Erratum: Comment on "Free-Electron-Bound-Electron Resonant Interaction" [Phys. Rev. Lett. 126, 019501 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.126.019501.

Inelastic Scattering of Electron Beams by Nonreciprocal Nanotructures.

Probing optical excitations with high resolution is important for understanding their dynamics and controlling their interaction with other photonic elements. This can be done using state-of-the-art electron microscopes, which provide the means to sample optical excitations with combined meV-sub-nm energy-space resolution. For reciprocal photonic systems, electrons traveling in opposite directions produce identical signals, while this symmetry is broken in nonreciprocal structures. Here, we theoretically investigate this phenomenon by analyzing electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) for structures consisting of magnetically biased InAs as an instance of gyrotropic nonreciprocal material. We find that the spectral features associated with excitations of InAs films depend on the electron propagation direction in both EELS and CL, and can be tuned by varying the applied magnetic field within a relatively modest subtesla regime. The magnetic field modifies the optical field distribution of the sampled resonances, and this in turn produces a direction-dependent coupling to the electron. The present results pave the way to the use of electron microscope spectroscopies to explore the near-field characteristics of nonreciprocal systems with high spatial resolution.

Electron Beam Aberration Correction Using Optical Near Fields.

The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we design optical near-field plates to imprint a lateral phase on the electron wave function that can largely correct spherical aberration without the involvement of electric or magnetic lenses in the electron optics, and further generate on-demand lateral focal spot profiles. Our work introduces a disruptive and powerful approach toward aberration correction based on light-electron interactions that could lead to compact and versatile time-resolved free-electron microscopy and spectroscopy.

Ultrafast Topological Engineering in Metamaterials.

Transient optical heating provides an efficient way to trigger phase transitions in naturally occurring media through ultrashort laser pulse irradiation. A similar approach could be used to induce topological transitions in the photonic response of suitably engineered artificial structures known as metamaterials. Here, we predict a topological transition in the isofrequency dispersion contours of a layered graphene metamaterial under optical pumping. We show that the contour topology transforms from elliptic to hyperbolic within a subpicosecond timescale by exploiting the extraordinary photothermal properties of graphene. This new phenomenon allows us to theoretically demonstrate applications in engineering the decay rate of proximal optical emitters, ultrafast beam steering, and dynamical far-field subwavelength imaging. Our study opens a disruptive approach toward ultrafast control of light emission, beam steering, and optical image processing.

Lasing and Amplification from Two-Dimensional Atom Arrays.

We explore the ability of two-dimensional periodic atom arrays to produce light amplification and generate laser emission when gain is introduced through external optical pumping. Specifically, we predict that lasing can take place for arbitrarily weak atomic scatterers assisted by cooperative interaction among atoms in a 2D lattice. We base this conclusion on analytical theory for three-level scatterers, which additionally reveals a rich interplay between lattice and atomic resonances. Our results provide a general background to understand light amplification and lasing in periodic atomic arrays, with promising applications in the generation, manipulation, and control of coherent photon states at the nanoscale.

Nonlinear Plasmonic Sensing with Nanographene.

Plasmons provide excellent sensitivity to detect analyte molecules through their strong interaction with the dielectric environment. Plasmonic sensors based on noble metals are, however, limited by the spectral broadening of these excitations. Here we identify a new mechanism that reveals the presence of individual molecules through the radical changes that they produce in the plasmons of graphene nanoislands. An elementary charge or a weak permanent dipole carried by the molecule are shown to be sufficient to trigger observable modifications in the linear absorption spectra and the nonlinear response of the nanoislands. In particular, a strong second-harmonic signal, forbidden by symmetry in the unexposed graphene nanostructure, emerges due to a redistribution of conduction electrons produced by interaction with the molecule. These results pave the way toward ultrasensitive nonlinear detection of dipolar molecules and molecular radicals that is made possible by the extraordinary optoelectronic properties of graphene.

Ultraefficient Coupling of a Quantum Emitter to the Tunable Guided Plasmons of a Carbon Nanotube.

We show that a single quantum emitter can efficiently couple to the tunable plasmons of a highly doped single-wall carbon nanotube (SWCNT). Plasmons in these quasi-one-dimensional carbon structures exhibit deep subwavelength confinement that pushes the coupling efficiency close to 100% over a very broad spectral range. This phenomenon takes place for distances and tube diameters comprising the nanometer and micrometer scales. In particular, we find a ß factor ≈1 for QEs placed 1-100 nm away from SWCNTs that are just a few nanometers in diameter, while the corresponding Purcell factor exceeds 10(6).

