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International Journal of Theoretical Physics

The Generalized Thermo Jaynes–Cummings Model and Its Energy Spectrum

Heng-Mei Li, Hong-Yi Fan

Published Sep 6, 2010• 0 citations
Publisher
DOI
10.1007/s10773-010-0480-5

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Based on the construction of supersymmetric generators, we use the Lewis–Riesenfeld invariant method to deduce the exact and explicit eigen-energy spectrum with the time-dependent thermo Jaynes–Cummings model. One of the advantages of this approach is that it can transform the hidden form, related to the chronological product, of the time evolution operator into an explicit expression. Moreover, the dynamical and statistics properties of physical quantities are obtained for the given initial states in the thermo Jaynes–Cummings system.
The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Specifically, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.