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Physical Review A

General framework for two-photon spontaneous emission near plasmonic nanostructures

S. Smeets, Björn Maes, Gilles Rosolen

Published Jun 27, 2023• 12 citations
Publisher

Abstract

The authors develop a framework for efficient calculation of two-photon spontaneous emission in arbitrary nanostructures using one-photon Purcell factors. The formalism will aid the design of entangled two-photon sources for various applications, including quantum technologies and spectroscopy.
DOI
10.1103/physreva.107.063516

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We summarize our studies of the plasmonic enhancements of the spontaneous two-photon emission. In particular, we draw attention to the rigorous investigation of quantum framework for the multi-photon spontaneous decay rates in an environment with arbitrary structure of electromagnetic modes. We demonstrate that nanostructured environment can be used for tailoring the basic characteristics of the two-photon emission such as spectrum, lifetime, and entanglement. Moreover, careful engineering of the two-photon Purcell enhancement may provide any desired spectral response and may serve as an ultimate route for designing light sources with novel properties.
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 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.
The ability to harness light-matter interactions at the few-photon level plays a pivotal role in quantum technologies. Single photons-the most elementary states of light-can be generated on demand in atomic and solid state emitters. Two-photon states are also key quantum assets, but achieving them in individual emitters is challenging because their generation rate is much slower than competing one-photon processes. We demonstrate that atomically thin plasmonic nanostructures can harness two-photon spontaneous emission, resulting in giant far field two-photon production, a wealth of resonant modes enabling tailored photonic and plasmonic entangled states, and plasmon-assisted single-photon creation orders of magnitude more efficient than standard one-photon emission. We unravel the two-photon spontaneous emission channels and show that their spectral line shapes emerge from an intricate interplay between Fano and Lorentzian resonances. Enhanced two-photon spontaneous emission in two-dimensional nanostructures paves the way to an alternative efficient source of light-matter entanglement for on-chip quantum information processing and free-space quantum communications.
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.
Single-photon and correlated two-photon sources are important elements for optical information systems. Nonlinear downconversion light sources are robust and stable emitters of single photons and entangled photon pairs. However, the rate of downconverted light emission, dictated by the properties of low-symmetry nonlinear crystals, is typically very small, leading to significant constraints in device design and integration. In this Letter, we study principles of spontaneous emission control (i.e., the Purcell effect) generalized to describe the enhancement of nonlinear generation of quantum light through spontaneous parametric downconversion. We develop a theoretical framework based on eigenmode analysis to study quantum nonlinear emission in a general anisotropic, dispersive, and lossy media. Our theory provides an unprecedented insight into the emission process. We find that spontaneous parametric downconversion in a media with hyperbolic dispersion is broadband and phase-mismatch-free. We further predict a significant enhancement of the downconverted emission rate in experimentally realistic nanostructures. Our theoretical formalism and approach to Purcell enhancement of nonlinear optical processes provides a framework for description of quantum nonlinear optical phenomena in complex nanophotonic structures.