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Physical Review Letters

Decay Rate of an Excited Atom in a Moving Medium

Reza Matloob

Published Feb 10, 2005• 12 citations
Publisher

Abstract

The effect of a uniformly moving medium on the decay rate of an excited atom is calculated. When the local field effects are neglected, the free space decay rate is modified by a factor which is a complicated function of refractive index, permeability, and velocity of the medium. It is shown that the decay rate vanishes if the velocity of the medium exceeds the phase velocity of light in the stationary medium.

DOI
10.1103/physrevlett.94.050404

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The effect of a uniformly moving medium on the decay rate of an excited atom is calculated. When the local field effects are neglected, the free space decay rate is modified by a factor which is a complicated function of refractive index, permeability, and velocity of the medium. It is shown that the decay rate vanishes if the velocity of the medium exceeds the phase velocity of light in the stationary medium.
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.
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 E1E1E1 & M1M1M1 Spontaneous Decay Rates for an Emitter Inside a Cavity Within a Medium
We discuss the E1E1E1 and M1M1M1 spontaneous decay rates of the an emitter residing inside of a real cavity carved out of a vast, uniform, homogenous, isotropic, linear, lossless, dispersionless, and continuous medium. The ratio of the medium rate to vacuum rate is given by Γm/Γ0=[G(u)]2n3/uΓ_m/Γ_0 = [G(u)]^2 n^3 / uΓm​/Γ0​=[G(u)]2n3/u, where G(u)=3u/(2u+1)G(u) = 3u/(2u+1)G(u)=3u/(2u+1) is the local field correction factor, n=εμ/(ε0μ0)n = \sqrt{εμ/(ε_0μ_0)}n=εμ/(ε0​μ0​)​ is the index of refraction of the medium, ε(ε0)ε(ε_0)ε(ε0​) is the electric permitivity of the medium (vacuum), μ(μ0)μ(μ_0)μ(μ0​) is the magnetic permeability of the medium (vacuum), and u=ε/ε0u = ε/ε_0u=ε/ε0​ for E1E1E1 transitions or u=μ0/μu = μ_0/μu=μ0​/μ for M1M1M1 transitions.
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.
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.
The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantum-mechanical model. The medium is a collection of randomly distributed thermally excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.