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Physical Review A

Two-mode two-photon Jaynes-Cummings model with atomic motion

Amitabh Joshi

Published Dec 1, 1998• 20 citations
Publisher

Abstract

We study the nonlinear transient effects similar to self-induced transparency and adiabatic following for a moving Rydberg atom undergoing a two-photon transition in an ideal cavity having a spatial field distribution for an uncorrelated two-mode coherent state. A comparative study is made of the case where an atom is undergoing a one-photon transition in a single-mode coherent field.

DOI
10.1103/physreva.58.4662

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We study the nonlinear transient effects similar to self-induced transparency and adiabatic following for a moving Rydberg atom undergoing a two-photon transition in an ideal cavity having a spatial field distribution for an uncorrelated two-mode coherent state. A comparative study is made of the case where an atom is undergoing a one-photon transition in a single-mode coherent field.
The nonlinear transient effects, similar to self-induced transparency and adiabatic following, are studied for a moving two-level atom that is entering into an ideal microwave cavity in a coherent superposition of its states. The atom undergoes a one-photon transition in the cavity, sustaining a spatial field distribution for a single-mode coherent (or thermal or Fock state) field. For some particular choice of parameters of atomic coherence, removal of an appreciable amount of field energy from the cavity could be observed.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.
We present the dynamics of nondegenerate as well as degenerate two-photon processes in a three-level Rydberg atom interacting with the eigenmodes of an ideal cavity. For large one-photon detuning, the results are compared with those obtained from an effective Hamiltonian and are found to be mostly different. However, for atom–field interaction times that are comparable with that in the two-photon micromaser experiment, the two models give similar results. We also discuss the time evolution of squeezing in the individual fields in the non-degenerate case. If the two modes are of frequencies ωf + ɛ and ωf − ɛ with ɛ ≪ ωf, the radiation field can be represented by a wave of frequency ωf with amplitudes modulated at ɛ. We find squeezing in the dynamical evolution of these amplitudes.