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Physical Review A

Linearization of the multiphoton single-atom Dicke Hamiltonian

Avia Rosenhouse, Jacob Katriel

Published Jan 1, 1990• 7 citations
Publisher

Abstract

The multiphoton single-atom Dicke Hamiltonian in the dipole and the rotating-wave approximations is shown to reduce to the one-photon single-atom Dicke Hamiltonian via an approximate linearization process. For the special case of the Jaynes-Cummings Hamiltonian, it is shown that it is possible to derive a linearized form that is exactly equal to the original Hamiltonian.

DOI
10.1103/physreva.41.531

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Modern Physics Letters B•Oct 20, 1992•0 citations
The multiphoton single-atom Dicke Hamiltonian in the dipole and the rotating-wave approximations is shown to reduce to the one-photon single-atom Dicke Hamiltonian via an approximate linearization process. For the special case of the Jaynes-Cummings Hamiltonian, it is shown that it is possible to derive a linearized form that is exactly equal to the original Hamiltonian.
We introduce a dynamical system that instead of exchanging a single photon as in the atomic system of the usual Jaynes-Cummings model (JCM), it exchanges instead a squeezed coherent photon. Accordingly, the creation and annihilation photon operators in the JCM are replaced by the creation and annihilation operators of squeezed coherent states, respectively. This transformation generates a photon Hamiltonian that modifies the JCM that includes terms usually omitted in the JCM when making the rotating-wave approximation and, in addition, the transformation introduces atom exchange terms absent in the JCM.