Marin Soljacic

We investigate two-dimensional spinless systems in which the fundamental domain in momentum space takes the form of a non-orientable closed manifold known as the real projective plane (RP2), in contrast to the usual case of a torus. We construct Wilson loops on RP2 to define a Z2 invariant that identifies topologically distinct phases. We find that the transition between the trivial and topological phases is mediated by an odd number of Weyl points within the fundamental domain, and that these Weyl points cannot all be annihilated. The topological phase is characterized by the presence of gapless bi-directional edge states, a feature attributed to the Fermi-arc connectivity of the Weyl points. Lastly, we demonstrate that these systems are examples of" momentum quadrupole insulators" that exhibit a linear response of momentum current to a translation gauge field.

Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman operator theory, which has found utility in applications because it allows for a linear representation of nonlinear dynamical systems, and natural gradient methods in quantum optimization, leading to a significant acceleration of gradient-based quantum optimization. We present Quantum-circuit Alternating Controlled Koopman learning (QuACK), a novel framework that leverages an alternating algorithm for efficient prediction of gradient dynamics on quantum computers. We demonstrate QuACK's remarkable ability to accelerate gradient-based optimization across a range of applications in quantum optimization and machine learning. In fact, our empirical studies, spanning quantum chemistry, quantum condensed matter, quantum machine learning, and noisy environments, have shown accelerations of more than 200x speedup in the overparameterized regime, 10x speedup in the smooth regime, and 3x speedup in the non-smooth regime. With QuACK, we offer a robust advancement that harnesses the advantage of gradient-based quantum optimization for practical benefits.

N02. 00012: Weyl points on non-orientable Brillouin zones: Nielsen-Ninomiya, Fermi arcs and Z2 topological charge*

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

Plasmons, collective excitations of electrons in solids, are associated with strongly confined electromagnetic fields, with wavelengths far below the wavelength of photons in free space. Such strong confinement nominally holds the potential to enable optoelectronic technologies that bridge the size difference between photonic and electronic devices. However, despite decades of research in plasmonics, many applications remain limited by plasmonic losses, thus motivating a search for new engineered plasmonic materials with lower losses. Among the promising candidates for low-loss plasmonic materials are solid-state lattices with flat and energetically isolated metallic bands—with commensurately small phase spaces for phonon-assisted optical losses, a major contributor to short plasmonic lifetimes. Such electronic band structures may be created by judiciously introducing an ordered lattice of defects in an …

G38. 00002: Geometry of contact: contact planning for multi-legged robots via spin models

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the $\textit{Time-Evolving Natural Gradient (TENG)}$, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimization to obtain high accuracy in neural-network-based PDE solutions. Our comprehensive development includes algorithms like TENG-Euler and its high-order variants, such as TENG-Heun, tailored for enhanced precision and efficiency. TENG's effectiveness is further validated through its performance, surpassing current leading methods and achieving machine precision in step-by-step optimizations across a spectrum of PDEs, including the heat equation, Allen-Cahn equation, and Burgers' equation.

Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix ρ is high-dimensional, customized deep generative neural networks have been instrumental in modeling ρ. However, the complex-valued nature and normalization constraints of ρ, as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here, we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding quasiprobability distribution Q, the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow …

Time-varying optical materials have attracted recent interest for their potential to enable frequency conversion, nonreciprocal physics, photonic time-crystals, and more. However, the description of time-varying materials has been largely limited to regimes where material resonances (i.e., dispersion) can be neglected. In this work, we describe how the optics of these dispersive time-varying materials emerge from microscopic quantum mechanical models of time-driven systems. Our results are based on a framework for describing the optics of dispersive time-varying materials through quantum mechanical linear response theory. Importantly, we clarify how response functions for time-varying materials are connected to energy transfer. We provide three examples of our framework applied to systems which can be used to model a wide variety of experiments: few level models that can describe atoms, spins, or …

