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Journal of Modern Optics

On the Multiphoton Multimode Interaction Between a Two Level Atom and a Quantum Electromagnetic Radiation Field

Avia Rosenhouse‐Dantsker

Published Jul 1, 1992• 16 citations
Publisher

Abstract

The multiphoton multimode generalization of Jaynes-Cummings Hamiltonian is both derived and linearized in the paper: it is derived from a first-principle Hamiltonian by adiabatic elimination and then shown to be exactly linearized to a form of a Jaynes-Cummings Hamiltonian, which enables an easy solution.
DOI
10.1080/09500349214551501

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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.
In this paper we consider the multimode multiphoton Jaynes–Cummings model, which consists of a two-level atom, initially prepared in an excited atomic state, interacting with N modes of electromagnetic field prepared in general pure quantum states. For this system we show that under certain conditions the evolution of the Wigner function at the phase-space origin provides direct information on the corresponding atomic inversion. This relation is also valid even if the system includes Kerr-like nonlinearity, Stark shift effect, different types of initial atomic states as well as moving atoms. Furthermore, based on this fact we discuss for the single-mode case the possibility of detecting the atomic inversion by means of techniques similar to those used for the Wigner function.