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Physical Review A

Influence of the Fock-state field on the many-atom radiation processes in a damped cavity

JOSIP SEKE, Frank Rattay

Published Jan 1, 1989• 33 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.39.171

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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.
An exact closed system of linear differential equations of the first order, which can be expressed by a simple recurrence equation, is derived for matrix elements of the statistical density operator. This exact recurrence equation opens the way for numerical solutions for collective many-atom spontaneous emission in cavities with arbitrary damping and detuning. For the first time to the authors’ knowledge, numerical results are presented for N = 10 and N = 15. Moreover, the influence of the cavity damping and detuning on the collective spontaneous emission is discussed. New effects, such as the suppression of the superfluorescent effects in strongly detuned cavities, are also pointed out.
An approximate solution is given for the interaction of a set of AAA two-level atoms with a single mode of a quantized radiation field when the field is damped by a reservoir at zero temperature. Assuming that the average photon number is much larger than the number of atoms, we study the influence of dissipation on the approximate factorization of the density matrix. For realistic values of the parameters, the factorization survives under the presence of field damping. The main effect of dissipation is an exponential decay of the average photon number and a loss of coherence among the different factorized states. The influence of field dissipation on the atomic inversion, purity, and field squeezing are studied.
The interaction is considered between NNN stationary two-level atoms and a radiation field described by a single cavity mode. The state vector for the complete system of atoms plus radiation is expressed as a linear superposition of states constructed from a product of photon states in the nnn representation and products of Pauli spin eigenstates describing all combinations of atoms in the lower and upper energy levels. Equations for the corresponding probability amplitudes are derived by substituting this superposition into the Schr\"odinger equation. The resulting equations are combined into bilinear form and phenomenological damping contributions are added. After the neglect of certain of the bilinear quantities, a master equation is derived which governs the probability Pmn{{P}_{m}}^{n}Pm​n of having mmm atoms in the lower level and nnn photons in the mode. This master equation takes account of multiple single-quantum absorption and emission processes but not of simultaneous multiple processes involving two or more atoms at a time. The equation which governs the expected number of photons 〈n〉〈n〉〈n〉 derived from the master equation bears a close resemblance to a rate equation. The effect of radiation loss from the cavity is incorporated into the master equation. Numerical calculations for a QQQ-spoiled laser show that the statistics of the number of photons in the mode bear a qualitative resemblance to Poisson statistics.