The Dynamics of Quantum States of Light in Lossy Coupled-Cavity Systems

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Seifoory, Hossein
Coupled-cavity system , Nonclassical light , Squeezed state , Continuous variable entanglement , Coupled resonator optical waveguide
Nonclassical states of light possess unique properties such as squeezing, antibunching, and entanglement, which have led to various interesting applications in quantum computing, quantum teleportation, and quantum information. However, practical implementation of some of these potential applications are hindered due to our lack of insight into how to treat loss in the system. The inclusion of loss is very important, as it can in some cases largely destroy the nonclassical properties of the light. The focus of this thesis is on squeezed states, as these are one of the most useful and important quantum states of light. First, I present a theoretical treatment of the nonclassical properties of squeezed states generated via parametric down conversion in a leaky cavity. By solving the Lindblad master equation for such a system, I analytically demonstrate that the exact time dependent solution is a squeezed thermal state. In addition, I examine the dynamics of generated nonclassical states of light in lossy coupled-cavity systems. I then apply the formalism developed to a coupled resonator optical waveguide structure and present the results for squeezed vacuum states. I next examine the coupled-cavity optical waveguide system as a platform to produce counterpropagating continuous variable entangled states. Using a tight-binding approximation, I develop analytic time-dependent expressions for the number of photons in each cavity, as well as for the correlation variance between the photons in different pairs of cavities. These expressions can be used to engineer the pumping configurations as well as the physical properties of the structure. Finally, employing a numerical singular value decomposition method, I show how the biphoton wave function can be Schmidt decomposed numerically, which together with the previously-developed analytic expressions provides a powerful computational platform. This is important as it can not only be used to check the validity of the approximations made in obtaining analytic expressions but can also be used to explore some interesting cases that were not possible to treat analytically.
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