| dc.description.abstract | 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. | en |
