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Quantum Electronics

Effect of layered nanostructures on the linewidth of forbidden E2 transitions

Dmitry V. Guzatov, В. В. Климов

Published Aug 3, 2017• 1 citation
Publisher

Abstract

In the framework of classical electrodynamics, analytical expressions are derived and investigated for the linewidth of forbidden E2 transitions in an atom (molecule) located near layered metal – dielectric nanostructures. It is shown that the radiation intensity at the forbidden transition during detection in the half-space behind a layered nanostructure can significantly exceed the intensity during detection in the half-space where an atom (molecule) is located.

DOI
10.1070/qel16413

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In the framework of classical electrodynamics, analytical expressions are derived and investigated for the linewidth of forbidden E2 transitions in an atom (molecule) located near layered metal – dielectric nanostructures. It is shown that the radiation intensity at the forbidden transition during detection in the half-space behind a layered nanostructure can significantly exceed the intensity during detection in the half-space where an atom (molecule) is located.
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.
We investigate the mediation of symmetry-forbidden atomic transitions using plasmonic nanostructures. We show that the excitation of the electric dipole-forbidden, quadrupole-allowed $6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{-}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ transition in cesium may be enhanced by more than 6 orders of magnitude in the intense, inhomogeneous near field of a plasmonic nanoantenna. Using optical reciprocity, the enhancement can be understood to apply to spontaneous emission as well, allowing the fast and efficient optical detection of excited atoms.
The energy–level shifts and the change in the rate of spontaneous emission are calculated for an atom located at a distanceZ from a dielectric half–space. The dielectric is a non–dispersive and non–absorbing medium characterized by a constant real refractive indexn. The explicit analytic formulae derived are applicable for arbitrary values ofn. All results are analysed in the non-retarded and retarded limits, which apply to the atom being close to or far from the interface, respectively, i.e. toZ being small or large on the scale of a wavelength of a typical atomic transition. For ground-state atoms, the energy–level shift varies as 1/Z3 in the non–retarded regime and as 1/Z4 in the retarded regime, which agrees with the Casimir–Polder result for the limitn→α. For excited–state atoms, the energy–level shifts receive additional contributions that oscillate with the distanceZ from the interface.
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.
Modification of the resonance fluorescence spectrum of a two-level atom driven by a monochromatic field in the close proximity of a plasmonic nanostructure (metal sphere) is studied in detail. It is shown that one can control this spectrum by varying several key parameters: (i) the radius of the nanosphere, (ii) polarization of the incident radiation, and (iii) the atom's location around the nanosphere (its radial coordinate and polar angle in the spherical coordinate system). These parameters affect the local field enhancement and the modification of the radiative decay rate of the atom interacting with the nanosphere, which leads to modification of the resonance fluorescence spectrum of the atom (e.g., frequency shift of the satellite lines in the Mollow-type triplet, widths of the lines, and the spectrum intensity) by contrast with that in free space. The permittivity of the metal the nanosphere is made of is also an additional parameter, which defines the nonradiative decay. The latter in combination with other parameters allows continuous control of the transition from resonance fluorescence enhancement to its quenching.
The energy–level shifts of an atom located at a distance Z outside a dielectric half–space are calculated at finite temperatures. The refractive index of the medium is real and frequency independent; the limiting case of perfect reflectors is also considered. The analytic expressions for the energy–level shifts are analysed in various regimes of temperature and of the distance of the atom from the surface. The significance of thermal corrections in comparison with zero–temperature effects is analysed in each regime and discussed for recent experiments.