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Undo approximations: Modeling quantum emitters in proximity of nanophotonic structures

Mhamad Hantro, Gilles Rosolen, Colin Jean-Louis Van Dyck

Published Nov 27, 2023• 0 citations
OpenAlex

Abstract

Several methods have been developed to calculate the spontaneous emission rate for extended emitters in the vicinity of a nanophotonic structure.While taking the emitter's spatial extension, these methods have taken approximations regarding the full interaction, either by coupling to one single plasmonic mode or adding higher order rates individually thus neglecting interference terms.Here we apply a new framework [1] to extended emitters, by which, all these interactions can be considered, and we show both under, and over-estimation of the Purcell Factor when using a point-dipole.

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Several methods have been developed to calculate the spontaneous emission rate for extended emitters in the vicinity of a nanophotonic structure.While taking the emitter's spatial extension, these methods have taken approximations regarding the full interaction, either by coupling to one single plasmonic mode or adding higher order rates individually thus neglecting interference terms.Here we apply a new framework [1] to extended emitters, by which, all these interactions can be considered, and we show both under, and over-estimation of the Purcell Factor when using a point-dipole.
We present a novel photonic model that enables an efficient computation of the two-photon Purcell effect of a quantum emitter in the vicinity of an arbitrary photonic structure. Our framework is relevant for the plasmonic nanocavities used to enhance higher-order light-matter interactions, as it goes beyond the dipolar approximation. The computation of Purcell factors through classical electromagnetic simulations determines the influence of the environment without tedious analytic calculations. We demonstrate that placing a hydrogen-like emitter close to a silver nanodisk enhances the transition rate by 5 and 11 orders of magnitude via electric dipole and quadrupole two-photon transitions, respectively. This process has exciting implications for future research, including the potential for efficient entangled two-photon sources.
We develop a rigorous theory for nanophotonic cooperative spontaneous emission of an ensemble of quantum emitters near matter, which also incorporates absorption. Such theory is highly requested since one should expect that in the field of nanophotonics the close-by emitters will emit cooperatively simultaneously with strong interaction with the exotic metamaterial complex dielectric function. The closed-form model developed here considers the buildup both of interemitter correlation over time through emitter transitions via the mutual field and of geometry-induced spatial correlation. The presence of matter alters the local density of states (LDOS), resulting in modified decay rate and emission intensity for the entire ensemble relative to values of spontaneous emission in free space. The superradiant total emission is separable into a quantum-mechanical time-dependent part and a classical space-dependent part, both being functions of the LDOS. Two distinct radiative emitter--far-field coupling mechanisms, which together account for the superradiant emission, are obtained---the coupling of every individual emitter with the far field and the coupling of emitter pairs to the far field. The calculations for superradiating emitters near silver and near-zero epsilon (NZE) materials were performed with the following results: the silver sphere augments the superradiant far-field intensity and rate by up to 400 and 1000%, respectively, while the NZE sphere enhances the far-field intensity and rate of the superradiance by approximately 1400 and 400%, respectively.
In this paper, we study the collective effects which appear as a pair of quantum emitters is positioned in close vicinity to a plasmonic nanoparticle. These effects include multipole-multipole interaction and collective decay, the strengths and rates of which are modified by the presence of the nanoparticle. As a result, entanglement is generated between the quantum emitters, which survives in the stationary state. To evaluate these effects, we exploit the Green's tensor-based quantization scheme in the Markovian limit, taking into account the corrections from light-matter coupling channels higher than the electric dipole. We find these higher-order channels to significantly influence the collective rates and degree of entanglement, and in particular, to qualitatively influence their spatial profiles. Our findings indicate that, apart from quantitatively modifying the results, the higher-order interaction channels may introduce asymmetry into the spatial distribution of the collective response.
Summary form only given. In the pioneering work of Purcell, the possibility to control spontaneous emission lifetimes of quantum emitters by tailoring their electromagnetic surroundings was widely investigated and verified in various types of cavities or band-gap environments. This includes semiconductor microstructures, photonic crystals, and plasmonic nanoparticles. Due to the extraordinary ability of plasmonic nanostructures to confine light into subwavelength spatial domains, steps beyond the paradigmatic electric dipole approximation in the theoretical description of this process may be necessary. In this contribution, we focus on the case of multiple in general nonidentical two-level emitters, sharing the same electromagnetic surroundings, whose local density of states could be tailored by a neighbouring nanostructure. In this case, the surroundings may serve as a long-distance emitter-emitter interaction carrier, or it may trigger collective emission processes, in analogy to Dicke superradiance. We describe these phenomena taking into account the electric dipole, magnetic dipole and electric quadrupole components of light-matter interaction Hamiltonian.
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.
When an emitter ensemble interacts with the electromagnetic field, dipole-dipole interactions are induced between the emitters. The magnitude and shape of these interactions are fully determined by the specific form of the electromagnetic field modes. If the emitters are placed in the vicinity of a nanophotonic waveguide, such as a cylindrical nanofiber, the complex functional form of these modes makes the analytical evaluation of the dipole-dipole interaction cumbersome and numerically costly. In this work, we provide a full detailed description of how to successfully calculate these interactions, outlining a method that can be easily extended to other environments and boundary conditions. Such exact evaluation is of importance as, due to the collective character of the interactions and dissipation in this kind of systems, any small modification of the interactions may lead to dramatic changes in experimental observables, particularly as the number of emitters increases. We illustrate this by calculating the transmission signal of the light guided by a cylindrical nanofiber in the presence of a nearby chain of emitters.