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Strong and ultrastrong light-matter coupling of small quantum systems near two-dimensional materials

Virginia N. Ciriano-Tejel

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

We present a full derivation of the coupling between a quantum emitter with two energy levels and the quantized electromagnetic field in media with absorption. This formalism has been applied to a system consisting of an emitter embedded in air in close proximity to a metallic surface. We find out that, by modifying the intrinsic decay rate of the emitter and the distance between, the emitter and the surface the system can reach the strong and even the ultrastrong coupling regime.

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We present a full derivation of the coupling between a quantum emitter with two energy levels and the quantized electromagnetic field in media with absorption. This formalism has been applied to a system consisting of an emitter embedded in air in close proximity to a metallic surface. We find out that, by modifying the intrinsic decay rate of the emitter and the distance between, the emitter and the surface the system can reach the strong and even the ultrastrong coupling regime.
Plasmons in nanostructured metals are widely utilized to trigger strong light-matter interactions with quantum light sources. While the nonclassical behavior of such quantum emitters (QEs) is well understood in this context, the role of quantum and surface effects in the plasmonic resonator is usually neglected. Here, we combine the Green's tensor approach with the Feibelman ddd-parameter formalism to theoretically explore the influence of quantum surface effects in metal-dielectric layered nanostructures on the relaxation dynamics of a proximal two-level QE. Having identified electron spill-out as the dominant source of quantum effects in jellium-like metals, we focus our study on sodium. Our results reveal a clear splitting in the emission spectrum, indicative of having reached the strong coupling regime, and, more importantly, non-Markovian relaxation dynamics of the emitter. Our findings establish that strong light-matter coupling is not suppressed by the emergence of nonclassical surface effects in the optical response of the metal.
Recent experiments have revealed ultrastrong coupling between light and matter as a promising avenue for modifying material properties, such as electrical transport, chemical reaction rates, and even superconductivity. Here, we explore (ultra)strong coupling as a means for manipulating the optical response of metamaterials based on ensembles of constituent units individually in the ultrastrong-coupling regime. We develop a framework based on linear response for quantum electrodynamical systems to study how light-matter coupling affects the optical response. We begin by applying this framework to find the optical response of a two-level emitter coupled to a single cavity mode, which could be seen as a ``meta-atom'' of a metamaterial built from repeated units of this system. We find optical behavior ranging from that of a simple two-level system (Lorentz-oscillator) to effectively transparent, as the coupling goes from the weak to deep strong-coupling regimes. We explore a one-dimensional chain of these meta-atoms, demonstrating the tunability of its optical behavior. Our scheme may ultimately provide a framework for designing metamaterials with low-loss, highly confined modes, as well as tunable (single-photon) nonlinearities.
Photon antibunching in the light scattered by single quantum emitters is one of the hallmarks of quantum optics, providing an unequivocal demonstration of the quantized nature of the electromagnetic field. Antibunching can be intuitively understood by the need for a two-level system lying in its lower state after emitting a photon to be re-excited into the upper one before a second emission can take place. Here we show that such a picture breaks down in the ultrastrong light–matter coupling regime, when the coupling strength becomes comparable to the bare emitter frequency. Specializing to the cases of both a natural and an artificial atom, we thus show that a single emitter coupled to a photonic resonator can emit bunched light. The result presented herein is clear evidence of how the ultrastrong coupling regime is able to change the nature of individual atoms.
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
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.
We develop a microscopic quantum theory of surface plasmon polaritons valid for arbitrary metal-dielectric geometries. Our framework is based on the Power-Zienau-Woolley representation of quantum electrodynamics, which provides an optimal separation between electronic and photonic degrees of freedom and is therefore particularly well suited for constructing quantum descriptions of polaritonic excitations in strongly dispersive media. Within this formulation, the fundamental electronic oscillator is identified as the bulk plasmon mode, which is nonperturbatively coupled to the radiative continuum of free photon modes. This coupling induces a geometry-dependent renormalization of the bulk plasma frequency, giving rise to confined plasmonic resonances. As specific applications, we recover the localized surface plasmon modes of metallic nanoparticles, including radiative frequency shifts and decay, as well as the exact dispersion relation of propagating surface plasmon polaritons at planar interfaces. Our quantum treatment further reveals that light-matter interactions at metal-dielectric interfaces are inherently in the ultrastrong coupling regime. As a result, in the quasistatic limit, the system exhibits unconventional ground-state quantum fluctuations that can be controlled through the refractive index. These results open new intriguing perspectives in the field of quantum plasmonics.