In ultrashort optical pulses, quantum correlations among photon numbers in different spectral components are essential for comprehending and characterizing the pulse's internal quantum structure and achieving amplitude squeezing through spectral filtering. Traditional tomographic and squeezing experiments only provide overall pulse statistics, averaging noise variances across all spectral and temporal modes, leaving the quantum characteristics of individual frequency components and the pulse's internal quantum structure unexplored. Attempts to observe multimode quantum correlations in fiber optics have been restricted to a limited number of wavelength modes, typically around 10, due to squared scaling with the required spectral filters and ill-conditioning of the inversion problem depending on the choice of filters (1). To address these limitations, we introduce a novel experimental method using arbitrarily …

Probabilistic machine learning utilizes controllable sources of randomness to encode uncertainty and enable statistical modeling. Harnessing the pure randomness of quantum vacuum noise, which stems from fluctuating electromagnetic fields, has shown promise for high speed and energy-efficient stochastic photonic elements. Nevertheless, photonic computing hardware which can control these stochastic elements to program probabilistic machine learning algorithms has been limited. Here, we implement a photonic probabilistic computer consisting of a controllable stochastic photonic element - a photonic probabilistic neuron (PPN). Our PPN is implemented in a bistable optical parametric oscillator (OPO) with vacuum-level injected bias fields. We then program a measurement-and-feedback loop for time-multiplexed PPNs with electronic processors (FPGA or GPU) to solve certain probabilistic machine learning tasks. We showcase probabilistic inference and image generation of MNIST-handwritten digits, which are representative examples of discriminative and generative models. In both implementations, quantum vacuum noise is used as a random seed to encode classification uncertainty or probabilistic generation of samples. In addition, we propose a path towards an all-optical probabilistic computing platform, with an estimated sampling rate of ~ 1 Gbps and energy consumption of ~ 5 fJ/MAC. Our work paves the way for scalable, ultrafast, and energy-efficient probabilistic machine learning hardware.

An optical neural network is constructed based on photonic integrated circuits to perform neuromorphic computing. In the optical neural network, matrix multiplication is implemented using one or more optical interference units, which can apply an arbitrary weighting matrix multiplication to an array of input optical signals. Nonlinear activation is realized by an optical nonlinearity unit, which can be based on nonlinear optical effects, such as saturable absorption. These calculations are implemented optically, thereby resulting in high calculation speeds and low power consumption in the optical neural network.

Self-trapped holes (STHs) are defects formed in silica when holes couple with phonons and localize. They play a crucial role in understanding silica's interaction with light in applications such as scintillators and optical fibers. Ab-initio studies of STHs through DFT have been performed and benchmarked against experimental data, but they considered only the final polaron and not its formation process. Additionally, the results were sensitive to the fraction of exact exchange used. In this work, we compute the Eliashberg spectral function and electron-phonon matrix elements to provide a more detailed description of STH formation, and we use Koopman's theorem to tune the amount of exact exchange to include, correcting both deficiencies with earlier studies. Our approach enables us to rationalize why certain types of STHs, differentiated by their geometry, are available in amorphous vs crystalline silica. Furthermore …

Recent advances in deep learning have provided impressive results across a wide range of computational problems such as computer vision, natural language, or reinforcement learning. However, many of these improvements are constrained to problems with large-scale curated datasets which require a lot of human labor to gather. Additionally, these models tend to generalize poorly under both slight distributional shifts and low-data regimes. In recent years, emerging fields such as meta-learning and self-supervised learning have been closing the gap between proof-of-concept results and real-life applications of machine learning by extending deep learning to the semi-supervised and few-shot domains. We follow this line of work and explore spatiotemporal structure in a recently introduced image-to-image translation problem for storm event imagery in order to: i) formulate a novel multi-task few-shot image …

An integrated optical beam steering device includes a planar Luneburg lens that collimates beams from different inputs in different directions within the lens plane. It also includes a curved (eg, semi-circular or arced) grating coupler that diffracts the collimated beams out of the lens plane. The beams can be steered in the plane by controlling the direction along which the lens is illuminated and out of the plane by varying the beam wavelength. Unlike other beam steering devices, this device can operate over an extremely wide field of view—up to 180—without any aberrations off boresight. In other words, the beam quality is uniform in all directions, unlike with aplanatic lenses, thanks to the circular symmetry of the planar Luneburg lens, which may be composed of subwavelength features. The lens is also robust to misalignment and fabrication imperfections and can be made using standard CMOS processes.

