Date of Award

5-2016

Document Type

Thesis - Open Access

Degree Name

Master of Science in Engineering Physics

Department

Physical Sciences

Committee Chair

Dr. Bereket Berhane

First Committee Member

Dr. Mahmut Reyhanoglu

Second Committee Member

Dr. Anthony Reynolds

Abstract

We study Magnus expansion (ME) approximation scheme for the interaction between an atom and a single quantized cavity mode (Jaynes-Cumming model) in a closed quantum system in resonance or near resonance for a time-dependent coupling coefficient g(t) in both the interaction and rotating picture by implementing a novel numerical method called MG4 and compare out results to the Runge-Kutta 4th (RK4) order solution to demonstrate the conservation of unitary evolution of the ME. A cursory study of open quantum system is given to encourage the study of ME for dissipative systems. Furthermore, we assume that our time-dependent coupling coefficient g(t) can take on two forms, Gaussian and sinusoidal, which are introduced as pulses to study the behavior and response of the cavity. Our results show that ME is a sufficient approximation scheme in our study of closed quantum systems which may have applications in quantum control.

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