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Photonic technologies continue to drive the quest for new optical materials with unprecedented responses. A major frontier in this field is the exploration of nonlocal (spatially dispersive) materials, going beyond the local, wavevector-independent assumption traditionally made in optical material modeling. On one end, the growing interest in plasmonic, polaritonic and quantum materials has revealed naturally occurring nonlocalities, emphasizing the need for more accurate models to predict and design their optical responses. This has major implications also for topological, nonreciprocal, and time-varying systems based on these material platforms. Beyond natural materials, artificially structured materials--metamaterials and metasurfaces--can provide even stronger and engineered nonlocal effects, emerging from long-range interactions or multipolar effects. This is a rapidly expanding area in the field of photonic metamaterials, with open frontiers yet to be explored. In the case of metasurfaces, in particular, nonlocality engineering has become a powerful tool for designing strongly wavevector-dependent responses, enabling enhanced wavefront control, spatial compression, multifunctional devices, and wave-based computing. Furthermore, nonlocality and related concepts play a critical role in defining the ultimate limits of what is possible in optics, photonics, and wave physics. This Roadmap aims to survey the most exciting developments in nonlocal photonic materials, highlight new opportunities and open challenges, and chart new pathways that will drive this emerging field forward--toward new scientific discoveries and technological advancements.

We investigate the directional characteristics of photon statistics in dimers of quantum emitters. For their analysis, we construct a two-point second-order correlation function that allows us to find a new mechanism for photon anticorrelation, termed as geometric antibunching. This phenomenon is completely agnostic to the quantum state of the emitters and emerges from quantum interference effects due to the indistinguishability of different two-photon optical pathways. Finally, we explore its occurrence in emitters placed in the vicinity of a flat substrate and a nanosphere, demonstrating its tunnability through the different material and geometric parameters of these structures., Comment: 11 pages, 6 figures

We provide a comprehensive study of the capabilities of modulated electron wavefunctions for the preparation and readout of the quantum state of the quantum emitters (QEs) they interact with. First, we consider perfectly periodic electron combs, which do not produce QE-electron entanglement, preserving the purity of the QE while inducing Rabi-like dynamics in it. We extend our findings to realistic, non-ideally modulated electron wavepackets, showing that the phenomenology persists, and exploring their use to prepare the emitter in a desired quantum state. Thus, we establish the balance that electron comb size, emitter radiative decay, and electron-emitter coupling strength must fulfil in order to implement our ideas in experimentally feasible platforms. Finally, moving into the limit of small electron combs, we reveal that these wavefunctions allow for quantum state tomography of their target, providing access not only to the populations, but also the coherences of the QE density matrix. We believe that our theoretical results showcase modulated free-electrons as very promising tools for quantum technologies based on light-matter coupling., Comment: 15 pages, 5 figures

Electron spin resonance (ESR) spectroscopy in scanning tunneling microscopy (STM) has enabled probing the electronic structure of single magnetic atoms and molecules on surfaces with unprecedented energy resolution, as well as demonstrating coherent manipulation of single spins. Despite this remarkable success, the field could still be greatly advanced by a more quantitative understanding of the ESR-STM physical mechanisms. Here, we present a theory of ESR-STM which quantitatively models not only the ESR signal itself, but also the full background tunneling current, from which the ESR signal is derived. Our theory is based on a combination of Green's function techniques to describe the electron tunneling and a quantum master equation for the dynamics of the spin system along with microwave radiation interacting with both the tunneling current and the spin system. We show that this theory is able to quantitatively reproduce the experimental results for a spin-1/2 system (TiH molecules on MgO) across many orders of magnitude in tunneling current, providing access to the relaxation and decoherence rates that govern the spin dynamics due to intrinsic mechanisms and to the applied bias voltage. More importantly, our work establishes that: (i) sizable ESR signals, which are a measure of microwave-induced changes in the junction magnetoresistance, require surprisingly high tip spin polarizations, (ii) the coupling of the magnetization dynamics to the microwave field gives rise to the asymmetric ESR spectra often observed in this spectroscopy. Additionally, our theory provides very specific predictions for the dependence of the relaxation and decoherence times on the bias voltage and the tip-sample distance. Finally, with the help of electromagnetic simulations, we find that the transitions in our ESR-STM experiments can be driven by the ac magnetic field at the junction., Comment: 17 pages, 6 figures

