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Quantum Electronics

Properties of spontaneous radiation of an atom located near a cluster of two spherical nanoparticles

Dmitry V. Guzatov, В. В. Климов

Published Oct 31, 2005• 8 citations
Publisher

Abstract

The analytic solution of the problem of spontaneous decay of an atom near a cluster of two perfectly conducting nanospheres is found. It is shown that spontaneous decay rates can considerably decrease or increase depending on the system geometry. In particular, within the framework of our model, the decay rate of an atom located between closely spaced spheres and having the transition dipole moment directed along the symmetry axis can be arbitrarily high.

DOI
10.1070/qe2005v035n10abeh013008

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The analytic solution of the problem of spontaneous decay of an atom near a cluster of two perfectly conducting nanospheres is found. It is shown that spontaneous decay rates can considerably decrease or increase depending on the system geometry. In particular, within the framework of our model, the decay rate of an atom located between closely spaced spheres and having the transition dipole moment directed along the symmetry axis can be arbitrarily high.
The optical properties of an atom located near a cluster of two arbitrarily arranged nanospheres of an arbitrary composition are studied. Changes in the spontaneous decay rates of excited states and emission frequency shifts are considered for different orientations of the dipole moment and different positions of the atom with respect to the cluster. It is shown that a two-nanosphere cluster can be used to control efficiently the spontaneous decay rates of excited states of the atom by changing the distance between spheres. It is found that spontaneous decay rates of the excited states of an atom located between silver nanospheres and having the dipole moment directed along the axis connecting the centres of spheres can increase by a factor of 10 5 and more when nanospheres are brought closer together.
The effect of nanobodies, i.e., the bodies whose size is small compared to the emission wavelength, on spontaneous emission of an atom located near them is considered. The results of calculations performed within the framework of quantum and classical electrodynamics are presented both in analytic and graphical forms and can be readily used for planning experiments and analysis of experimental data. It is shown that nanobodies can be used to control efficiently the rate of spontaneous transitions. Thus, an excited atom located near a nanocylinder or a nanospheroid pole, whose transition dipole moment is directed normally to the nanobody surface, can decay with the rate that is tens and hundreds times higher than the decay rate in a free space. In the case of some (negative) dielectric constants, the decay rate can increase by a factor of 10 5 —10 6 and more. On the other hand, the decay of an excited atom whose transition dipole moment is directed tangentially to the nanobody surface substantially slows down. The probability of nonradiative decay of the excited state is shown to increase substantially in the presence of na-nobodies possessing losses.
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.
In the framework of classical electrodynamics we have obtained and investigated analytical expressions for the radiation linewidth of forbidden E2 transitions in an atom located near a dimer of spherical particles. It is shown that the material of particles, their location and size have a significant effect on the linewidth of the E2 transition in the atom. It is found that in the gap between metal spherical nanoparticles, the linewidth of E2 transitions in the atom can take on substantially larger values than in the case of an atom near a single metal nanoparticle.
The structure of spontaneous decay of atoms in the vicinity of a surface is shown to be determined by spatial symmetries. The spontaneous-decay operator for a degenerate two level atom is derived, and with symmetry considerations the number of free parameters is reduced to two. Only the dimensionless and normalized inverse lifetimes b-parallel and b-perpendicular for a parallel and perpendicular dipole moment with respect to the surface, respectively, enter the expression for the relaxation operator for any atom near any surface. These two parameters incorporate the atom-surface-distance dependence of all Einstein coefficients for spontaneous decay, and all optical properties of the substrate material. It is shown that the specific features of spontaneous decay are mainly geometrical, and a consequence of symmetries of the vacuum radiation field, irrespective of the presence of the atom. With an example, it is shown how the parameters b-parallel and b-perpendicular can be calculated in a particular case. It is also pointed out that an explicit quantization of the radiation field can be avoided, even though the process of spontaneous emission is purely quantum mechanical.