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Physical Review A

Squeezing in nondegenerate two-photon processes in a cavity quantum electrodynamics of a three-level and a two-level Rydberg atom

N. Nayak

Published Mar 1, 1993• 0 citations
Publisher

Abstract

The time evolution of squeezing in the two-photon interaction of a Rydberg atom with two nondegenerate modes of an ideal cavity is analyzed. The study compares the results from the two representations of the atom by a three-level system and an effective two-level system. We find the time evolution of the squeezing in the two systems to be different, including the regimes where the dynamics of the population are similar.

DOI
10.1103/physreva.47.2276

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The time evolution of squeezing in the two-photon interaction of a Rydberg atom with two nondegenerate modes of an ideal cavity is analyzed. The study compares the results from the two representations of the atom by a three-level system and an effective two-level system. We find the time evolution of the squeezing in the two systems to be different, including the regimes where the dynamics of the population are similar.
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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 ${\mathrm{\ensuremath{\omega}}}_{0}$.
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.
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.
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.
The generation and evolution of entanglement and squeezing for the two-mode fields are discussed in a cascade three-level atomic system. Two photons of a strong external pump field induce atomic coherence between the top and bottom levels. The dynamics of this system in the presence of cavity losses is studied. It is shown that entanglement and squeezing between the two modes increase initially, then decrease and eventually disappear. The periods of them are extended with the increasing of the pump field intensity. The effects of the cavity losses on squeezing and entanglement are also discussed.