Analytic Solutions of Two Electrons in Harmonic Confinement in an Optical Cavity
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.