Date of Award
Spring 5-2016
Access Type
Thesis - Open Access
Degree Name
Master of Science in Engineering Physics
Department
Physical Sciences
Committee Chair
Bereket Berhane
First Committee Member
Mahmut Reyhanoglu
Second Committee Member
Mark 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.
Scholarly Commons Citation
Jalandoni, Javier, "Numerical Case Study of an Atom-Photon Interaction in a Cavity Exploring Quantum Control" (2016). Doctoral Dissertations and Master's Theses. 217.
https://commons.erau.edu/edt/217