A general theoretical and experimental framework for nanoscale electromagnetism.

The macroscopic electromagnetic boundary conditions, which have been established for over a century1, are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies2-4, exemplars of extremely interface-localized fields, rely on their validity. This classical description, however, neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres5-10. The onset of these discrepancies has a mesoscopic character: it lies between the granular microscopic (electronic-scale) and continuous macroscopic (wavelength-scale) domains. Existing top-down phenomenological approaches deal only with individual aspects of these omissions, such as nonlocality11-13 and local-response spill-out14,15. Alternatively, bottom-up first-principles approaches-for example, time-dependent density functional theory16,17-are severely constrained by computational demands and thus become impractical for multiscale problems. Consequently, a general and unified framework for nanoscale electromagnetism remains absent. Here we introduce and experimentally demonstrate such a framework-amenable to both analytics and numerics, and applicable to multiscale problems-that reintroduces the electronic length scale via surface-response functions known as Feibelman d parameters18,19. We establish an experimental procedure to measure these complex dispersive surface-response functions, using quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects. We observe nonclassical spectral shifts in excess of 30 per cent and the breakdown of Kreibig-like broadening in a quintessential multiscale architecture: film-coupled nanoresonators, with feature sizes comparable to both the wavelength and the electronic length scale. Our results provide a general framework for modelling and understanding nanoscale (that is, all relevant length scales above about 1 nanometre) electromagnetic phenomena.

Large-Area Superconducting Nanowire Single-Photon Detectors for Operation at Wavelengths up to 7.4 µm.

The optimization of superconducting thin-films has pushed the sensitivity of superconducting nanowire single-photon detectors (SNSPDs) to the mid-infrared (mid-IR). Earlier demonstrations have shown that straight tungsten silicide nanowires can achieve unity internal detection efficiency (IDE) up to λ = 10 µm. For a high system detection efficiency (SDE), the active area needs to be increased, but material nonuniformity and nanofabrication-induced constrictions make mid-IR large-area meanders challenging to yield. In this work, we improve the sensitivity of superconducting materials and optimize a high-resolution nanofabrication process to demonstrate large-area SNSPDs with unity IDE at 7.4 µm. Our approach yields large-area meanders down to 50 nm width, with average line-width roughness below 10%, and with a lower impact from constrictions compared to previous demonstrations. Our methods pave the way to high-efficiency SNSPDs in the mid-IR band with potential impacts on astronomy, imaging, and physical chemistry.

New Constraints on Dark Photon Dark Matter with Superconducting Nanowire Detectors in an Optical Haloscope.

Uncovering the nature of dark matter is one of the most important goals of particle physics. Light bosonic particles, such as the dark photon, are well-motivated candidates: they are generally long-lived, weakly interacting, and naturally produced in the early universe. In this work, we report on Light A^{'} Multilayer Periodic Optical SNSPD Target, a proof-of-concept experiment searching for dark photon dark matter in the eV mass range, via coherent absorption in a multilayer dielectric haloscope. Using a superconducting nanowire single-photon detector (SNSPD), we achieve efficient photon detection with a dark count rate of ∼6×10^{-6} counts/s. We find no evidence for dark photon dark matter in the mass range of ∼0.7-0.8 eV with kinetic mixing ε≳10^{-12}, improving existing limits in ε by up to a factor of 2. With future improvements to SNSPDs, our architecture could probe significant new parameter space for dark photon and axion dark matter in the meV to 10 eV mass range.

Broadband Solenoidal Haloscope for Terahertz Axion Detection.

We introduce the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design and science program. This haloscope plans to search for bosonic dark matter across the [10^{-3},1] eV ([0.24, 240] THz) mass range. BREAD proposes a cylindrical metal barrel to convert dark matter into photons, which a novel parabolic reflector design focuses onto a photosensor. This unique geometry enables enclosure in standard cryostats and high-field solenoids, overcoming limitations of current dish antennas. A pilot 0.7 m^{2} barrel experiment planned at Fermilab is projected to surpass existing dark photon coupling constraints by over a decade with one-day runtime. Axion sensitivity requires <10^{-20} W/sqrt[Hz] sensor noise equivalent power with a 10 T solenoid and 10 m^{2} barrel. We project BREAD sensitivity for various sensor technologies and discuss future prospects.

Enhancing Plasmonic Spectral Tunability with Anomalous Material Dispersion.

