Analytic Solutions of Two Electrons in Harmonic Confinement in an Optical Cavity
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Date
2021-12
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Vanderbilt University. Dept. of Physics and Astronomy
Abstract
The possibility to control quantum systems with photons has stimulated
recent interest in the study of quantum optical systems. While
simple classical quantum systems admit well-known solutions, analysis
of light-coupling quantum regimes remains lacking. In this work,
we obtain analytic solutions for a light-coupling electron pair in harmonic
confinement in a cavity by separating center-of-mass (CM) and
relative motions. The CM part can be calculated in closed form or
by exact diagonalization of the Hamiltonian, and the relative part is
quasi-exactly solvable. We analyze the 2D results produced by the
exact diagonalization method and reach conclusions on the effects of
different system parameters. We also present 1D numerical simulations
by Stochastic Variational Method (SVM) using Explicitly Correlated
Gaussian (ECG) bases, which agree with our analysis in 2D. Our analytic
solutions may provide a valuable calibration point for simulations
in the quantum optical regime.
Description
Vanderbilt physics honor thesis of Chenhang Huang, in partial fulfillment of the requirements for the honor degree of
Bachelor of Arts in Physics. Advisor: Kalman Varga.
Keywords
physics, honors thesis, condensed matter physics, material physics