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arXiv:1110.3927 · Physical Review B

Controlling the dynamics of quantum mechanical systems sustaining dipole-forbidden transitions via optical nanoantennas

Robert Filter, Stefan Mühlig, Toni Eichelkraut, Carsten Rockstuhl, F. Lederer

Published Jul 5, 2012• 73 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.86.035404

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•Jan 1, 2012•0 citations
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 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.
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.
Summary form only given. Although it is often assumed that all light-matter interactions at optical frequencies are mediated by electric dipole transitions, strong optical-frequency magnetic dipoles do exist. In fact, we see magnetic dipole emission every day from the many lanthanide ions (such as erbium, europium, and terbium) that help to illuminate everything from fluorescent lighting to telecom fiber amplifiers. Higher-order processes such as magnetic dipole and electric quadrupole transitions also play an important part in the light emission from transition metal ions and semiconductor quantum dots. Nevertheless, most applications have overlooked the device implications of these electric-dipole-forbidden transitions throughout the visible and near-infrared regime, and their contributions to many important emitters have not been fully characterized.In this presentation, we will experimentally characterize the "forbidden" transitions in a range of solid-state emitters and investigate their applications and implications for nanophotonics. We will examine the electric dipole approximation commonly used to describe light-matter interactions and discuss naturally occurring systems that exhibit higher-order magnetic dipole and electric quadrupole emission. We will illustrate how these nanoscale quantum transitions can provide both a new way to probe magnetic light-matter interactions and a new degree of design freedom for active electronic and photonic devices. Specifically, we will demonstrate how the different symmetries of multipolar transitions can be exploited to identify, quantify, and control light emission, even at sub-lifetime scales. Despite similar radiation patterns, magnetic and electric dipole emitters have different symmetries with respect to polarization and phase. Thus, in an inhomogeneous environment, we can tailor interference effects and the local density of optical states to selectively enhance either electric or magnetic dipole emission [1,2]. To examine the scope of such higher-order transitions, we will present quantum mechanical calculations that identify all the magnetic dipole and electric quadrupole emission lines in the trivalent lanthanide series in the visible to near-infrared spectrum [3]. Then, we will present an energyand momentum-resolved spectroscopy technique to directly quantify the electric and magnetic dipole contributions from any mixed transition. [4] Using energy-momentum spectroscopy, we will experimentally examine the higher order transitions in lanthanide ions [4,5], transition metal ions [6], and epitaxial quantum dots [7]. If time permits, we will then show how the symmetry differences between magnetic and electric dipoles can be used to address specific electronic states [6] and to dynamically tune emission spectra at sub-lifetime-scales [8].
We develop a framework that computes two-photon spontaneous emission (TPSE) spectra of a quantum emitter near an arbitrarily shaped nanostructure. The model considers the interaction up to the electric quadrupolar order, which is relevant for nanophotonic structures sustaining strongly confined fields that are used to enhance and to tailor spontaneous emission processes. Moreover, we consider interference effects between multipolar two-photon emission channels, for the first time to our knowledge. First, we show for a s → s transition of a hydrogen atom placed under a silver plasmonic nanodisk a substantial enhancement in the photon-pair emission rates by 5 and 11 orders of magnitude for the two-electric dipole (2ED) and two-electric quadrupole (2EQ) transitions, respectively. Then for the same emitter under a plasmonic graphene nanotriangle, we demonstrate a breakdown of the electric dipole approximation in the TPSE process where the interference between the 2ED and 2EQ transitions is important, as it increases the total rate by 63 %. Third, we explore platforms where entangled photons of different energy are emitted in the far-field in different directions. In the end, our framework is a complete tool to design emitters and nanostructures for the TPSE process, leading to a rich assortment of functional nanoantennas.
The natural electromagnetic modes spontaneously emitted by an atom in free space are spherical vector waves (SVWs). Each SVW mode is uniquely linked to a specific dynamical--spherical--multipole--moment of the atomic system. In this work, we introduce a general formalism for evaluating spherical multipole transition rates under different boundary conditions, considering the superposition between a given SVW and the modes resulting from the boundary conditions. This formalism is applied to study the radiative properties of an atomic system trapped near the focus of a 4πππ optical array. By appropriately selecting the external light field, the juxtaposed lenses of the optical array allow the atom to be illuminated with approximate spherical vector waves. Explicit expressions for the resulting multipole transition rates are presented as a function of the numerical aperture of the lenses. The feasibility of enhancing and inhibiting electric dipole-forbidden transitions using such an array, under current experimental capabilities, is briefly discussed.
We provide an overview of our latest activities on using optical meta-atoms to mediate the interaction of light with molecular systems. The first subject concerns the control of the dynamics of quantum mechanical systems featuring dipole-forbidden transitions. There, the meta-atoms provide local fields that exhibit a large electric quadrupole moment. The second issue is related to the enhancement of the upconversion process in erbium-doped glasses. There, the optical meta-atom has to show a resonance at multiple frequencies which matches the term schema of erbium. It will be concluded that optical meta-atoms are promising to enable inaccessible processes in a quantum mechanical system which will allow groundbreaking applications.