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arXiv:1802.01871 · Physical Review A

Riesz-projection-based theory of light-matter interaction in dispersive nanoresonators

Lin Zschiedrich, Felix Binkowski, Niko Nikolay, Oliver J. Benson, Günter Kewes, Sven Burger

Published Oct 3, 2018• 61 citations
arXivHTMLPDF

Abstract

We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the structure and how it couples to a background, also in the presence of general dispersive media. Quantification on this level is essential for designing and analyzing topical nanophotonic setups, e.g., in quantum technology applications. We use a numerical implementation of the theory for computing modal and background decay rates of a single-photon emitter in a diamond nanoresonator.

DOI
10.1103/physreva.98.043806

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We introduce a theory to analyze the behavior of light emitters in nanostructured environments rigorously. Based on spectral theory, the approach opens the possibility to quantify precisely how an emitter decays to resonant states of the structure and how it couples to a background, also in the presence of general dispersive media. Quantification on this level is essential for designing and analyzing topical nanophotonic setups, e.g., in quantum technology applications. We use a numerical implementation of the theory for computing modal and background decay rates of a single-photon emitter in a diamond nanoresonator.
The control of interactions among quantum emitters through nanophotonic structures offers significant opportunities for quantum technologies. However, a rigorous theoretical description of the interaction of multiple quantum emitters with complex, dispersive dielectric objects remains challenging. Here, we introduce an approach based on the modified Langevin noise formalism that unveils the roles of both the noise polarization currents of the dielectrics and the vacuum fluctuations of the electromagnetic field scattered by the dielectrics. This work extends Refs. \cite{miano_quantum_2025} and \cite{miano_spectral_2025} to the general case of an arbitrary number of emitters. The proposed approach allows us to describe the dynamics of the quantum emitters for arbitrary initial quantum states of the electromagnetic environment, consisting of two independent bosonic reservoirs, a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density matrix. Specifically, we examine situations where both reservoirs are initially in thermal quantum states but have different temperatures. Understanding how these reservoirs shape the dynamics of the emitters is crucial for understanding light-matter interactions in complex electromagnetic environments and for improving intrinsic emitter properties within structured environments.
By embedding a single quantum emitter inside a nanoresonator that strongly localizes optical field, it is possible to achieve a very strong light-matter interaction. The strength of this interaction is characterized by the coherent emitter-field coupling strength (g), which increases with reduction in the optical mode volume and which also sets the limit on the operational speed of such a system. With InAs quantum dots inside GaAs photonic crystal cavities, coupling strengths of 40 GHz can be reached (much greater than the record values in atom-cavity QED systems), while nanometallic cavities could increase them over 100 GHz, as a result of the further reduction in the mode volume. Such a quantum dot-nanocavity platform is of interest for various quantum technologies, as well as in optical switching/computing.
The interaction of light with nanoscale structures is at the core of nano-optics. As the structures become smaller and smaller the laws of quantum mechanics will become apparent. In this limit, the discrete nature of atomic states gives rise to resonant light-matter interactions. In atoms, molecules, and nanoparticles, such as semiconductor nanocrystals and other “quantum confined” systems, these resonances occur when the photon energy matches the energy difference of discrete internal (electronic) energy levels. Owing to the resonant character, light-matter interaction can often be approximated by treating these quantum emitters as effective two-level systems, i.e. by considering only those two (electronic) levels whose difference in energy is close to the interacting photon energy ħω 0 . In this chapter we discuss quantum emitters that are used in optical experiments. We will discuss their use as single-photon sources and analyze their photon statistics. While the radiative properties of quantum emitters have been discussed in Chapter 8, this chapter focuses on the properties of the quantum emitters themselves. We adopt a rather practical perspective since more detailed accounts can be found elsewhere (see e.g. [1–4]). Types of quantum emitters The possibility of detecting single quantum emitters optically relies mostly on the fact that redshifted emission can be very efficiently discriminated against excitation light [5, 6]. This opens the road for experiments in which the properties of these emitters are studied or in which they are used as discrete light sources.
We present a modal analysis of a popular modeling framework for studying light-matter interaction between quantum emitters and general electromagnetic resonators, in which the active materials are modeled via Lorentzian material responses. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the active material and without fitting to calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anticrossing of the emitter and cavity resonance frequencies, and comparing with independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. To connect with the Jaynes-Cummings model, we relate the classical description of the emitter to the dipole moment in the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way. The methodology is expected to be useful in the design and interpretation of ongoing and future experiments and devices involving single-photon sources for quantum information and quantum communication technology.
The full information about the interaction between a quantum emitter and an arbitrary electromagnetic environment is encoded in the so-called spectral density. We present an approach for describing such interaction in any coupling regime, providing a Lindblad-like master equation for the emitter dynamics when coupled to a general nanophotonic structure. Our framework is based on the splitting of the spectral density into two terms. On the one hand, a spectral density responsible for the non-Markovian and strong-coupling-based dynamics of the quantum emitter. On the other hand, a residual spectral density including the remaining weak-coupling terms. The former is treated nonperturbatively with a collection of lossy interacting discrete modes whose parameters are determined by a fit to the original spectral density in a frequency region encompassing the quantum emitter transition frequencies. The latter is treated perturbatively under a Markovian approximation. We illustrate the power and validity of our approach through numerical simulations in three different setups, thus offering a variety of scenarios for a full test, including the ultra-strong coupling regime.