Biasing the quantum vacuum to control macroscopic probability distributions.

Quantum field theory suggests that electromagnetic fields naturally fluctuate, and these fluctuations can be harnessed as a source of perfect randomness. Many potential applications of randomness rely on controllable probability distributions. We show that vacuum-level bias fields injected into multistable optical systems enable a controllable source of quantum randomness, and we demonstrated this concept in an optical parametric oscillator (OPO). By injecting bias pulses with less than one photon on average, we controlled the probabilities of the two possible OPO output states. The potential of our approach for sensing sub-photon-level fields was demonstrated by reconstructing the temporal shape of fields below the single-photon level. Our results provide a platform to study quantum dynamics in nonlinear driven-dissipative systems and point toward applications in probabilistic computing and weak field sensing.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum.

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n >  10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.

Photonic flatband resonances for free-electron radiation.

Flatbands have become a cornerstone of contemporary condensed-matter physics and photonics. In electronics, flatbands entail comparable energy bandwidth and Coulomb interaction, leading to correlated phenomena such as the fractional quantum Hall effect and recently those in magic-angle systems. In photonics, they enable properties including slow light1 and lasing2. Notably, flatbands support supercollimation-diffractionless wavepacket propagation-in both systems3,4. Despite these intense parallel efforts, flatbands have never been shown to affect the core interaction between free electrons and photons. Their interaction, pivotal for free-electron lasers5, microscopy and spectroscopy6,7, and particle accelerators8,9, is, in fact, limited by a dimensionality mismatch between localized electrons and extended photons. Here we reveal theoretically that photonic flatbands can overcome this mismatch and thus remarkably boost their interaction. We design flatband resonances in a silicon-on-insulator photonic crystal slab to control and enhance the associated free-electron radiation by tuning their trajectory and velocity. We observe signatures of flatband enhancement, recording a two-order increase from the conventional diffraction-enabled Smith-Purcell radiation. The enhancement enables polarization shaping of free-electron radiation and characterization of photonic bands through electron-beam measurements. Our results support the use of flatbands as test beds for strong light-electron interaction, particularly relevant for efficient and compact free-electron light sources and accelerators.

Single fibre enables acoustic fabrics via nanometre-scale vibrations.

Fabrics, by virtue of their composition and structure, have traditionally been used as acoustic absorbers1,2. Here, inspired by the auditory system3, we introduce a fabric that operates as a sensitive audible microphone while retaining the traditional qualities of fabrics, such as machine washability and draping. The fabric medium is composed of high-Young's modulus textile yarns in the weft of a cotton warp, converting tenuous 10-7-atmosphere pressure waves at audible frequencies into lower-order mechanical vibration modes. Woven into the fabric is a thermally drawn composite piezoelectric fibre that conforms to the fabric and converts the mechanical vibrations into electrical signals. Key to the fibre sensitivity is an elastomeric cladding that concentrates the mechanical stress in a piezocomposite layer with a high piezoelectric charge coefficient of approximately 46 picocoulombs per newton, a result of the thermal drawing process. Concurrent measurements of electric output and spatial vibration patterns in response to audible acoustic excitation reveal that fabric vibrational modes with nanometre amplitude displacement are the source of the electrical output of the fibre. With the fibre subsuming less than 0.1% of the fabric by volume, a single fibre draw enables tens of square metres of fabric microphone. Three different applications exemplify the usefulness of this study: a woven shirt with dual acoustic fibres measures the precise direction of an acoustic impulse, bidirectional communications are established between two fabrics working as sound emitters and receivers, and a shirt auscultates cardiac sound signals.

A framework for scintillation in nanophotonics.

Bombardment of materials by high-energy particles often leads to light emission in a process known as scintillation. Scintillation has widespread applications in medical imaging, x-ray nondestructive inspection, electron microscopy, and high-energy particle detectors. Most research focuses on finding materials with brighter, faster, and more controlled scintillation. We developed a unified theory of nanophotonic scintillators that accounts for the key aspects of scintillation: energy loss by high-energy particles, and light emission by non-equilibrium electrons in nanostructured optical systems. We then devised an approach based on integrating nanophotonic structures into scintillators to enhance their emission, obtaining nearly an order-of-magnitude enhancement in both electron-induced and x-ray-induced scintillation. Our framework should enable the development of a new class of brighter, faster, and higher-resolution scintillators with tailored and optimized performance.

Enabling Manufacturable Optical Broadband Angular-Range Selective Films.

The ability to control the propagation direction of light has long been a scientific goal. However, the fabrication of large-scale optical angular-range selective films is still a challenge. This paper presents a polymer-enabled large-scale fabrication method for broadband angular-range selective films that perform over the entire visible spectrum. Our approach involves stacking together multiple one-dimensional photonic crystals with various engineered periodicities to enlarge the bandgap across a wide spectral range based on theoretical predictions. Experimental results demonstrate that our method can achieve broadband transparency at a range of incident angles centered around normal incidence and reflectivity at larger viewing angles, doing so at large scale and low cost.

A Brewster route to Cherenkov detectors.

