Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model |
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Authors: | Luis Medina-Dozal Irn Ramos-Prieto Jos Rcamier |
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Affiliation: | Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apdo. Postal 48-3, Cuernavaca, Morelos 62251, Mexico; (L.M.-D.); (I.R.-P.) |
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Abstract: | In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable. |
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Keywords: | Jaynes-Cummings model hybird system evolution Wei-Norman theorem |
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