Memoryless (Markovian) system-bath interactions are of fundamental interest in physics. While typically, the absence of memory originates from the characteristics of the bath, here we demonstrate that it can result from the system becoming lossy due to the Markovian interaction with a second bath. This uncovers an interesting interplay between independent baths and suggests that Markovianity is ``contagious'', i.e., it can be transferred from one bath to another through the system with which they both interact. We introduce a Bloch-Redfield-inspired approach that accounts for this distinct origin of Markovianity and uniquely combines non-Hermitian Hamiltonian formalism with master equations. This method significantly improves the description of the interaction between a lossy system (associated with a Lindblad master equation) and a non-Markovian bath, reducing the computational demands of complex system-bath setups across various fields.

Plasmonic nanoantennas, metallodielectric structures with engineered size and shape, have attracted much attention lately as they make the control of the directionality and temporal characteristics of light emitted by fluorophores possible. Nanoantennas exploit light-matter interactions mediated by Localized Surface Plasmon Resonances and, so far, have been demonstrated using metallic nanoparticles or other metallic nanostructures. Plasmonic picocavities, i.e., plasmonic cavities with mode volumes below 1 cubic nanometer, could act as antennas to mediate light-matter interaction even more efficiently than their nanoscale counterparts due to their extreme field confinement, but the directionality on their emission is difficult to control. In this work, we show that the plasmonic picocavity formed between the tip of a Scanning Tunnelling Microscope and a metal surface with a monoatomic step shows directional emission profiles and, thus, can be considered as a realization of a picoantenna. Comparison with electromagnetic calculations demonstrates that the observed directionality arises from light emission tilting of the picocavity plasmons. Our results, thus, pave the way to exploiting picoantennas as an efficient way to control light-matter interaction at the nanoscale.

We present a proposal for a tunable source of single photons operating in the terahertz (THz) regime. This scheme transforms incident visible photons into quantum THz radiation by driving a single polar quantum emitter with an optical laser, with its permanent dipole enabling dressed THz transitions enhanced by the resonant coupling to a cavity. This mechanism offers optical tunability of properties such as the frequency of the emission or its quantum statistics (ranging from antibunching to entangled multi-photon states) by modifying the intensity and frequency of the drive. We show that the implementation of this proposal is feasible with state-of-the-art photonics technology., Comment: 18 pages, 14 figures

The manipulation of coupled quantum excitations is of fundamental importance in realizing novel photonic and optoelectronic devices. We use electroluminescence to probe plasmon-exciton coupling in hybrid structures consisting of a nanoscale plasmonic tunnel junction and few-layer two-dimensional transition-metal dichalcogenide transferred onto the junction. The resulting hybrid states act as a novel dielectric environment that affects the radiative recombination of hot carriers in the plasmonic nanostructure. We determine the plexcitonic spectrum from the electroluminescence and find Rabi splittings exceeding 50 meV in strong coupling regime. Our experimental findings are supported by electromagnetic simulations that enable us to explore systematically, and in detail, the emergence of plexciton polaritons as well as the polarization characteristics of their far-field emission. Electroluminescence modulated by plexciton coupling provides potential applications for engineering compact photonic devices with tunable optical and electrical properties., Comment: 28 pages, 4 figures, plus supplementary information (24 pages, 14 figures)

Single-photon sources are in high demand for quantum information applications. A paradigmatic way to achieve single-photon emission is through anharmonicity in the energy levels, such that the absorption of a single photon from a coherent drive shifts the system out of resonance and prevents absorption of a second one. We identify a novel mechanism for single-photon emission through non-Hermitian anharmonicity, i.e., anharmonicity in the losses instead of in the energy levels. We demonstrate the mechanism in two types of systems, including a feasible setup consisting of a hybrid metallodielectric cavity weakly coupled to a two-level emitter, and show that it induces high-purity single-photon emission at high repetition rates.

In the last decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light-matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On the one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light-matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modelling of interacting molecular and optical states with increasing complexity.

