Intense Squeezed Light from Lasers with Sharply Nonlinear Gain at Optical Frequencies.

Nonclassical states of light, such as number-squeezed light, with fluctuations below the classical shot noise level, have important uses in metrology, communication, quantum information processing, and quantum simulation. However, generating these nonclassical states of light, especially with high intensity and a high degree of squeezing, is challenging. To address this problem, we introduce a new concept which uses gain to generate intense sub-Poissonian light at optical frequencies. It exploits a strongly nonlinear gain for photons which arises from a combination of frequency-dependent gain and Kerr nonlinearity. In this laser architecture, the interaction between the gain medium and Kerr nonlinearity suppresses the spontaneous emission at high photon number states, leading to a strong "negative feedback" that suppresses photon-number fluctuations. We discuss realistic implementations of this concept based on the use of solid-state gain media in laser cavities with Kerr nonlinear materials, showing how 90% squeezing of photon number fluctuations below the shot noise level can be realized.

Topological electromagnetic waves in dispersive and lossy plasma crystals.

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on dielectric materials with weak dispersions, this study focuses on topological phases in dispersive materials and presents a numerical study of Chern insulators in gaseous-phase plasma cylinder cells. We develop a numerical framework to address the complex material dispersion arising from the plasma medium and external magnetic fields and identify Chern insulator phases that are experimentally achievable. Using this numerical tool, we also explain the flat bands commonly observed in periodic plasmonic structures, via local resonances, and how edge states change as the edge termination is periodically modified. This work opens up opportunities for exploring band topology in new materials with non-trivial dispersions and has potential radio frequency (RF) applications, ranging from plasma-based lighting to plasma propulsion engines.

Deep Learning and Symbolic Regression for Discovering Parametric Equations.

Symbolic regression is a machine learning technique that can learn the equations governing data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and dimensionality of the systems that it can analyze. Deep learning, on the other hand, has transformed machine learning in its ability to analyze extremely complex and high-dimensional datasets. We propose a neural network architecture to extend symbolic regression to parametric systems where some coefficient may vary, but the structure of the underlying governing equation remains constant. We demonstrate our method on various analytic expressions and partial differential equations (PDEs) with varying coefficients and show that it extrapolates well outside of the training domain. The proposed neural-network-based architecture can also be enhanced by integrating with other deep learning architectures such that it can analyze high-dimensional data while being trained end-to-end. To this end, we demonstrate the scalability of our architecture by incorporating a convolutional encoder to analyze 1-D images of varying spring systems.

Discovering conservation laws using optimal transport and manifold learning.

Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical information or rely on black box parametric deep learning methods. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach for discovering conserved quantities. We test this new approach on a variety of physical systems and demonstrate that our method is able to both identify the number of conserved quantities and extract their values. Using tools from optimal transport theory and manifold learning, our proposed method provides a direct geometric approach to identifying conservation laws that is both robust and interpretable without requiring an explicit model of the system nor accurate time information.

Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics.

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution.

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.

Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials.

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered using methods that involve symmetry-based analysis of the quantum wave function. Here we use machine learning to develop a simple-to-use heuristic chemical rule that diagnoses with a high accuracy whether a material is topological using only its chemical formula. This heuristic rule is based on a notion that we term topogivity, a machine-learned numerical value for each element that loosely captures its tendency to form topological materials. We next implement a high-throughput procedure for discovering topological materials based on the heuristic topogivity-rule prediction followed by ab initio validation. This way, we discover new topological materials that are not diagnosable using symmetry indicators, including several that may be promising for experimental observation.

End-to-end metasurface inverse design for single-shot multi-channel imaging.

We introduce end-to-end inverse design for multi-channel imaging, in which a nanophotonic frontend is optimized in conjunction with an image-processing backend to extract depth, spectral and polarization channels from a single monochrome image. Unlike diffractive optics, we show that subwavelength-scale "metasurface" designs can easily distinguish similar wavelength and polarization inputs. The proposed technique integrates a single-layer metasurface frontend with an efficient Tikhonov reconstruction backend, without any additional optics except a grayscale sensor. Our method yields multi-channel imaging by spontaneous demultiplexing: the metaoptics front-end separates different channels into distinct spatial domains whose locations on the sensor are optimally discovered by the inverse-design algorithm. We present large-area metasurface designs, compatible with standard lithography, for multi-spectral imaging, depth-spectral imaging, and "all-in-one" spectro-polarimetric-depth imaging with robust reconstruction performance (≲ 10% error with 1% detector noise). In contrast to neural networks, our framework is physically interpretable and does not require large training sets. It can be used to reconstruct arbitrary three-dimensional scenes with full multi-wavelength spectra and polarization textures.

Surrogate- and invariance-boosted contrastive learning for data-scarce applications in science.

Deep learning techniques have been increasingly applied to the natural sciences, e.g., for property prediction and optimization or material discovery. A fundamental ingredient of such approaches is the vast quantity of labeled data needed to train the model. This poses severe challenges in data-scarce settings where obtaining labels requires substantial computational or labor resources. Noting that problems in natural sciences often benefit from easily obtainable auxiliary information sources, we introduce surrogate- and invariance-boosted contrastive learning (SIB-CL), a deep learning framework which incorporates three inexpensive and easily obtainable auxiliary information sources to overcome data scarcity. Specifically, these are: abundant unlabeled data, prior knowledge of symmetries or invariances, and surrogate data obtained at near-zero cost. We demonstrate SIB-CL's effectiveness and generality on various scientific problems, e.g., predicting the density-of-states of 2D photonic crystals and solving the 3D time-independent Schrödinger equation. SIB-CL consistently results in orders of magnitude reduction in the number of labels needed to achieve the same network accuracies.

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.

Submicrometer perovskite plasmonic lasers at room temperature.

Plasmonic lasers attracted interest for their ability to generate coherent light in mode volume smaller than the diffraction limit of photonic lasers. While nanoscale devices in one or two dimensions were demonstrated, it has been difficult to achieve plasmonic lasing with submicrometer cavities in all three dimensions. Here, we demonstrate submicrometer-sized, plasmonic lasers using cesium-lead-bromide perovskite (CsPbBr3) crystals, as small as 0.58 µm by 0.56 µm by 0.32 µm (cuboid) and 0.79 µm by 0.66 µm by 0.18 µm (plate), on polymer-coated gold substrates at room temperature. Our experimental and simulation data obtained from more than 100 plasmonic and photonic devices showed that enhanced optical gain by the Purcell effect, large spontaneous emission factor, and high group index are key elements to efficient plasmonic lasing. The results shed light on the three-dimensional miniaturization of plasmonic lasers.

Quantum surface-response of metals revealed by acoustic graphene plasmons.

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light-matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultraconfined acoustic graphene plasmons in graphene-dielectric-metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman d-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the acoustic graphene plasmons dispersion, and demonstrate that the high field confinement of acoustic graphene plasmons can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of acoustic graphene plasmons as plasmon rulers with ångström-scale accuracy.

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.

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.