Model stitching (Lenc & Vedaldi 2015) is a compelling methodology to compare different neural network representations, because it allows us to measure to what degree they may be interchanged. We expand on a previous work from Bansal, Nakkiran & Barak which used model stitching to compare representations of the same shapes learned by differently seeded and/or trained neural networks of the same architecture. Our contribution enables us to compare the representations learned by layers with different shapes from neural networks with different architectures. We subsequently reveal unexpected behavior of model stitching. Namely, we find that stitching, based on convolutions, for small ResNets, can reach high accuracy if those layers come later in the first (sender) network than in the second (receiver), even if those layers are far apart.

Artificial intelligence (AI) has revolutionized the field of materials science by improving the prediction of properties and accelerating the discovery of novel materials. In recent years, publicly available material data repositories containing data for various material properties have grown rapidly. In this work, we introduce Multimodal Learning for Crystalline Materials (MLCM), a new method for training a foundation model for crystalline materials via multimodal alignment, where high-dimensional material properties (i.e. modalities) are connected in a shared latent space to produce highly useful material representations. We show the utility of MLCM on multiple axes: (i) MLCM achieves state-of-the-art performance for material property prediction on the challenging Materials Project database; (ii) MLCM enables a novel, highly accurate method for inverse design, allowing one to screen for stable material with desired properties; and (iii) MLCM allows the extraction of interpretable emergent features that may provide insight to material scientists. Further, we explore several novel methods for aligning an arbitrary number of modalities, improving upon prior art in multimodal learning that focuses on bimodal alignment. Our work brings innovations from the ongoing AI revolution into the domain of materials science and identifies materials as a testbed for the next generation of AI.

We demonstrate the generation of random bits with tunable probability distribution in an optical parametric oscillator. Bits are encoded into the phase statistics of the signal field, which are tuned by a small bias field.

How do self-supervised models actually train? We study the training dynamics of contrastive learning in three settings: a theoretical linear setting, on a low-dimensional physics-inspired dataset, and on full-fledged computer vision datasets including ImageNet. In all three settings, we show the existence of *phases*, i.e. locally stable or metastable representations, and of *phase transitions*, wherein a model rapidly and unexpectedly switches between different phases. Geometrically motivated metrics are developed to measure phase transitions. Finally, we show that phase transitions can be sped up with more robust augmentations. Code and visualizations will be made public upon publication.

Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix , which is the fundamental description for the dynamics of such systems, is high-dimensional, customized deep generative neural networks have been instrumental in modeling . However, the complex-valued nature and normalization constraints of , as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution , the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach Q-Flow and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including the dissipative harmonic oscillator and the dissipative bosonic model. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.

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 …

The design of convolutional neural networks has been increasingly focused on small and efficient models to meet the modern demands of edge devices. Thus, analyzing the theoretical limits of convolutional layers of previously unexplored complexities is critical. Here, we present a logarithmic-scale efficient convolutional neural network architecture. Our model is based on the well-known depthwise convolution, and on two new layers, which we introduce in this work: an asymmetric grouped convolution and a depthwise fast wavelet transform layer. By applying asymmetry in channel dimensions and applying a provably optimal fast algorithm we shrink the complexity of convolutional blocks by an factor (from to , where is the number of channels. Experiments on CIFAR-10, CIFAR100 and ImageNet classification show superior/comparable performances of our model to classical …

Probabilistic computing based on electronic implementations has shown promising applications in integer factorization and other types of combinatorial problems. Its key building block, a probabilistic bit (p-bit), consists of a tunable random number generator whose probability distribution can be tailored on-demand. We demonstrate an optical p-bit based on the spontaneous symmetry breaking of a bi-stable system. Optical parametric oscillators (OPO) are bistable nonlinear systems in which the phase of a down-converted signal ω can take two discrete values (0 or π). The randomness of the measured phase originates from the quantum vacuum field and is therefore truly random. We show coherent control of the OPO's phase probability distribution, exhibiting a continuous transition from purely random (50/50 distribution of 0/π phase) to purely deterministic (phase determined by the bias field). We first confirm that …

