The Hong-Ou-Mandel Effect was originally observed in 1987 by C.K. Hong, Z.Y. Ou, and L. Mandel. Their experiments found that only two of the four classically predicted outcomes were observed when two indistinguishable photons were fired at a 50 : 50 beam splitter within a very small (on the order of picoseconds) time interval. Our objective was to explore the theoretical framework for this experimental phenomenon using well-studied topics in quantum physics. We used the Monte Carlo quantum jump approach with a pair of non-interacting two-level atoms, assuming these atoms begin in the excited state and decay to the ground at two arbitrary times. We defined two jump operators for use in the approach, each corresponding to detecting a photon at one of two possible detectors. For our calculations, we evolved our state (using the unitary time-evolution operator derived from the time-dependent Schrodinger equation) to the next arbitrary ’time-stamp,’ then applied one of the two jump operators, repeating the process from the beginning until we’d obtained a result for each of the four combinations of jumps. We determined the probability of the two photons being found at different detectors to be zero. Moreover, we calculated the probability of two photons being found at the same detector to be one, aligning well with the results of the 1987 experiment. Ultimately, this effect allows us to exert control over a quantum system by limiting its possible outcomes, making it a viable component of logical operations in quantum computing.
Author(s): Caden McCollum, Lexi Dudones and Imran Mirza, PhD
Advisor: Imran Mirza, Department of Physics
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