Cherenkov detectors enable a valuable tool to identify high-energy particles. However, their sensitivity and momentum coverage are limited by the refractive index of host materials. Especially, identifying particles with energy above multiple gigaelectronvolts requires host materials with a near-unity refractive index, which are limited to bulky gas chambers. Overcoming this fundamental material limit is important for future particle detectors yet remains a long-standing challenge. Here, we propose a different paradigm for Cherenkov detectors that utilizes the broadband angular filter made from stacks of variable one-dimensional photonic crystals. Owing to the Brewster effect, the angular filter is transparent only to Cherenkov photons from a precise incident angle. Particle identification is achieved by mapping each Cherenkov angle to the peak-intensity position of transmitted photons in the detection plane. Such angular filtering effect, although decreases the photon number collected in the detection plane, enables the realization of a non-dispersive pseudo refractive index over the entire visible spectrum. Moreover, the pseudo refractive index can be flexibly designed to different values close to unity. Our angular-selective Brewster paradigm offers a feasible solution to implement compact and highly sensitive Cherenkov detectors especially in beam lines with a small angular divergence using regular dielectrics.

Casimir Light in Dispersive Nanophotonics.

Time-varying optical media, whose dielectric properties are actively modulated in time, introduce a host of novel effects in the classical propagation of light, and are of intense current interest. In the quantum domain, time-dependent media can be used to convert vacuum fluctuations (virtual photons) into pairs of real photons. We refer to these processes broadly as "dynamical vacuum effects" (DVEs). Despite interest for their potential applications as sources of quantum light, DVEs are generally very weak, presenting many opportunities for enhancement through modern techniques in nanophotonics, such as using media which support excitations such as plasmon and phonon polaritons. Here, we present a theory of weakly modulated DVEs in arbitrary nanostructured, dispersive, and dissipative systems. A key element of our framework is the simultaneous incorporation of time-modulation and "dispersion" through time-translation-breaking linear response theory. As an example, we use our approach to propose a highly efficient scheme for generating entangled surface polaritons based on time-modulation of the optical phonon frequency of a polar insulator.

Digital electronics in fibres enable fabric-based machine-learning inference.

Digital devices are the essential building blocks of any modern electronic system. Fibres containing digital devices could enable fabrics with digital system capabilities for applications in physiological monitoring, human-computer interfaces, and on-body machine-learning. Here, a scalable preform-to-fibre approach is used to produce tens of metres of flexible fibre containing hundreds of interspersed, digital temperature sensors and memory devices with a memory density of ~7.6 × 105 bits per metre. The entire ensemble of devices are individually addressable and independently operated through a single connection at the fibre edge, overcoming the perennial single-fibre single-device limitation and increasing system reliability. The digital fibre, when incorporated within a shirt, collects and stores body temperature data over multiple days, and enables real-time inference of wearer activity with an accuracy of 96% through a trained neural network with 1650 neuronal connections stored within the fibre. The ability to realise digital devices within a fibre strand which can not only measure and store physiological parameters, but also harbour the neural networks required to infer sensory data, presents intriguing opportunities for worn fabrics that sense, memorise, learn, and infer situational context.

Control of quantum electrodynamical processes by shaping electron wavepackets.

Fundamental quantum electrodynamical (QED) processes, such as spontaneous emission and electron-photon scattering, encompass phenomena that underlie much of modern science and technology. Conventionally, calculations in QED and other field theories treat incoming particles as single-momentum states, omitting the possibility that coherent superposition states, i.e., shaped wavepackets, can alter fundamental scattering processes. Here, we show that free electron waveshaping can be used to design interferences between two or more pathways in a QED process, enabling precise control over the rate of that process. As an example, we show that free electron waveshaping modifies both spatial and spectral characteristics of bremsstrahlung emission, leading for instance to enhancements in directionality and monochromaticity. The ability to tailor general QED processes opens up additional avenues of control in phenomena ranging from optical excitation (e.g., plasmon and phonon emission) in electron microscopy to free electron lasing in the quantum regime.

100 m Long Thermally Drawn Supercapacitor Fibers with Applications to 3D Printing and Textiles.

Supercapacitor fibers, with short charging times, long cycle lifespans, and high power densities, hold promise for powering flexible fabric-based electronics. To date, however, only short lengths of functioning fiber supercapacitors have been produced. The primary goal of this study is to introduce a supercapacitor fiber that addresses the remaining challenges of scalability, flexibility, cladding impermeability, and performance at length. This is achieved through a top-down fabrication method in which a macroscale preform is thermally drawn into a fully functional energy-storage fiber. The preform consists of five components: thermally reversible porous electrode and electrolyte gels; conductive polymer and copper microwire current collectors; and an encapsulating hermetic cladding. This process produces 100 m of continuous functional supercapacitor fiber, orders of magnitude longer than any previously reported. In addition to flexibility (5 mm radius of curvature), moisture resistance (100 washing cycles), and strength (68 MPa), these fibers have an energy density of 306 µWh cm-2 at 3.0 V and ≈100% capacitance retention over 13 000 cycles at 1.6 V. To demonstrate the utility of this fiber, it is machine-woven and used as filament for 3D printing.

Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses.

We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including reconfigurable lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and widely separated multi-wavelength lenses (λ = 1 µm and 10 µm). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths in diameter before requiring domain-decomposition approximations, while multilayer topology optimization with ∼105 degrees of freedom can tackle challenging design problems even when restricted to axisymmetric structures.

Non-Abelian generalizations of the Hofstadter model: spin-orbit-coupled butterfly pairs.

The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

Heuristic recurrent algorithms for photonic Ising machines.

The inability of conventional electronic architectures to efficiently solve large combinatorial problems motivates the development of novel computational hardware. There has been much effort toward developing application-specific hardware across many different fields of engineering, such as integrated circuits, memristors, and photonics. However, unleashing the potential of such architectures requires the development of algorithms which optimally exploit their fundamental properties. Here, we present the Photonic Recurrent Ising Sampler (PRIS), a heuristic method tailored for parallel architectures allowing fast and efficient sampling from distributions of arbitrary Ising problems. Since the PRIS relies on vector-to-fixed matrix multiplications, we suggest the implementation of the PRIS in photonic parallel networks, which realize these operations at an unprecedented speed. The PRIS provides sample solutions to the ground state of Ising models, by converging in probability to their associated Gibbs distribution. The PRIS also relies on intrinsic dynamic noise and eigenvalue dropout to find ground states more efficiently. Our work suggests speedups in heuristic methods via photonic implementations of the PRIS.

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.

Synthesis and observation of non-Abelian gauge fields in real space.

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

Structured multimaterial filaments for 3D printing of optoelectronics.

Simultaneous 3D printing of disparate materials; metals, polymers and semiconductors with device quality interfaces and at high resolution remains challenging. Moreover, the precise placement of discrete and continuous domains to enable both device performance and electrical connectivity poses barriers to current high-speed 3D-printing approaches. Here, we report filaments with disparate materials arranged in elaborate microstructures, combined with an external adhesion promoter, to enable a wide range of topological outcomes and device-quality interfaces in 3D printed media. Filaments, structured towards light-detection, are printed into fully-connected 3D serpentine and spherical sensors capable of spatially resolving light at micron resolution across its entire centimeter-scale surface. 0-dimensional metallic microspheres generate light-emitting filaments that are printed into hierarchical 3D objects dotted with electroluminescent pixels at high device resolution of 55 µm not restricted by surface tension effects. Structured multimaterial filaments provides a path towards custom three-dimensional functional devices not realizable by existing approaches.

Towards integrated tunable all-silicon free-electron light sources.

Extracting light from silicon is a longstanding challenge in modern engineering and physics. While silicon has underpinned the past 70 years of electronics advancement, a facile tunable and efficient silicon-based light source remains elusive. Here, we experimentally demonstrate the generation of tunable radiation from a one-dimensional, all-silicon nanograting. Light is generated by the spontaneous emission from the interaction of these nanogratings with low-energy free electrons (2-20 keV) and is recorded in the wavelength range of 800-1600 nm, which includes the silicon transparency window. Tunable free-electron-based light generation from nanoscale silicon gratings with efficiencies approaching those from metallic gratings is demonstrated. We theoretically investigate the feasibility of a scalable, compact, all-silicon tunable light source comprised of a silicon Field Emitter Array integrated with a silicon nanograting that emits at telecommunication wavelengths. Our results reveal the prospects of a CMOS-compatible electrically-pumped silicon light source for possible applications in the mid-infrared and telecommunication wavelengths.

Diode fibres for fabric-based optical communications.

Semiconductor diodes are basic building blocks of modern computation, communications and sensing1. As such, incorporating them into textile-grade fibres can increase fabric capabilities and functions2,  to encompass, for example,  fabric-based communications or physiological monitoring. However, processing challenges have so far precluded the realization of semiconducting diodes of high quality in thermally drawn fibres. Here we demonstrate a scalable thermal drawing process of electrically connected diode fibres. We begin by constructing a macroscopic preform that hosts discrete diodes internal to the structure alongside hollow channels through which conducting copper or tungsten wires are fed. As the preform is heated and drawn into a fibre, the conducting wires approach the diodes until they make electrical contact, resulting in hundreds of diodes connected in parallel inside a single fibre. Two types of in-fibre device are realized: light-emitting and photodetecting p-i-n diodes. An inter-device spacing smaller than 20 centimetres is achieved, as well as light collimation and focusing by a lens designed in the fibre cladding. Diode fibres maintain performance throughout ten machine-wash cycles, indicating the relevance of this approach to apparel applications. To demonstrate the utility of this approach, a three-megahertz bi-directional optical communication link is established between two fabrics containing receiver-emitter fibres. Finally, heart-rate measurements with the diodes indicate their potential for implementation in all-fabric physiological-status monitoring systems. Our approach provides a path to realizing ever more sophisticated functions in fibres, presenting  the prospect of a fibre 'Moore's law' analogue  through the increase of device density and function in thermally drawn textile-ready fibres.