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Optics Express

Excitation enhancement in electric multipole transitions near a nanoedge

Kosuke Shibata, Satoshi Tojo, Daniel Bloch

Published Apr 14, 2017• 14 citations
Publisher

Abstract

We investigate enhancement of electric multipole excitations of atoms in the vicinity of an object with a nanoscale edge resulted from a large electromagnetic field gradient. We calculate the excitation efficiencies of a Rb atom around a nanoedge and find the excitations are enhanced by several orders of magnitude. The efficiencies with the change in the magnetic quantum number resolved are also examined. Each resolved efficiency shows rotationally symmetric spatial distribution, with continuous modification in shape from the far field to the near field. Furthermore, we estimate photon emission rates accompanied with multipole excitations in alkali (Rb and Cs) atoms and discuss the possibility to observe the enhancement in the multi-pole excitation in cold atoms.

DOI
10.1364/oe.25.009476

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We investigate enhancement of electric multipole excitations of atoms in the vicinity of an object with a nanoscale edge resulted from a large electromagnetic field gradient. We calculate the excitation efficiencies of a Rb atom around a nanoedge and find the excitations are enhanced by several orders of magnitude. The efficiencies with the change in the magnetic quantum number resolved are also examined. Each resolved efficiency shows rotationally symmetric spatial distribution, with continuous modification in shape from the far field to the near field. Furthermore, we estimate photon emission rates accompanied with multipole excitations in alkali (Rb and Cs) atoms and discuss the possibility to observe the enhancement in the multi-pole excitation in cold atoms.
We have studied a mathematical framework of higher-order multipole fields in the vicinity of optical nanoantennas. We have exemplified at suitably chosen Nanoantennas i.e. a Nano antenna which strongly enhances the quadruple field. The modification of excitation rates in quantum mechanical systems due to this quadrupolar enhancement was studied. The hybrid system consisting of an optical Nano antenna and a quantum mechanical three level system was studied in detail. A properly designed Nano-antenna can excite dipole for bidden transitions in three level systems due to the enhanced higher order multipole fields. The dynamics of the system is strongly altered by the presence of the nanoantenna and cannot be done by the quadrupolar enhancement alone. This can be achieved by enhancing higher order multipole fields near the antenna. A quadrupole transition as the dominant excitation channel in a three level system was considered. It was found that the enhancement of this transition significantly intensify subsequent emission processes with respect to altered emission characteristics. The effects depend on geometrical parameters; the properties of the optical nanoantenna can be tailored and hence allowed for direct implementations in spectroscopies schemes. The obtained results were found in good agreement with previously obtained results.
The spontaneous relaxation rates for an atom in free space and close to an absorbing surface are calculated to various orders of the electromagnetic multipole expansion. The spontaneous decay rates for dipole, quadrupole, and octupole transitions are calculated in terms of their respective primitive electric multipole moments and the magnetic relaxation rate is calculated for the dipole and quadrupole transitions in terms of their respective primitive magnetic multipole moments. The theory of electromagnetic-field quantization in magnetoelectric materials is used to derive general expressions for the decay rates in terms of the dyadic Green's function. We focus on the decay rates in free space and near an infinite half space. For the decay of atoms near to an absorbing dielectric surface, we find a hierarchy of scaling laws depending on the atom-surface distance zzz.
We suggest to excite dipole-forbidden transitions in quantum mechanical systems by using appropriately designed optical nanoantennas. The antennas are tailored such that their near field contains sufficiently strong contributions of higher-order multipole moments. The strengths of these moments exceed their free-space analogs by several orders of magnitude. The impact of such excitation enhancement is exemplarily investigated by studying the dynamics of a three-level system. It decays upon excitation by an electric quadrupole transition via two electric dipole transitions. Since one dipole transition is assumed to be radiative, the enhancement of this emission serves as a figure of merit. Such self-consistent treatment of excitation, emission, and internal dynamics as developed in this contribution is the key to predict any observable quantity. The suggested scheme may represent a blueprint for future experiments and will find many obvious spectroscopic and sensing applications.
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 photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green's tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily.
In addition to electric and magnetic multipoles, the expansion of current density also yields toroidal terms, a lesser-known family of multipoles. A recent proposal, I. Kuprov et al.\textit{et al.}et al., Science Adv. 8 abq6751 (2022), explores the possibility of a direct observation of optical toroidal transitions in hydrogen and alkali atoms in the presence of a large magnetic field that decouples the spin and the angular momentum of the electron. However, the difficulty of observing these transitions against the nearby electric dipole (E1) transitions were underestimated because of extra admixture coming from diamagnetic coupling. Here, we revisit the toroidal coupling in atoms, taking diamagnetic contribution into account, and discuss the technical challenges of observing toroidal coupling in atomic physics. We show that toroidal transition should be searched in transitions with low principal quantum numbers. The remaining strong electric-dipole contribution could be removed using an appropriate differential measurement.