The control of the interaction between several quantum emitters using nanophotonic structures holds great promise for quantum technology applications. However, the theoretical description of such processes for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes are in principle described by a high-dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a "minimal" number of discrete modes. This extends the previous work in [Medina et al., Phys. Rev. Lett. 126, 093601 (2021)] to the case of an arbitrary number of emitters with arbitrary orientations, without any restrictions on the emitter level structure or dipole operators. We illustrate the power of our approach for a model system formed by three emitters placed in different positions within a metallodielectric photonic structure consisting of a metallic dimer embedded in a dielectric nanosphere. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We show that excitation transfer between the emitters is highly sensitive to the properties of the hybrid photonic-plasmonic modes, demonstrating the potential of such structures for achieving control over emitter interactions.

When arranged in a periodic geometry, arrays of metallic nanostructures are capable of supporting collective modes known as lattice resonances. These modes, which originate from the coherent multiple scattering between the elements of the array, give rise to very strong and spectrally narrow optical responses. Here, we show that, thanks to their collective nature, the lattice resonances of a periodic array of metallic nanoparticles can mediate an efficient long-range coupling between dipole emitters placed near the array. Specifically, using a coupled dipole approach, we calculate the Green tensor of the array connecting two points and analyze its spectral and spatial characteristics. This quantity represents the electromagnetic field produced by the array at a given position when excited by a unit dipole emitter located at another one. We find that, when a lattice resonance is excited, the Green tensor is significantly larger and decays more slowly with distance than the Green tensor of vacuum. Therefore, in addition to advancing the fundamental understanding of lattice resonances, our results show that periodic arrays of nanostructures are capable of enhancing the long-range coupling between collections of dipole emitters, which makes them a promising platform for applications such as nanoscale energy transfer and quantum information processing., Comment: 13 pages, 9 figures

Bound-states-in-the-continuum (BIC)is a wave-mechanical concept that generates resonances with vanishing spectral linewidths. It has many practical applications in Optics, such as narrow-band filters, mirror-less lasing, and nonlinear harmonic generation. As true BIC optical modes non-radiative and confined to the near field of nanostructures, they cannot be excited using propagating light. As a result, their direct experimental observation has been elusive. Rather than using light, we demonstrate probing BIC modes on arrays of silicon nanoantennas using a focused beam of electrons in a tranmission electron microscope. By combining cathodoluminescence (CL) and monochromated electron energy-loss spectroscopy (EELS) with controlled nanofabrication, we provide direct experimental evidence of "true" BIC modes, and demonstrate a BIC mode in the visible spectrum at 720 nm. The ability to observe and quantify these guided resonances with a spatial precision more than two orders of magnitude higher than previous far-field measurements allows the probing of individual elements in the nano-antenna arrays. The high-resolution experimental results are supported by numerical simulations as well as multipolar decomposition analysis, allowing us to demonstrate that the coherent interaction length of the quasi-BIC resonance requires at least 6 neighboring antenna elements, achieving over 60 times higher emissivity than for unpatterned silicon., Comment: 30 pages, 4 figures in the main text, 6 figures in the supplementary information

We present an overview of the framework of macroscopic quantum electrodynamics from a quantum nanophotonics perspective. Particularly, we focus our attention on three aspects of the theory which are crucial for the description of quantum optical phenomena in nanophotonic structures. First, we review the light-matter interaction Hamiltonian itself, with special emphasis on its gauge independence and the minimal and multipolar coupling schemes. Second, we discuss the treatment of the external pumping of quantum-optical systems by classical electromagnetic fields. Third, we introduce an exact, complete and minimal basis for the field quantization in multi-emitter configurations, which is based on the so-called emitter-centered modes. Finally, we illustrate this quantization approach in a particular hybrid metallodielectric geometry: two quantum emitters placed in the vicinity of a dimer of Ag nanospheres embedded in a SiN microdisk.

We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral density, obtained through classical electromagnetic simulations, to a model system involving a small number of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and electric field dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.

We review the latest theoretical advances in the application of the framework of Transformation Optics for the analytical description of deeply sub-wavelength electromagnetic phenomena. First, we present a general description of the technique, together with its usual exploitation for metamaterial conception and optimization in different areas of wave physics. Next, we discuss in detail the design of plasmonic metasurfaces, including the description of singular geometries which allow for broadband absorption in ultrathin platforms. Finally, we discuss the quasi-analytical treatment of plasmon-exciton strong coupling in nanocavities at the single emitter level.

