamics And Transmissivity Of Quantum Optomechanical System

Quantum optomechanics is an interdisciplinary grooming research field combining the principles of quantum mechanics with quantum optics. Optomechanics has attained a great attention in the last decade, which explains the quantum mechanical interaction between electromagnetic radiation and mechanical degrees of freedom. Optomechanics enhances the understanding of basics of physics ranging from classical physics to quantum physics. Many of questions potentially can be answered within this new field optomechanics, which can improve the understanding of the fundamentals of quantum mechanics. The basic prin-ciples of optomechanics lead to fundamental investigations and its potential applications. Optomechanics has contributed not only to the field of science but also to the exploration of quantum regime of the mechanical devices and applications. These applications are the precision measurement of small displacements, forces and masses i.e.(quantum-sensitive force detection), available on-chip technology, the quantum interfaces between solid state quan-tum bits and photons with applications in information storage and processing. Laser-cooling (side-band cooling), amplification and back action evasion are also the amazing applications of optomechanics. Generating superposition states, entanglement of mechanical motion and light, observations of the optical spring effects, optical nonlinearity and bistability, obser-vation of mechanically induced optical transparency and ponderomotive squeezing are the unique physical phenomena studied in optomechanics.The thesis mainly focuses on the novel theoretical study of quantum optomechanics. The dynamics and optical response of the optomechanical system are the prime objectives. Being closely related to the dynamics of quantum mechanical systems, the work presented here will contribute to the development of quantum optomechanics as well as the understanding of basic concepts in quantum physics.In chapter 1, we present motivation, background and basic introduction of the physical phenomena which are used in optomechanics. At the end of the chapter the outline of the thesis is presented. In 2nd chapter the detail of cavities, light-matter interaction, force due to the radiation pressure, the basic Hamiltonian, various parameters scale, classical and quantum picture of optomechanics are presented. The detail of the mechanical response in the detuning regions, light modification of mechanical response, shift in frequency, optical damping, optomechanical coupling and input output formalism for an optical cavity are also discussed.In chapters 3,4 and 5, represent our studies on this topic. In chapter 3, we take the inter-action of light with optomechanical cavity containing a two-level atomic system. In this case, we have shown that how light can be used to modify the dynamics of a quantum-mechanical oscillator through the radiation-pressure force. For the dynamics of the optomechanical sys-tem operators the master equation is used. Then the steady state solutions, the transmission and reflection coefficient and their intensities are calculated analytically. Dynamical evolu-tion of system’s operators and the transmission intensities are also shown in the numerical simulations. The motivation behind this work is, because in many optomechanical setups transmitted and reflected signals are the real signature obtained in the experiments, from which the researchers deduced the properties of the system e.g. the quantum state of the system sitting inside the cavity. In many of experimental research work it is shown that by the cavity transmission signal can be used to read out the qubit. Such a system can also be applied to atoms and molecules in cavity optomechanics spectroscopy. So this work is a mile stone to other analysis of the dynamics of ensembles system inside the optical cavities and quantum memory effect for photons. In many of the research articles, an atom is considered like an optical switch and gated transistor for the photon. In this chapter the transmission of the system shows that the coupling plays a major role in the transmission, which acts like an optical switch. In chapter 4, we study the dynamics and transmissivity of the optomechanical system in squeezed environment, in which we consider an optomechanical system that interact with an external single mode coherent laser field. We also study the time evolution of intracavity field intensity, oscillating mirror momentum and position operators. The interaction give rise to dynamics, the dynamics are calculated and numerical simulations of dynamics are discussed for different values of squeezed parameters. The output transmission coefficient for field as well as for the intensity are also calculated analytically. From the transmission, it is witnessed that the squeezed parameter plays an important role. As squeezing is important in quantum metrology for improving the accuracy in quantum measurements. In some cases, spin squeezing can be employed to detect entanglement. The unique feature of the squeezed light can overcome many complexities in the optical setups and experimental procedures. Therefore it remained as the focus research subject and received more attention in theoretical and experimental research, where the generation of light states with fluctuations below that of its vacuum got a central position.Chapter 5 concerns the study of the optomechanical induced transparency (OMIT) un-der the influence of the N spin ensemble system. Our model is generic, deduced the dynamics for system’s operators and calculated the relations for absorption. The result shows op-tomechanical induced transparency. The numerical results show that the optomechanical transparency increases with the increase in the coupling constant between the cavity field and spin ensemble, while decreases with the increase in the decay rate of the spin ensemble system. The details of OMIT are extended to the resolved side-band in this chapter. The optomechanical induced transparency is analogous to atomic EIT, where light can be slowed and stopped. Therefore OMIT also can be extended to potential applications in quantum optics and quantum information.Finally, conclusion and outlook are presented in chapter 6.