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 …

In recent years contrastive learning has become a state-of-the-art technique in representation learning, but the exact mechanisms by which it trains are not well understood. By focusing on physics-inspired datasets with low intrinsic dimensionality, we are able to visualize and study contrastive training procedures in better resolution. We empirically study the geometric development of contrastively learned embeddings, discovering phase transitions between locally metastable embedding conformations towards an optimal structure. Ultimately we show a strong experimental link between stronger augmentations and decreased training time for contrastively learning more geometrically meaningful representations.

We present a method for x-ray spectroscopy, combining nanophotonic scintillator inverse design with an image reconstruction algorithm. We demonstrate our pipeline on 3-energy x-ray spectroscopy, achieving 8% reconstruction error under 1% Gaussian noise

I will present some novel AI techniques for photonics and physics in general. In particular, techniques which enable AI training with orders of magnitude less data (so-called few-shot learning techniques) will be discussed, including transfer learning and contrastive learning. Next, certain interpretable AI techniques will be discussed, including symbolic regression. Finally, our new concept of machine-learned chemical property (which we call “topogivity”) will be presented: roughly, topogivity of a given atom presents that material’s propensity to form topological materials.

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 …

Electromagnetic energy transfer is facilitated. In accordance with an example embodiment, a first resonator transmits electromagnetic energy using an electromagnetic wave, based on frequency matching and alignment of an electromagnetic field with a second resonator within a distance of one wavelength of the electromagnetic wave from the first resonator. An electromagnetic energy reflector adjacent the first resonator redirects reflected portions of the electromagnetic wave back towards the first resonator.

The topological characteristics of photonic crystals have been the subject of intense research in recent years. Despite this, the basic question of whether photonic band topology is rare or abundant -- i.e., its relative prevalence -- remains unaddressed. Here, we determine the prevalence of stable, fragile, and higher-order photonic topology in the 11 two-dimensional crystallographic symmetry settings that admit diagnosis of one or more of these phenomena by symmetry analysis. Our determination is performed on the basis of a data set of 550000 randomly sampled, two-tone photonic crystals, spanning 11 symmetry settings and 5 dielectric contrasts, and examined in both transverse electric (TE) and magnetic (TM) polarizations. We report the abundance of nontrivial photonic topology in the presence of time-reversal symmetry and find that stable, fragile, and higher-order topology are generally abundant. Below the first band gap, which is of primary experimental interest, we find that stable topology is more prevalent in the TE polarization than the TM; is only weakly, but monotonically, dependent on dielectric contrast; and that fragile topology is near-absent. In the absence of time-reversal symmetry, nontrivial Chern phases are also abundant in photonic crystals with 2-, 4-, and 6-fold rotational symmetries but comparatively rare in settings with only 3-fold symmetry. Our results elucidate the interplay of symmetry, dielectric contrast, electromagnetic polarization, and time-reversal breaking in engendering topological photonic phases and may inform general design principles for their experimental realization.

We introduce a general mechanism for obtaining Weyl points in a stack of two-dimensional (2D) quasicrystals, which can be extended to any stack of aperiodic layers. We do so by driving a topological phase transition with the vertical crystal momentum as the tuning parameter, which leads to gap closures at the critical points sourcing Berry curvature. To illustrate, we use a simple 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. The presence of Weyl points is established via the local Chern marker, projected band structure, and density of states. Interestingly, we uncover an analog of Fermi arcs in the quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed lines connecting the band degeneracies and indexed by the Bragg peaks. Signatures of such surface states in quantum oscillations and the prospect of a fully quasicrystalline Weyl system are also discussed …

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 light and lasing. Notably, flatbands support supercollimation—diffractionless wavepacket propagation—in both systems,. 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 lasers, microscopy and spectroscopy,, and particle accelerators,, 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 …

