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Physical Review A

Quantum electrodynamics of a three-level and a two-level Rydberg atom in a bimodal ideal cavity

N. Nayak, Vasileios Bartzis

Published Sep 1, 1990• 12 citations
Publisher

Abstract

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 ${\mathrm{\ensuremath{\omega}}}_{0}$.

DOI
10.1103/physreva.42.2953

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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 \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​ and \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​ in an ideal cavity. In the case \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​=\ensuremathω0{\mathrm{\ensuremath{\omega}}}_{0}\ensuremathω0​+\ensuremath{\epsilon} and \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​=\ensuremathω0{\mathrm{\ensuremath{\omega}}}_{0}\ensuremathω0​-\ensuremath{\epsilon} (\ensuremath{\epsilon}\ensuremath{\ll}\ensuremathω0{\mathrm{\ensuremath{\omega}}}_{0}\ensuremathω0​), we present the time evolution of squeezing in the amplitudes (modulated at \ensuremath{\epsilon}) of waves of frequency \ensuremathω0{\mathrm{\ensuremath{\omega}}}_{0}\ensuremathω0​.
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.
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.
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 consider two modes of the electromagnetic field interacting via a three-level atom in a ladder configuration. We calculate the squeezing spectra of the sum and difference of the two output beams. The usefulness of this system as a quantum-nondemolition-measurement scheme is analyzed and a prediction is made using the parameters of a recent experiment by Grangier et al. [Phys. Rev. Lett. 66, 1418 (1991)]. We use a full three-level model in the most general case and in particular the influence of both the one-photon and the two-photon detunings are investigated.
The behavior of the dipole moment of a three-level atom interacting with cavity fields of arbitrary detunings is investigated. The time evolution and squeezing conditions of the components and correlation function of the dipole moment are calculated for three cases: one-mode field and a \ensuremath{\Xi}-type atom initially in the upper state, two-mode field and a \ensuremath{\Lambda}-type atom initially in the upper state, and two-mode field and a \ensuremath{\Lambda}-type atom initially in one of the lower states. A number of interesting features are found and discussed.