Active tunable absorption enhancement with graphene nanodisk arrays.

If not for its inherently weak optical absorption at visible and infrared wavelengths, graphene would show exceptional promise for optoelectronic applications. Here we show that by nanopatterning a graphene layer into an array of closely packed graphene nanodisks, its absorption efficiency can be increased from less than 3% to 30% in the infrared region of the spectrum. We examine the dependence of the enhanced absorption on nanodisk size and interparticle spacing. By incorporating graphene nanodisk arrays into an active device, we demonstrate that this enhanced absorption efficiency is voltage-tunable, indicating strong potential for nanopatterned graphene as an active medium for infrared electro-optic devices.

Quantum effects in the interaction of low-energy electrons with light.

The interaction between free electrons and optical fields constitutes a unique platform to investigate ultrafast processes in matter and explore fundamental quantum phenomena. Specifically, optically modulated electrons in ultrafast electron microscopy act as noninvasive probes that push space-time-energy resolution to the picometer-attosecond-microelectronvolt range. Electron energies well above the involved photon energies are commonly used, rendering a low electron-light coupling and, thus, only providing limited access to the wealth of quantum nonlinear phenomena underlying the dynamical response of nanostructures. Here, we theoretically investigate electron-light interactions between photons and electrons of comparable energies, revealing quantum and recoil effects that include a nonvanishing coupling of surface-scattered electrons to light plane waves, inelastic electron backscattering from confined optical fields, and strong electron-light coupling under grazing electron diffraction by an illuminated crystal surface. Our exploration of electron-light-matter interactions holds potential for applications in ultrafast electron microscopy.

Generation of entangled waveguided photon pairs by free electrons.

Entangled photons are a key resource in quantum technologies. While intense laser light propagating in nonlinear crystals is conventionally used to generate entangled photons, such schemes have low efficiency due to the weak nonlinear response of known materials and losses associated with in/out photon coupling. Here, we show how to generate entangled polariton pairs directly within optical waveguides using free electrons. The measured energy loss of undeflected electrons heralds the production of counter-propagating polariton pairs entangled in energy and emission direction. For illustration, we study the excitation of plasmon polaritons in metal strip waveguides that strongly enhance light-matter interactions, rendering two-plasmon generation dominant over single-plasmon excitation. We demonstrate that electron energy losses detected within optimal frequency ranges can reliably signal the generation of plasmon pairs entangled in energy and momentum. Our proposed scheme is directly applicable to other types of optical waveguides for in situ generation of entangled photon pairs.

Gate-tunable negative refraction of mid-infrared polaritons.

Negative refraction provides a platform to manipulate mid-infrared and terahertz radiation for molecular sensing and thermal emission applications. However, its implementation based on metamaterials and plasmonic media presents challenges with optical losses, limited spatial confinement, and lack of active tunability in this spectral range. We demonstrate gate-tunable negative refraction at mid-infrared frequencies using hybrid topological polaritons in van der Waals heterostructures. Specifically, we visualize wide-angle negatively refracted polaritons in α-MoO3 films partially decorated with graphene, undergoing reversible planar nanoscale focusing. Our atomically thick heterostructures weaken scattering losses at the interface while enabling an actively tunable transition of normal to negative refraction through electrical gating. We propose polaritonic negative refraction as a promising platform for infrared applications such as electrically tunable super-resolution imaging, nanoscale thermal manipulation, enhanced molecular sensing, and on-chip optical circuitry.

Enhancing the radiative rate in III-V semiconductor plasmonic core-shell nanowire resonators.

We investigate the radiative properties of plasmonic core-shell nanowire resonators and, using boundary element method calculations, demonstrate enhanced radiative decay rate by up to 3500 times in nanoscale compound semiconductor/metal cavities. Calculation of the local density of optical states enables identification of new types of modes in cavities with mode volumes on the order of 10(-4)(λ/n)(3). These modes dramatically enhance the radiative decay rate and significantly modify the polarization of far-field emission.

Ultrafast Transverse Modulation of Free Electrons by Interaction with Shaped Optical Fields.

Spatiotemporal electron-beam shaping is a bold frontier of electron microscopy. Over the past decade, shaping methods evolved from static phase plates to low-speed electrostatic and magnetostatic displays. Recently, a swift change of paradigm utilizing light to control free electrons has emerged. Here, we experimentally demonstrate arbitrary transverse modulation of electron beams without complicated electron-optics elements or material nanostructures, but rather using shaped light beams. On-demand spatial modulation of electron wavepackets is obtained via inelastic interaction with transversely shaped ultrafast light fields controlled by an external spatial light modulator. We illustrate this method for the cases of Hermite-Gaussian and Laguerre-Gaussian modulation and discuss their use in enhancing microscope sensitivity. Our approach dramatically widens the range of patterns that can be imprinted on the electron profile and greatly facilitates tailored electron-beam shaping.