The field confinement of plasmonic systems enables spectral tunability under structural variations or environmental perturbations, which is the principle for various applications including nanorulers, sensors, and color displays. Here, we propose and demonstrate that materials with anomalous dispersion, such as Ge in the visible, improve spectral tunability. We introduce our proposal with a semianalytical guided mode picture. Using Ge-based film (Ag/Au)-coupled gap plasmon resonators, we implement two architectures and demonstrate the improved tunability with single-particle dark-field scattering, ensemble reflection, and color generation. We observe three-fold enhancement of tunability with Ge nanodisks compared with that of Si, a normal-dispersion material in the visible. The structural color generation of large array systems, made of inversely fabricated Ge-Ag resonators, exhibits a wide gamut. Our results introduce anomalous material dispersion as an extra degree of freedom to engineer the spectral tunability of plasmonic systems, especially relevant for actively tunable plasmonics and metasurfaces.

Determining Dark-Matter-Electron Scattering Rates from the Dielectric Function.

We show that the rate for dark-matter-electron scattering in an arbitrary material is determined by an experimentally measurable quantity, the complex dielectric function, for any dark matter interaction that couples to electron density. This formulation automatically includes many-body effects, eliminates all systematic theoretical uncertainties on the electronic wave functions, and allows a direct calibration of the spectrum by electromagnetic probes such as infrared spectroscopy, x-ray scattering, and electron energy-loss spectroscopy. Our formalism applies for several common benchmark models, including spin-independent interactions through scalar and vector mediators of arbitrary mass. We discuss the consequences for standard semiconductor and superconductor targets and find that the true reach of superconductor detectors for light mediators exceeds previous estimates by several orders of magnitude, with further enhancements possible due to the low-energy tail of the plasmon. Using a heavy-fermion superconductor as an example, we show how our formulation allows a rapid and systematic investigation of novel electron scattering targets.

Single-Photon Single-Flux Coupled Detectors.

In this work, we present a novel device that is a combination of a superconducting nanowire single-photon detector and a superconducting multilevel memory. We show that these devices can be used to count the number of detections through single-photon to single-flux conversion. Electrical characterization of the memory properties demonstrates single-flux quantum (SFQ) separated states. Optical measurements using attenuated laser pulses with different mean photon number, pulse energies and repetition rates are shown to differentiate single-photon detection from other possible phenomena, such as multiphoton detection and thermal activation. Finally, different geometries and material stacks to improve device performance, as well as arraying methods, are discussed.

Resolving Photon Numbers Using a Superconducting Nanowire with Impedance-Matching Taper.

Time- and number-resolved photon detection is crucial for quantum information processing. Existing photon-number-resolving (PNR) detectors usually suffer from limited timing and dark-count performance or require complex fabrication and operation. Here, we demonstrate a PNR detector at telecommunication wavelengths based on a single superconducting nanowire with an integrated impedance-matching taper. The taper provides a kΩ load impedance to the nanowire, making the detector's output amplitude sensitive to the number of photon-induced hotspots. The prototyping device was able to resolve up to four absorbed photons with 16.1 ps timing jitter and <2 c.p.s. device dark count rate. Its exceptional distinction between single- and two-photon responses is ideal for high-fidelity coincidence counting and allowed us to directly observe bunching of photon pairs from a single output port of a Hong-Ou-Mandel interferometer. This detector architecture may provide a practical solution to applications that require high timing resolution and few-photon discrimination.

Electron energy loss of ultraviolet plasmonic modes in aluminum nanodisks.

We theoretically investigated electron energy loss spectroscopy (EELS) of ultraviolet surface plasmon modes in aluminum nanodisks. Using full-wave Maxell electromagnetic simulations, we studied the impact of the diameter on the resonant modes of the nanodisks. We found that the mode behavior can be separately classified for two distinct cases: (1) flat nanodisks where the diameter is much larger than the thickness and (2) thick nanodisks where the diameter is comparable to the thickness. While the multipolar edge modes and breathing modes of flat nanostructures have previously been interpreted using intuitive, analytical models based on surface plasmon polariton (SPP) modes of a thin-film stack, it has been found that the true dispersion relation of the multipolar edge modes deviates significantly from the SPP dispersion relation. Here, we developed a modified intuitive model that uses effective wavelength theory to accurately model this dispersion relation with significantly less computational overhead compared to full-wave Maxwell electromagnetic simulations. However, for the case of thick nanodisks, this effective wavelength theory breaks down, and such intuitive models are no longer viable. We found that this is because some modes of the thick nanodisks carry a polar (i.e., out of the substrate plane or along the electron beam direction) dependence and cannot be simply categorized as radial breathing modes or angular (azimuthal) multipolar edge modes. This polar dependence leads to radiative losses, motivating the use of simultaneous EELS and cathodoluminescence measurements when experimentally investigating the complex mode behavior of thick nanostructures.

Design and characterization of superconducting nanowire-based processors for acceleration of deep neural network training.