Disentangling the contributions of radiative and non-radiative localized plasmonic modes from the photonic density of states of metallic nanocavities between atomically-sharp tips and flat substrates remains an experimental challenge nowadays. Electroluminescence due to tunnelling through the tip-substrate gap allows discerning solely the excitation of radiative modes, but this information is inherently convolved with that of the electronic structure of the system. In this work we present a fully experimental procedure to eliminate the electronic-structure factors from the scanning tunnelling microscope luminescence spectra by confronting them with spectroscopic information extracted from elastic current measurements. Comparison against electromagnetic calculations demonstrates that this procedure allows characterizing the meV shifts experienced by the dipolar and quadrupolar plasmonic modes supported by the nanocavity under atomic-scale gap size changes. Our method, thus, gives us access to the frequency-dependent radiative Purcell enhancement that a microscopic light emitter would undergo when placed at the nanocavity.

Recently, exciton-photon strong coupling has been proposed as a means to control and enhance energy transfer in ensembles of organic molecules. Here, we demonstrate that the exciton dynamics in an archetypal purple bacterial photosynthetic unit, composed of six LH2 antennas surrounding a single LH1 complex, is greatly modified by its interaction with an optical cavity. We develop a Bloch-Redfield master equation approach that accounts for the interplay between the B800 and B850 bacteriochlorophyll molecules within each LH2 antenna, as well as their interactions with the central LH1 complex. Using a realistic parametrization of both photosynthetic unit and optical cavity, we investigate the formation of polaritons in the system, revealing that these can be tuned to accelerate its exciton dynamics by three orders of magnitude. This yields a significant occupation of the LH1 complex, the stage immediately prior to the reaction center, with only a few-femtosecond delay after the initial excitation of the LH2 B800 pigments. Our theoretical findings unveil polaritonic phenomena as a promising route for the characterization, tailoring, and optimization of light-harvesting mechanisms in natural and artificial photosynthetic processes., Comment: 21 pages, 4 figures

We study surface second-harmonic generation (SHG) from a singular plasmonic structure consisting of touching metallic wires. We use the technique of transformation optics and relate the structure to a rather simpler geometry, a slab waveguide. This allows us to obtain an analytical solution to the problem, revealing rich physical insights. We identify various conditions that govern the SHG efficiency. Importantly, our analysis demonstrates that apart from the mode-matching condition, phase-matching condition is relevant even for this sub-wavelength structure. Furthermore, we identify a geometric factor which was not identified before. We support our analysis with numerical simulations.

Strong light-matter interactions enabled by surface plasmons have given rise to a wide range of photonic, optoelectronic and chemical functionalities. In recent years, the interest in this research area has focused on the quantum regime, aiming to developing ultra-compact nanoscale instruments operating at the single (few) photon(s) level. In this perspective, we provide a general overview of recent experimental and theoretical advances as well as near-future challenges towards the design and implementation of plasmon-empowered quantum optical and photo-emitting devices based on the building blocks of nanophotonics technology: metallo-dielectric nanostructures and microscopic light sources.

Very recently it has been predicted that the far-field radiative heat transfer between two macroscopic systems can largely overcome the limit set by Planck's law if one of their dimensions becomes much smaller than the thermal wavelength ($\lambda_{\rm Th} \approx 10\, \mu$m at room temperature). To explore the ultimate limit of the far-field violation of Planck's law, here we present a theoretical study of the radiative heat transfer between two-dimensional (2D) materials. We show that the far-field thermal radiation exchanged by two coplanar systems with a one-atom-thick geometrical cross section can be more than 7 orders of magnitude larger than the theoretical limit set by Planck's law for blackbodies and can be comparable to the heat transfer of two parallel sheets at the same distance. In particular, we illustrate this phenomenon with different materials such as graphene, where the radiation can also be tuned by a external gate, and single-layer black phosphorus. In both cases the far-field radiative heat transfer is dominated by TE-polarized guiding modes and surface plasmons play no role. Our predictions provide a new insight into the thermal radiation exchange mechanisms between 2D materials., Comment: 19 pages, 4 figures

We present a theoretical analysis that demonstrates that the far-field radiative heat transfer between objects with dimensions smaller than the thermal wavelength can overcome the Planckian limit by orders of magnitude. We illustrate this phenomenon with micron-sized structures that can be readily fabricated and tested with existing technology. Our work shows the dramatic failure of the classical theory to predict the far-field radiative heat transfer between micro- and nano-devices., Comment: 6 pages, 4 figures, supplemental material available upon request