Entangled photon pairs are a vital resource for quantum information, computation, and metrology. Although these states are routinely generated at optical frequencies, sources of quantum of light are notably lacking at extreme ultraviolet (XUV) and soft X-ray frequencies. Here, we show that strongly driven systems used for high harmonic generation (HHG) can become versatile sources of entangled photon pairs at these high frequencies. We present a general theory of photon pair emission from non-perturbatively driven systems, which we refer to as "strong field pair generation" (SFPG). We show that strongly driven noble gases can generate thousands of entangled pairs per shot over a large XUV bandwidth. The emitted pairs have distinctive properties in angle and frequency, which can be exploited to discriminate them from the background HHG signal. We connect SFPG theory to the three-step-model of HHG, showing that this pair emission originates from the impact of high frequency vacuum fluctuations on electron recombination. The light produced by SFPG exhibits attosecond Hong-Ou-Mandel correlations, and can be leveraged as a source of heralded single photon attosecond pulses. Our findings aid ongoing efforts to propel quantum optics into the XUV and beyond.

When impinging on optical structures or passing in their vicinity, free electrons can spontaneously emit electromagnetic radiation, a phenomenon generally known as cathodoluminescence. Free-electron radiation comes in many guises: Cherenkov, transition, and Smith–Purcell radiation, but also electron scintillation, commonly referred to as incoherent cathodoluminescence. While those effects have been at the heart of many fundamental discoveries and technological developments in high-energy physics in the past century, their recent demonstration in photonic and nanophotonic systems has attracted a great deal of attention. Those developments arose from predictions that exploit nanophotonics for novel radiation regimes, now becoming accessible thanks to advances in nanofabrication. In general, the proper design of nanophotonic structures can enable shaping, control, and enhancement of free-electron …

Plasmons, collective excitations of electrons in solids, are associated with strongly confined electromagnetic fields, with wavelengths far below the wavelength of photons in free space. This strong confinement promises the realization of optoelectronic devices that could bridge the size difference between photonic and electronic devices. However, despite decades of research in plasmonics, many applications remain limited by plasmonic losses, thus motivating a search for new engineered plasmonic materials with lower losses. A promising pathway for low-loss plasmonic materials is the engineering of materials with flat and energetically isolated metallic bands, which can strongly limit phonon-assisted optical losses, a major contributor to short plasmonic lifetimes. Such electronic band structures may be created by judiciously introducing an ordered lattice of defects in an insulating host material. Here, we explore this approach, presenting several low-loss, highly-confined, and tunable plasmonic materials based on arrays of carbon substitutions in hexagonal boron nitride (hBN) monolayers. From our first-principles calculations based on density functional theory (DFT), we find plasmonic structures with mid-infrared plasmons featuring very high confinements ( exceeding 2000) and quality factors in excess of 1000. We provide a systematic explanation of how crystal structure, electronic bandwidth, and many-body effects affect the plasmonic dispersions and losses of these materials. The results are thus of relevance to low-loss plasmon engineering in other flat band systems.

Quantum mechanics imposes fluctuations onto physical quantities, leading to sources of noise absent in the classical world. For light, quantum fluctuations limit many applications requiring high sensitivities, resolutions, or bandwidths. In many cases, taming quantum fluctuations requires dealing with highly multimode systems with both light and matter degrees of freedom - a regime which has traditionally eluded mechanistic insights, and for which general rules are largely lacking. In this work, we introduce and experimentally test a new theoretical framework for describing quantum noise in multimode systems of light and matter, called quantum sensitivity analysis. The framework leads to new general rules and mechanisms for quantum noise propagation - and accurately models all known quantum noise phenomena in nonlinear optics. We develop experiments to test unexplored aspects of our theory in the quantum noise dynamics of ultrafast multimode systems. For example, in physical effects related to supercontinuum generation, we observe and account for a proliferation of ultra low-noise pairs of wavelengths, despite that individual wavelengths are very noisy due to strong nonlinear amplification of vacuum fluctuations. We then show that by taking advantage of the spectral dynamics of quantum noise, it is possible to generate quantum light states, such as squeezed states, even with very noisy and complex light states - by exploiting the spectral dynamics of vacuum fluctuations undergoing nonlinearity and Raman scattering. Effects like these can widely extend the range of sources that can be used for quantum metrology, bringing quantum …

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and inductive bias. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions, allows for exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on quantum state learning as well as finding the ground state of the challenging 2D - Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for quantum many-body physics simulation, quantum technology design, and generative modeling in artificial intelligence.

