Supersymmetry in nonlinear and linear Quantum Optics: the Kerr-like and multiphoton Jaynes-Cummings models

A novel approach is proposed to analyze a rather vast counter-rotating Hamiltonian interaction in the context of quantum optics.The method relies upon the supersymmetric mapping of the corresponding rotating interaction and allows the analysis of thedynamics in the counter-rotating system in a fully general and exact analytical manner by diagonalizing the correspondingHamiltonian. Intriguing features of the counter-rotating system are revealed through the simple supersymmetric transformation.In turn, such interesting attributes have an important range of potential technological applications. In this way, supersymmetryemerges as a useful tool to both connect and construct exactly solvable photonic systems in quantum optics, as well as toanalyze the corresponding physical consequences and their possible technology implementations.