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AIP conference proceedings

Supersymmetry in the Jaynes-Cummings model

Octavio Castaños

Published Jan 1, 2013• 2 citations
Publisher

Abstract

A review is presented of the Darboux method and its relation to the supersymmetric quantum mechanics, together with the embedding of a n-dimensional scalar Hamiltonian into a supersymmetric matrix. It is also shown that the Jaynes-Cummings model, with or without rotating wave approximation, admit a supersymmetric quantum mechanics description.

DOI
10.1063/1.4810775

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Journal of Physics A Mathematical and General•Aug 18, 2006•6 citations
A review is presented of the Darboux method and its relation to the supersymmetric quantum mechanics, together with the embedding of a n-dimensional scalar Hamiltonian into a supersymmetric matrix. It is also shown that the Jaynes-Cummings model, with or without rotating wave approximation, admit a supersymmetric quantum mechanics description.
Using a realization of the noncompact orthosymplectic superalgebra Osp(22,R)\mathrm{Osp}(\frac{2}{2}, R)Osp(22​,R), the two-level Jaynes-Cummings Hamiltonian is shown to be a supersymmetric quantum-mechanical system in the sense of Witten. The existence of the supersymmetry is shown to place a restriction on the physical parameters of the Hamiltonian.
Abstract 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.