Stimulated light emission and inelastic scattering by a classical linear system of rotating particles.

The rotational dynamics of particles subject to external illumination is found to produce light amplification and inelastic scattering at high rotation velocities. Light emission at frequencies shifted with respect to the incident light by twice the rotation frequency dominates over elastic scattering within a wide range of light and rotation frequencies. Remarkably, net amplification of the incident light is produced in this classical linear system via stimulated emission. Large optically induced acceleration rates are predicted in vacuum accompanied by moderate heating of the particle, thus supporting the possibility of observing these effects under extreme rotation conditions.

Optical coherence transfer mediated by free electrons.

We theoretically investigate the quantum-coherence properties of the cathodoluminescence (CL) emission produced by a temporally modulated electron beam. Specifically, we consider the quantum-optical correlations of CL produced by electrons that are previously shaped by a laser field. Our main prediction is the presence of phase correlations between the emitted CL field and the electron-modulating laser, even though the emission intensity and spectral profile are independent of the electron state. In addition, the coherence of the CL field extends to harmonics of the laser frequency. Since electron beams can be focused to below 1 Å, their ability to transfer optical coherence could enable the ultra-precise excitation, manipulation, and spectrally resolved probing of nanoscale quantum systems.

Spontaneous and stimulated electron-photon interactions in nanoscale plasmonic near fields.

The interplay between free electrons, light, and matter offers unique prospects for space, time, and energy resolved optical material characterization, structured light generation, and quantum information processing. Here, we study the nanoscale features of spontaneous and stimulated electron-photon interactions mediated by localized surface plasmon resonances at the tips of a gold nanostar using electron energy-loss spectroscopy (EELS), cathodoluminescence spectroscopy (CL), and photon-induced near-field electron microscopy (PINEM). Supported by numerical electromagnetic boundary-element method (BEM) calculations, we show that the different coupling mechanisms probed by EELS, CL, and PINEM feature the same spatial dependence on the electric field distribution of the tip modes. However, the electron-photon interaction strength is found to vary with the incident electron velocity, as determined by the spatial Fourier transform of the electric near-field component parallel to the electron trajectory. For the tightly confined plasmonic tip resonances, our calculations suggest an optimum coupling velocity at electron energies as low as a few keV. Our results are discussed in the context of more complex geometries supporting multiple modes with spatial and spectral overlap. We provide fundamental insights into spontaneous and stimulated electron-light-matter interactions with key implications for research on (quantum) coherent optical phenomena at the nanoscale.

Electrically driven photon emission from individual atomic defects in monolayer WS2.

Quantum dot-like single-photon sources in transition metal dichalcogenides (TMDs) exhibit appealing quantum optical properties but lack a well-defined atomic structure and are subject to large spectral variability. Here, we demonstrate electrically stimulated photon emission from individual atomic defects in monolayer WS2 and directly correlate the emission with the local atomic and electronic structure. Radiative transitions are locally excited by sequential inelastic electron tunneling from a metallic tip into selected discrete defect states in the WS2 bandgap. Coupling to the optical far field is mediated by tip plasmons, which transduce the excess energy into a single photon. The applied tip-sample voltage determines the transition energy. Atomically resolved emission maps of individual point defects closely resemble electronic defect orbitals, the final states of the optical transitions. Inelastic charge carrier injection into localized defect states of two-dimensional materials provides a powerful platform for electrically driven, broadly tunable, atomic-scale single-photon sources.

Anisotropy and particle-size effects in nanostructured plasmonic metamaterials.

We study the optical properties of metamaterials formed by layers of metallic nanoparticles. The effective optical constants of these materials are retrieved from the calculated angle-dependent Fresnel reflection coefficients for s and p incident-light polarization. We investigate the degree of anisotropy in the effective permittivity as a function of inter-layer spacing, particle size, filling fraction of the metal, and particle shape. For layers of spherical particles periodically arranged in a hexagonal lattice, the anisotropy disappears for the three inter-layer spacings corresponding to simple cubic (sc), bcc, and fcc volume symmetry. For non-spherical particles, an isotropic response can be still obtained with other values of the inter-layer spacing. Finally, we provide a quantitative answer to the question of how many layers are needed to form an effectively homogeneous metamaterial slab. Surprisingly, only one layer can be enough, except in the spectral range close to the particle plasmon resonances.