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

Quantum near-field effects and spontaneous decay

Sergey V. Sukhov

Published Nov 15, 2001• 0 citations
Publisher

Abstract

In the frames of quantum electrodynamics, the behavior of spontaneous decay is investigated for a single two-level atom embedded into a microscopic object (cluster). The transition frequency of cluster atoms is supposed to be considerably detuned from the transition frequency of decaying atom. The consideration is performed on the base of fully microscopic quantum-electrodynamical approach with simultaneous solution of Heisenberg equations for atomic and quantum field operators. The special attention is paid to the investigation of renormalization of spontaneous emission rate due to proper account of discrete structure of medium. The formula for decay rate is obtained without using the notion of refractive index. It is obtained that spontaneous decay strongly depends on the geometrical arrangement of atoms in microstructure. For some form of clusters, decay rate is found to be considerably large compared to its vacuum value that is not the case for macroscopically large dielectrics.

DOI
10.1117/12.447959

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In the frames of quantum electrodynamics, the behavior of spontaneous decay is investigated for a single two-level atom embedded into a microscopic object (cluster). The transition frequency of cluster atoms is supposed to be considerably detuned from the transition frequency of decaying atom. The consideration is performed on the base of fully microscopic quantum-electrodynamical approach with simultaneous solution of Heisenberg equations for atomic and quantum field operators. The special attention is paid to the investigation of renormalization of spontaneous emission rate due to proper account of discrete structure of medium. The formula for decay rate is obtained without using the notion of refractive index. It is obtained that spontaneous decay strongly depends on the geometrical arrangement of atoms in microstructure. For some form of clusters, decay rate is found to be considerably large compared to its vacuum value that is not the case for macroscopically large dielectrics.
We have theoretically investigated the process of spontaneous emission of initially excited two-level atom inside and outside of ultra-thin dielectric film. Dielectric medium is considered as discrete-continuous system of interacting dipoles. For the solution of this boundary problem of quantum optics we use Heisenberg equations for atomic operators. Mode functions of ultra-thin film are calculated by direct solution of integro-differential field equation. Coordinate dependences of excited state life time are analyzed and it is shown that consideration of near-field effect may essentially change spectral properties of the atoms located at small distances from the surface.
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 have calculated the effect of material absorption on the rate of spontaneous emission by an embedded atom using a macroscopic Green-function approach and a microscopic Hamiltonian method that includes reservoir damping. When local field effects are neglected, the free-space emission rate is modified by the real part of the refractive index at the transition frequency of the embedded atom. Local field effects are introduced via a local field correction factor. This modification of the spontaneous emission rate generalizes a well-known result for transparent media and is of crucial importance in assessing the degree of inhibition of spontaneous emission for frequencies close to the resonances of the dielectric.
The formulas of the quantum electrodynamics have been applied to calculate the spontaneous emission rate of excited atom in dielectric microcavity. The results exhibit damping oscillating patterns which depend sensitively on the scaling parameter and geometrical structure. Compared with the case that the emitting atom is immersed in dielectric, the spontaneous emission rate is depressed obviously and the center or the mean value of the oscillations is intimately related to the real refractive index of the local position where the atom is. In order to explain this phenomenon, we utilize the closed-orbit theory to deal with the classical trajectories of the emitted photon, and extract the corresponding frequencies of the oscillations by Fourier transform. It is found that the oscillations can be represented in terms of the closed-orbits of the photon motion constrained in dielectric microcavity, thus providing another perspective on the spontaneous emission of atom sandwiched by dielectric slabs.
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).