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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Collective dynamics of two three-level atoms in the finite-Q cavity

Eugene K. Bashkirov

Published Apr 20, 2004• 0 citations
Publisher

Abstract

On the basis of the master equation for the density matrix the dynamics of the collective spontaneous radiation of two Λ - type three-level atoms interacting with two modes of quantum electromagnetic field in the damped cavity has been considered. The behaviour of the photon numbers in modes has been investigated in the case when both atoms are in excited state at the initial time.

DOI
10.1117/12.561000

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On the basis of the master equation for the density matrix the dynamics of the collective spontaneous radiation of two Λ - type three-level atoms interacting with two modes of quantum electromagnetic field in the damped cavity has been considered. The behaviour of the photon numbers in modes has been investigated in the case when both atoms are in excited state at the initial time.
The dynamics of few two-level atoms interacting with one cavity mode is described in master equation formalism. Two different configurations are considered: a transient one with all atoms initially in the excited state and a stationary one where a coherent pump acts on either the atoms or the cavity mode. Superradiance, resonant scattering and switching between a low and a high emission state are considered. Cooperation and decoherence as well as the statistics of the emitted radiation field in both cases are discussed.
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.
Radiation effects from two-level atoms caused by the presence of a Fock-state field in a damped single-mode cavity are examined. An exact recurrence differential equation for density-matrix elements valid for any number of atoms or photons is derived. Numerical solutions for different cavity dampings (low- and high-Q cavities) and different photon numbers of the Fock-state field being present initially in the cavity are presented. Collective effects caused by the presence of many atoms are investigated. It is shown that new quasistationary states as well as collective radiation inhibition appear in the time behavior of the atomic energy expectation value. These effects arise from averaging over an ensemble of which each member consists of N identical two-level atoms placed into a resonant single-mode cavity. A comparison of the obtained results with those for an initial coherent or thermal field is also given.