We study second-harmonic generation (SHG) arising from surface nonlinearity at a metal-dielectric interface using a spectral decomposition method. Since our method avoids the need to consider the generalized boundary condition across the metal-dielectric interface in the presence of a perpendicular surface source, we retrieve the known discontinuity of the tangential component of the electric field ($E_{\parallel}^ {2\omega}$) for a general geometry, based on a purely mathematical argument. Further, we reaffirm the standard convention of the implementation of this condition, namely, that the surface dipole source radiates as if placed outside the metal surface for arbitrary geometries. We also study and explain the spectral dependence of the discontinuity of the tangential component of the electric field at second harmonic. Finally, we note that the default settings of the commercial numerical package COMSOL Multiphysics fail to account for the $E_{\parallel}^ {2\omega}$-discontinuity. We provide a simple recipe that corrects the boundary condition within these existing settings.

Metallic nanostructures provide a toolkit for the generation of coherent light below the diffraction limit. Plasmonic based lasing relies on the population inversion of emitters (such as organic fluorophores) along with feedback provided by plasmonic resonances. In this regime, known as weak light matter coupling, the radiative characteristics of the system can be described by the Purcell effect. Strong light matter coupling between the molecular excitons and electromagnetic field generated by the plasmonic structures leads to the formation of hybrid quasi-particles known as plasmon exciton polaritons (PEPs). Due to the bosonic character of these quasi particles, exciton polariton condensation can lead to laser-like emission at much lower threshold powers than in conventional photon lasers. Here, we observe PEP lasing through a dark plasmonic mode in an array of metallic nanoparticles with a low threshold in an optically pumped organic system. Interestingly, the threshold power of the lasing is reduced by increasing the degree of light matter coupling in spite of the degradation of the quantum efficiency of the active material, highlighting the ultrafast dynamic responsible for the lasing, i.e., stimulated scattering. These results demonstrate a unique roomtemperature platform for exploring the physics of exciton polaritons in an open cavity architecture and pave the road toward the integration of this on-chip lasing device with the current photonics and active metamaterial planar technologies.

We theoretically demonstrated and experimentally verified high-order radial spoof localized surface plasmon resonances supported by textured metal particles. Through an effective medium theory and exact numerical simulations, we show the emergence of these geometrically-originated electromagnetic modes at microwave frequencies. The occurrence of high-order radial spoof plasmon resonances is experimentally verified in ultrathin disks. Their spectral and near-field properties are characterized experimentally, showing an excellent agreement with theoretical predictions. Our findings shed light into the nature of spoof localized surface plasmons, and open the way to the design of broadband plasmonic devices able to operate at very different frequency regimes., Comment: 29 pages, 10 figures

Transformation optics (TO) is a new tool for controlling electromagnetic fields. In the context of metamaterial technology, it provides a direct link between a desired electromagnetic (EM) phenomenon and the material response required for its occurrence. Recently, this powerful framework has been successfully exploited to study surface plasmon assisted phenomena such as light harvesting. Here, we review the general strategy based on TO to design plasmonic devices capable of harvesting light over a broadband spectrum and achieving considerable field confinement and enhancement. The methodology starts with two-dimensional (2D) cases, such as 2D metal edges, crescent-shaped cylinders, nanowire dimers, and rough metal surfaces, and has been well extended to fully-fledged three-dimensional (3D) situations. The largely analytic approach gives physical insights into the processes involved and suggests the way forward to study a wide variety of plasmonic nanostructures., Comment: 20 pages, 10 figures, Accepted for publication by Science China Information Sciences

We study a "strongly-coupled" (SC) polariton system formed between the atom-like intersubband transitions in a semiconductor nanostructure and the THz optical modes that are localised at the edges of a gold aperture. The polaritons can be excited optically, by incoherent excitation with bandgap radiation, and we find that they also coherently scatter the same input laser, to give strikingly sharp "sideband" (SB) spectral peaks in the backscattered spectrum. The SB intensity is a sensitive track of the polariton density and they can be detected down to a quantum noise floor that is more than 2500 times lower than the excitation thresholds of comparable quantum cascade laser diodes. Compared with other coherent scattering mechanisms, higher order SB scattering events are readily observable, and we speculate that the effect may find utility as a passive all-optical wavelength shifting mechanism in telecommunications systems., Comment: 4 pages