Training of deep neural networks (DNNs) is a computationally intensive task and requires massive volumes of data transfer. Performing these operations with the conventional von Neumann architectures creates unmanageable time and power costs. Recent studies have shown that mixed-signal designs involving resistive crossbar architectures are capable of achieving acceleration factors as high as 30 000 × over the state of the art digital processors. These approaches involve utilization of non-volatile memory elements as local processors. However, no technology has been developed to-date that can satisfy the strict device requirements for the unit cell. This paper presents the superconducting nanowire-based processing element as a crosspoint device. The unit cell has many programmable non-volatile states that can be used to perform analog multiplication. Importantly, these states are intrinsically discrete due to quantization of flux, which provides symmetric switching characteristics. Operation of these devices in a crossbar is described and verified with electro-thermal circuit simulations. Finally, validation of the concept in an actual DNN training task is shown using an emulator.

Focused-helium-ion-beam blow forming of nanostructures: radiation damage and nanofabrication.

Targeted irradiation of nanostructures by a finely focused ion beam provides routes to improved control of material modification and understanding of the physics of interactions between ion beams and nanomaterials. Here, we studied radiation damage in crystalline diamond and silicon nanostructures using a focused helium ion beam, with the former exhibiting extremely long-range ion propagation and large plastic deformation in a process visibly analogous to blow forming. We report the dependence of damage morphology on material, geometry, and irradiation conditions (ion dose, ion energy, ion species, and location). We anticipate that our method and findings will not only improve the understanding of radiation damage in isolated nanostructures, but will also support the design of new engineering materials and devices for current and future applications in nanotechnology.

Detecting Sub-GeV Dark Matter with Superconducting Nanowires.

We propose the use of superconducting nanowires as both target and sensor for direct detection of sub-GeV dark matter. With excellent sensitivity to small energy deposits on electrons and demonstrated low dark counts, such devices could be used to probe electron recoils from dark matter scattering and absorption processes. We demonstrate the feasibility of this idea using measurements of an existing fabricated tungsten-silicide nanowire prototype with 0.8-eV energy threshold and 4.3 ng with 10 000 s of exposure, which showed no dark counts. The results from this device already place meaningful bounds on dark matter-electron interactions, including the strongest terrestrial bounds on sub-eV dark photon absorption to date. Future expected fabrication on larger scales and with lower thresholds should enable probing of new territory in the direct detection landscape, establishing the complementarity of this approach to other existing proposals.

Exploring proximity effects and large depth of field in helium ion beam lithography: large-area dense patterns and tilted surface exposure.

Helium ion beam lithography (HIL) is an emerging nanofabrication technique. It benefits from a reduced interaction volume compared to that of an electron beam of similar energy, and hence reduced long-range scattering (proximity effect), higher resist sensitivity and potentially higher resolution. Furthermore, the small angular spread of the helium ion beam gives rise to a large depth of field. This should enable patterning on tilted and curved surfaces without the need of any additional adjustments, such as laser-auto focus. So far, most work on HIL has been focused on exploiting the reduced proximity effect to reach single-digit nanometer resolution, and has thus been concentrated on single-pixel exposures over small areas. Here we explore two new areas of application. Firstly, we investigate the proximity effect in large-area exposures and demonstrate HIL's capabilities in fabricating precise high-density gratings on large planar surfaces (100 µm × 100 µm, with pitch down to 35 nm) using an area dose for exposure. Secondly, we exploit the large depth of field by making the first HIL patterns on tilted surfaces (sample stage tilted 45°). We demonstrate a depth of field greater than 100 µm for a resolution of about 20 nm.

Optical modeling of superconducting nanowire single photon detectors using the transfer matrix method: publisher's note.

This publisher's note amends the Funding and Acknowledgment sections in Appl. Opt.57, 4872 (2018)APOPAI0003-693510.1364/AO.57.004872.

Optical modeling of superconducting nanowire single photon detectors using the transfer matrix method.

We present optical modeling of superconducting nanowire single photon detector devices using an analytical approach based on the transfer matrix method. We find that the optimal dielectric layer thicknesses vary slightly with the thickness and fill factor of the NbN layer and explore novel device geometries that can be described as a stack of thin films, such as devices on multilayered substrates, free-standing membranes, and optical fiber facets. In addition, the analytical results here show the importance of accounting for coherence correctly when an integrated cavity is included in the device structure and the relative insignificance of an anti-reflection coating in most cases.

Mapping Photoemission and Hot-Electron Emission from Plasmonic Nanoantennas.

