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Atomic decay rates in a dielectric medium: a test of the standard QED Hamiltonian

Seng‐Tiong Ho, Prem Kumar

Published May 21, 1990• 0 citations
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Abstract

Recently, there has been great experimental interest in studying the behavior of active atoms embedded in a dielectric medium because of the possibility of manipulating the spontaneous decay rate of these atoms.1 More important, the decay rate of such atoms warrants special study as it is affected by additional physical factors not present in cavity QED. We show that the usual value given for one of these additional factors is incorrect, and the correct value can be related to a basic property of the standard QED Hamiltonian.

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Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
Recently, there has been great experimental interest in studying the behavior of active atoms embedded in a dielectric medium because of the possibility of manipulating the spontaneous decay rate of these atoms.1 More important, the decay rate of such atoms warrants special study as it is affected by additional physical factors not present in cavity QED. We show that the usual value given for one of these additional factors is incorrect, and the correct value can be related to a basic property of the standard QED Hamiltonian.
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.
Decay of an excited molecule (atom) has been considered in an absorbing dielectric. The decay rate has been derived calculating the total rate of excitation transfer to the surrounding species. The contribution due to the far-zone energy transfer yields the rate of photon emission in the absorbing medium. The analysis is based on a microscopic QED theory of energy transfer in condensed phases. As a result, effects due to discreteness of the medium (such as the local field effects) are reflected intrinsically in the decay rates. The microscopic approach supports the previous introduction of the local field factors on a phenomenological basis.
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 present calculations of the rates of decay of an excited atom embedded in an absorbing dielectric. Decay can occur by spontaneous emission into transverse radiative modes of the electromagnetic field and by Joule heating via longitudinal coupling of the atom to the dielectric. The spontaneous emission (transverse) decay rate is modified in a dielectric, being the free-space rate multiplied by the real part of the refractive index at the transition frequency of the atom. There is a further modification due to the difference between the macroscopic dielectric field and the local field at the position of the atom. In addition there is a longitudinal decay rate which is proportional to the imaginary part of the dielectric constant and therefore vanishes in non-absorbing media. We derive expressions for each of these rates of decay and discuss the physical mechanisms leading to them.
The spontaneous decay rates of atoms can be altered by embedding them in a bulk dielectric medium. The alteration of the decay rates depends on three physical factors: a photon density of state factor, a local-field correction factor, and a field normalization factor. There are conflicting expressions in the literature for the local-field correction and field normalization factors. However, it is expected that for a thin slab a change in the total decay rate for an embedded atom or exciton should change when the slab thickness is approximately ( λ )/2πn. We are fabricating dielectric slabs with dimensions in this range that will allow us to demonstrate both the dependence of decay rate on the slab thickness and the index of the surrounding medium. Our experiment involves a technique for embedding thin GaAs/AlGaAs quantum well structures in different dielectric media with n ranging 1.5–3.5 and measuring the spontaneous decay rates.