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arXiv:1102.0393

Spontaneous emission of an atom in a uniform and nonuniform spaces

V. S. Zuev

Published Feb 2, 2011• 0 citations
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Abstract

On purpose to establish the differences in probabilities of spontaneous radiative emission of an atom in a free space and in a nonuniform space with a nanospheroid the field strength E and the density of states rho_E of the mode n_10 of a free space and of the TM_0 nanocylinder mode are defined. A nanocylinder is an approximate model of a nanospheroid. The probability of a spontaneous transition is proportional to E^2*rho_E in the both cases. It is found that the emission probability to the nanospheroid mode is hundreds times and more higher than the spontaneous emission probability in the free space.

DOI
10.48550/arxiv.1102.0393

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On purpose to establish the differences in probabilities of spontaneous radiative emission of an atom in a free space and in a nonuniform space with a nanospheroid the field strength E and the density of states rho_E of the mode n_10 of a free space and of the TM_0 nanocylinder mode are defined. A nanocylinder is an approximate model of a nanospheroid. The probability of a spontaneous transition is proportional to E^2*rho_E in the both cases. It is found that the emission probability to the nanospheroid mode is hundreds times and more higher than the spontaneous emission probability in the free space.
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.
The spontaneous decay rate of an excited atom placed near a dielectric cylinder is investigated. Special attention is paid to the case when the cylinder radius is small in comparison with radiation wavelength (nanofiber or photonic wire). In this case, the analytical expressions of the transition rates for different orientations of a dipole are derived. It is shown that the main contribution to decay rates is due to the quasistatic interaction of the atom dipole momentum with the nanofiber, and the contributions of guided modes are exponentially small. On the contrary, in the case when the radius of the fiber is only slightly less than the radiation wavelength, the influence of guided modes can be substantial. The results obtained are compared with the case of a dielectric nanospheroid and an ideally conducting wire.
The spontaneous emission rate $\ensuremath{\gamma}$ of a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing NNN wave channels, the distribution of $\ensuremath{\gamma}$ is given by $P(\ensuremath{\gamma})\ensuremath{\propto}{\ensuremath{\gamma}}^{N/2\ensuremath{-}1}(\ensuremath{\gamma}+{\ensuremath{\gamma}}_{0}{)}^{\ensuremath{-}N\ensuremath{-}1}$, where ${\ensuremath{\gamma}}_{0}$ is the free-space rate. For small NNN the most probable value of $\ensuremath{\gamma}$ is much smaller than the mean value ${\ensuremath{\gamma}}_{0}$.
The spontaneous emission of a set of NNN identical two-level atoms interacting with a quantized electromagnetic field is studied. The atoms are assumed to be close together compared to the mean wavelength of the emitted radiation, and their initial state is either a Dicke state or a superposition of the ground and excited state for each atom. Approximate expressions are obtained for transition probabilities, expectation values, and correlations as functions of time. The spontaneous emission for a very large separation of the atoms is also studied. In this case the directional properties of the emitted radiation, as well as the time within which the atoms decay to their ground state, depend on the position of each atom.
It is well known that spontaneous emission is not an intrinsic atomic property, but rather results from the coupling of the atom to the vacuum modes of the electromagnetic field. As such, it can be modified by tailoring the electromagnetic environment into which the atom can radiate. This was already realized by Purcell, who noted that the spontaneous emission rate can be enhanced if the atom placed inside a cavity is resonant with one of the cavity is resonant with one of the cavity modes, and by Kleppner, who discussed the opposite case of inhibited spontaneous emission. It has also been recognized that spontaneous emission need not be an irreversible process. Indeed, a system consisting of a single atom coupled to a single mode of the electromagnetic field undergoes a periodic exchange of excitation between the atom and the field. This periodic exchange remains dominant as long as the strength of the coupling between the atom and a cavity mode is itself dominant. 23 refs., 6 figs.