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Journal of Modern Optics

Spontaneous emission rate and level shift of an atom inside a dielectric microsphere

В. В. Климов, M. Ducloy, Vladilen S Letokhov

Published Mar 1, 1996• 58 citations
Publisher

Abstract

The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.

DOI
10.1080/09500349608232764

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The transition frequency shift and the spontaneous decay rate (the radiative linewidth) variation of an atom placed in a transparent dielectric microsphere are presented. It is demonstrated that with the refractive index of the microsphere material (e.g. diamond) being high enough, the size of the microsphere can be selected such that the spontaneous decay rate decreases (or increases) several times, depending on the position of the atom. At the same time, the atomic transition frequency shift proves to depend more strongly on the position of the atom, reaching high values near the surface of the microsphere.
Spontaneous decay of an excited atom near a dispersing and absorbing microsphere of given complex permittivity that satisfies the Kramers-Kronig relations is studied, with special emphasis on a Drude-Lorentz permittivity. Both the whispering gallery field resonances below the band gap (for a dielectric sphere) and the surface-guided field resonances inside the gap (for a dielectric or a metallic sphere) are considered. Since the decay rate mimics the spectral density of the sphere-assisted ground-state fluctuation of the radiation field, the strengths and widths of the field resonances essentially determine the feasible enhancement of spontaneous decay. In particular, strong enhancement can be observed for transition frequencies within the interval in which the surface-guided field resonances strongly overlap. When material absorption becomes significant, then the highly structured emission pattern that can be observed when radiative losses dominate, reduces to that of a strongly absorbing mirror. Accordingly, nonradiative decay becomes dominant. In particular, if the distance between the atom and the surface of the microsphere is small enough, the decay becomes purely nonradiative.
The rates of spontaneous emission and stimulated emission and absorption for a two-level atom in a dielectric microsphere are calculated for weak E1 coupling. The A coefficient for spontaneous emission is proportional to the zero-point fluctuation of the electric field ℰij evaluated in the previous paper [ J. Opt. Soc. Am. B4, 1995 ( 1987)], which shows sharp resonances in frequency (Q > 104). It is verified that the ratio of the A and B coefficients is determined by the spectral density of thermal radiation. The level shift tends to repel the transition line away from the cavity resonance.
We study spontaneous radiative decay of translational levels of an atom in the vicinity of a semi-infinite dielectric. We systematically derive the microscopic dynamical equations for the spontaneous decay process. We calculate analytically and numerically the radiative linewidths and the spontaneous transition rates for the translational levels. The roles of the interference between the emitted and reflected fields and of the transmission into the evanescent modes are clearly identified. Our numerical calculations for the silica-cesium interaction show that the radiative linewidths of the bound excited levels with large enough but not too large vibrational quantum numbers are moderately enhanced by the emission into the evanescent modes and those for the deep bound levels are substantially reduced by the surface-induced redshift of the transition frequency.
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 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.
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.