Understanding plasmon-mediated electron emission and energy transfer on the nanometer length scale is critical to controlling light-matter interactions at nanoscale dimensions. In a high-resolution lithographic material, electron emission and energy transfer lead to chemical transformations. In this work, we employ such chemical transformations in two different high-resolution electron-beam lithography resists, poly(methyl methacrylate) (PMMA) and hydrogen silsesquioxane (HSQ), to map local electron emission and energy transfer with nanometer resolution from plasmonic nanoantennas excited by femtosecond laser pulses. We observe exposure of the electron-beam resists (both PMMA and HSQ) in regions on the surface of nanoantennas where the local field is significantly enhanced. Exposure in these regions is consistent with previously reported optical-field-controlled electron emission from plasmonic hotspots as well as earlier work on low-electron-energy scanning probe lithography. For HSQ, in addition to exposure in hotspots, we observe resist exposure at the centers of rod-shaped nanoantennas in addition to exposure in plasmonic hotspots. Optical field enhancement is minimized at the center of nanorods suggesting that exposure in these regions involves a different mechanism to that in plasmonic hotspots. Our simulations suggest that exposure at the center of nanorods results from the emission of hot electrons produced via plasmon decay in the nanorods. Overall, the results presented in this work provide a means to map both optical-field-controlled electron emission and hot-electron transfer from nanoparticles via chemical transformations produced locally in lithographic materials.

Superconductor-superconductor bilayers for enhancing single-photon detection.

Here, we optimized ultrathin films of granular NbN on SiO2 and of amorphous αW5Si3. We showed that hybrid superconducting nanowire single-photon detectors (SNSPDs) made of 2 nm thick αW5Si3 films over 2 nm thick NbN films exhibit advantageous coexistence of timing (<5 ns reset time and 52 ps timing jitter) and efficiency (>96% quantum efficiency) performance. We discuss the governing mechanism of this hybridization via the proximity effect. Our results demonstrate saturated SNSPDs performance at 1550 nm optical wavelength and suggest that such hybridization can significantly expand the range of available superconducting properties, impacting other nano-superconducting technologies. Lastly, this hybridization may be used to tune properties, such as the amorphous character of superconducting films.

Dimensional Tailoring of Hydrothermally Grown Zinc Oxide Nanowire Arrays.

Hydrothermally synthesized ZnO nanowire arrays are critical components in a range of nanostructured semiconductor devices. The device performance is governed by relevant nanowire morphological parameters that cannot be fully controlled during bulk hydrothermal synthesis due to its transient nature. Here, we maintain homeostatic zinc concentration, pH, and temperature by employing continuous flow synthesis and demonstrate independent tailoring of nanowire array dimensions including areal density, length, and diameter on device-relevant length scales. By applying diffusion/reaction-limited analysis, we separate the effect of local diffusive transport from the c-plane surface reaction rate and identify direct incorporation as the c-plane growth mechanism. Our analysis defines guidelines for precise and independent control of the nanowire length and diameter by operating in rate-limiting regimes. We validate its utility by using surface adsorbents that limit reaction rate to obtain spatially uniform vertical growth rates across a patterned substrate.

Using Geometry To Sense Current.

We describe a superconducting three-terminal device that uses a simple geometric effect known as current crowding to sense the flow of current and actuate a readout signal. The device consists of a "Y"-shaped current combiner, with two currents (sense and bias) entering separately through the top arms of the "Y", intersecting, and then exiting together through the bottom leg of the "Y". When current is added to or removed from one of the arms (e.g., the sense arm), the superconducting critical current in the other arm (i.e., the bias arm) is modulated. The current in the sense arm can thus be determined by measuring the critical current of the bias arm, or inversely, the sense current can be used to modulate the state of the bias arm. The dependence of the bias critical current on the sense current occurs due to the geometric current crowding effect, which causes the sense current to interact locally with the bias arm. Measurement of the critical current in the bias arm does not break the superconducting state of the sense arm or of the bottom leg, and thus, quantized currents trapped in a superconducting loop were able to be repeatedly measured without changing the state of the loop. Current crowding is a universal effect in nanoscale superconductors, and so this device has potential for applicability across a broad range of superconducting technologies and materials. More generally, any technology in which geometrically induced flow crowding exists in the presence of a strong nonlinearity might make use of this type of device.

High-Energy Surface and Volume Plasmons in Nanopatterned Sub-10 nm Aluminum Nanostructures.

In this work, we use electron energy-loss spectroscopy to map the complete plasmonic spectrum of aluminum nanodisks with diameters ranging from 3 to 120 nm fabricated by high-resolution electron-beam lithography. Our nanopatterning approach allows us to produce localized surface plasmon resonances across a wide spectral range spanning 2-8 eV. Electromagnetic simulations using the finite element method support the existence of dipolar, quadrupolar, and hexapolar surface plasmon modes as well as centrosymmetric breathing modes depending on the location of the electron-beam excitation. In addition, we have developed an approach using nanolithography that is capable of meV control over the energy and attosecond control over the lifetime of volume plasmons in these nanodisks. The precise measurement of volume plasmon lifetime may also provide an opportunity to probe and control the DC electrical conductivity of highly confined metallic nanostructures. Lastly, we show the strong influence of the nanodisk boundary in determining both the energy and lifetime of surface plasmons and volume plasmons locally across individual aluminum nanodisks, and we have compared these observations to similar effects produced by scaling the nanodisk diameter.