Quantum State Reconstruction in Quantum Optomechanics
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The ability to perform mechanical states reconstruction is an essential task in quantum optomechanics to understand different quantum aspects of mechanical states of motion. Many interesting phenomena appear when the light and mechanical motion are coupled through the radiationpressure coupling. Preparing, controlling, and measuring mechanical states are all very crucial in the study and development of quantum optomechanics. In this dissertation, we introduce a practical scheme for mechanical states reconstruction in the weak optomechancial coupling regime in which most optomechanical systems operates. The scheme relies on sending a beam of two-level atoms to pass through an optomechanical cavity where an oscillating mirror is coupled to a cavity field. The atoms interact resonantly with the cavity field as they pass through the cavity. As the oscillating mirror modifies the dynamics of the atoms, we show in this dissertation that by measuring the atomic population inversion of the atoms when they exit the optomechanical cavity, it is possible to obtain the mirror’s state by analyzing the measured data of the population inversion. In the first part of this dissertation, we study a hybrid system in which a two-level atom is placed inside a cavity field where one side of the cavity is free to move. The two-level atom is coupled to the cavity field through the well known Jaynes-Cummings coupling, whereas the mechanical mirror and the cavity field are coupled to each other via the radiation-pressure coupling. A complete analytical and numerical study is performed on this system, and it is shown that the mechanical mirror modifies the atomic population inversion in such a way that each mechanical state changes the signal of the population inversion of the atom differently. From the results in this part of the dissertation, we concluded that the population inversion can be analyzed and employed to extract the quantum state of the mechanical mirror. Second, as each specific mechanical state affects the atomic population inversion differently, we developed the idea of using the atom as a tool to reconstruct the quantum state of the mechanical mirror. We first assumed that the two-level atom is initially in a superposition of its excited and ground states while both the cavity field and the mechanical mirror are in general superposiii tion of Fock states with unknown coefficients. The derived general expression of the population inversion indicates that it is sufficient to initially prepare the atoms in the excited states before passing through the optomechancial cavity and the cavity field is in vacuum state. The population inversion of the atoms exiting the cavity can then be measured, and the collected data can be used to determine the full state of the mechanical mirror. The scheme in this part of the dissertation is only developed for measuring pure mechanical states. Third, we extended the scheme of mechanical states reconstruction to the more practical states of the mirror in which the mirror is initially in a mixed state. We derived a general analytical solution of the population inversion allowing us to reconstruct more experimentally feasible states of the mechanical mirror such as thermal states.
Asiri, Saeed Mater M (2018). Quantum State Reconstruction in Quantum Optomechanics. Doctoral dissertation, Texas A & M University. Available electronically from