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arXiv:2401.12762 · Laser Physics

Dynamics of a two-level atom in the presence of a medium-assisted thermal field

Razieh Gonouiezadeh, Hassan Safari

Published Jul 16, 2024• 0 citations
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Abstract

Abstract In this paper, the time evolution of a two-level atom in the presence of a medium-assisted thermal field is explored through which the formula for the decay rate of an excited atom is generalized in two aspects. The obtained formula applies to a thermal electromagnetic field as well as to the presence of an arbitrary arrangement of magnetoelectric media. In order to be general with respect to the material environment, the Green’s function approach is used. It is shown that the non-zero temperature contributes to the decay rate via an additive term that is equal to the zero-temperature result multiplied by two times the photon number at the atomic transition frequency.

DOI
10.1088/1555-6611/ad4bb5

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Abstract In this paper, the time evolution of a two-level atom in the presence of a medium-assisted thermal field is explored through which the formula for the decay rate of an excited atom is generalized in two aspects. The obtained formula applies to a thermal electromagnetic field as well as to the presence of an arbitrary arrangement of magnetoelectric media. In order to be general with respect to the material environment, the Green’s function approach is used. It is shown that the non-zero temperature contributes to the decay rate via an additive term that is equal to the zero-temperature result multiplied by two times the photon number at the atomic transition frequency.
Starting from first principles we simulate numerically the dynamics of a system of two-level atoms interacting with a multimode electromagnetic field in a one-dimensional cavity. In particular, we investigate the spontaneous emission of an excited two-level atom in the cavity. We show how the decay depends on the mode spectrum and on the position of the atom in the cavity. We study how the spontaneous emission is modified when the initially excited atom is surrounded by a material medium modeled as a system of two-level atoms. We also study the propagation of photon wave packets emitted by the atom within the material media. Our microscopic model provides us with a deeper understanding of the atom-field interaction and offers us a framework for a systematic investigation of the transition from a microscopic to a macroscopic (phenomenological) description of the spontaneous decay in material media (e.g., dielectrics).
Starting from the quantized version of Maxwell's equations for the electromagnetic field in an arbitrary linear Kramers-Kronig dielectric, the Heisenberg equations of motion for a two-level atom resonantly coupled to the radiation field in the presence of dispersive and absorbing dielectric bodies are derived. The theory is applied to the problem of spontaneous decay of excited atoms in absorbing media. The decay rate is calculated for the (Glauber-Lewenstein) real-cavity model, and a comparison with the recently studied (Clausius-Mosotti) virtual-cavity model [S. Scheel, L. Kn\"oll, D.-G. Welsch, and S. M. Barnett, Phys. Rev. A 60, 1590 (1999)] is given. It is shown that owing to nonradiative decay associated with absorption, the rate of spontaneous decay sensitively depends on the cavity radius, particularly when the atomic transition frequency approaches an absorption band of the medium. Only when the effect of absorption is fully disregarded, is the familiar local-field correction factor recovered.
We study the cooperative two-photon spontaneous decay of an excited atomic system in a microcavity whose size is of the order of several wavelengths of atomic radiation. We show that a thermalized electromagnetic field in the microcavity strongly affects the two-photon cooperative spontaneous emission of radiation. The increase in the rate of spontaneous cooperative decay is due to the presence of a small number of thermalized photons in a microcavity mode. At low temperatures, the two-photon absorption probability is found to be a linear function of the two-photon flux, and photon superbunching is observed.
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We investigate the dynamical properties of the radiation field emitted from an excited two-level atom in a photonic crystal. If the transition frequency of the atom lies within a certain frequency range above the band edge, the emitted field consists of two components that show a different decay dynamics. In particular it is shown that one field component decreases faster than the atomic population with a decay constant depending on the distance from the atom. As a consequence, the decay rate of the electromagnetic field is spatially varying and, in general, can not be identified with the corresponding rate for the atomic population.
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