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Journal of the Optical Society of America B

Two-photon Jaynes–Cummings model

Vasileios Bartzis, N. Nayak

Published Aug 1, 1991• 26 citations
Publisher

Abstract

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.

DOI
10.1364/josab.8.001779

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We show the differences in the dynamics of a three-level and a two-level Rydberg atom interacting with two nondegenerate modes of frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ in an ideal cavity. In the case ${\mathrm{\ensuremath{\omega}}}_{1}$=${\mathrm{\ensuremath{\omega}}}_{0}$+\ensuremath{\epsilon} and ${\mathrm{\ensuremath{\omega}}}_{2}$=${\mathrm{\ensuremath{\omega}}}_{0}$-\ensuremath{\epsilon} (\ensuremath{\epsilon}\ensuremath{\ll}${\mathrm{\ensuremath{\omega}}}_{0}$), we present the time evolution of squeezing in the amplitudes (modulated at \ensuremath{\epsilon}) of waves of frequency ${\mathrm{\ensuremath{\omega}}}_{0}$.
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.
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.
We consider a single Rydberg atom having two degenerate levels interacting with the radiation field in a single-mode ideal cavity. The transition between the levels is carried out by a ΛΛΛ-type degenerate two-photon process via a third level far away from single-photon resonance. At the start of interaction, the atom is considered to be in a coherent superposition of its two levels and the field in a coherent state. We study the dynamics of the atomic as well as the field states. The squeezing in the quadratures of atomic states can reach up to 100%100\%100%. The cavity field evolves to a statistical mixture of two coherent fields with the phase difference between them decided by the interaction time. Analysis of entropies of the atom and the field shows that the two systems are dis-entangled periodically in certain cases.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.