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Tailoring two-photon spontaneous emission: Framework and nanoantenna design for interference and directionality

Steve Smeets, Björn Maes, Gilles Rosolen

Published Jan 1, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1051/epjconf/202430908012

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•Jan 1, 2020•6 citations
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.
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.
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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.
The rate of spontaneous emission is known to depend on the environment of a emitter, and the enhancement of one-photon emission in a resonant cavity is known as the Purcell effect. Here we develop a theory of spontaneous two-photon emission for a general electromagnetic environment including inhomogeneous dispersive and absorptive media. This theory is used to evaluate the two-photon Purcell enhancement in the vicinity of metallic nanoparticles and demonstrates that the surface-plasmon resonances supported by these particles can increase the emission rate by more than two orders of magnitude. The control over two-photon Purcell enhancement given by tailored nanostructured environments could provide an emitter with any desired spectral response and may serve as an ultimate route for designing light sources with novel properties.
We analyze the two-time intensity correlation function of the fluorescent field emitted by a three-level V-type quantum emitter located in the vicinity of a two-dimensional periodic plasmonic nanostructure. Due to the interaction of the quantum emitter with an electromagnetic field, the ground state population is excited to the upper levels, presenting decay due to spontaneous emission. The distinctive characteristic of this system is that the decay rates for a quantum emitter with dipole orientation perpendicular and normal to the surface of the nanostructure array exhibit large differences which vary with the distance between the quantum emitter and the two-dimensional nanoparticle array. This leads to simulation of quantum interference effects in spontaneous emission. By studying the dependence of the two-time intensity correlation function on specific physical parameters of the hybrid structure, including the intensity of the applied field, the detuning from resonance, the distance between the quantum emitter and the plasmonic nanostructure, as well as the spacing between the upper levels, we demonstrate a strong modification of the two-time intensity correlation functions. We also identify the conditions under which the two-time intensity correlation function is maximized, an effect which is associated to the bunching to antibunching transition of the emitted photons.
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.