We predict that a combination of frequency-dependent outcoupling and optical nonlinearity in semiconductor lasers can create sharply intensity-dependent loss that squeezes intensity noise far below the shot noise limit.

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 …

Interactions between photons (nonlinearities) enable a powerful form of control over the state of light. This control has enabled technologies such as light sources at new wavelengths, ultra-short optical pulses, frequency-comb metrology systems, even quantum light sources. Common to a wide variety of nonlinear optical technologies is an equilibrium between an energy source, such as an external laser, and dissipation, such as radiation loss or absorption. In the vast majority of these systems, the coupling between the system and the outside world (which leads to loss) is well-described as ``Markovian,'' meaning that the outside world has no memory of its past state. In this work, we introduce a class of driven-dissipative systems in which a nonlinear cavity experiences non-Markovian coupling to the outside world. In the classical regime, we show that these non-Markovian cavities can have extremely low thresholds for nonlinear effects, as well as self-pulsing instabilities at THz rates, and rich phase diagrams with alternating regions of stability and instability. In the quantum regime, we show how these system, when implemented on state-of-the-art platforms, can enable generation of strongly squeezed cavity states with intensity fluctuations that can be more than 15 dB below the classical limit, in contrast to the Markovian driven-dissipative cavity, in which the limit is 3 dB. In the regime of few-photon nonlinearity, such non-Markovian cavities can enable a deterministic protocol to generate Fock states of high order, which are long-desired, but still elusive at optical frequencies. We expect that exploiting non-Markovian couplings in nonlinear optics …

We introduce a general mechanism for obtaining Weyl points in a stack of 2D quasicrystals, which can be extended to any stack of aperiodic layers. It relies on driving a topological phase transition by tuning the vertical crystal-momentum, forcing gap closures at the critical points. We illustrate our theory in a 3D generalization of the Qi-Wu-Zhang model defined on a Penrose quasicrystal. We establish the Weyl-point character of the band closings by a number of distinct signatures, including via the local Chern marker, the bulk dispersion, and the density of states. Interestingly, we also uncover an analogue of Fermi arcs in the quasicrystalline setting, manifested by densely distributed lines in the Fourier-resolved spectrum, in one-to-one correspondence with the Bragg peaks of the structure factor. Possible experimental realizations and connections to the recently observed band crossings in a stack of chalcogenide …

Meta learning methods have found success when applied to few shot classification problems, in which they quickly adapt to a small number of labeled examples. Prototypical representations, each representing a particular class, have been of particular importance in this setting, as they provide a compact form to convey information learned from the labeled examples. However, these prototypes are just one method of representing this information, and they are narrow in their scope and ability to classify unseen examples. We propose the implementation of contextualizers, which are generalizable prototypes that adapt to given examples and play a larger role in classification for gradient-based models. We demonstrate how to equip meta learning methods with contextualizers and show that their use can significantly boost performance on a range of few shot learning datasets. We also present figures of merit …

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 …

State-of-the-art (SOTA) semi-supervised learning (SSL) methods have been highly successful in leveraging a mix of labeled and unlabeled data, often via self-training or pseudo-labeling. During pseudo-labeling, the model's predictions on unlabeled data are used for training and may result in confirmation bias where the model reinforces its own mistakes. In this work, we show that SOTA SSL methods often suffer from confirmation bias and demonstrate that this is often a result of using a poorly calibrated classifier for pseudo labeling. We introduce BaM-SSL, an efficient Bayesian Model averaging technique that improves uncertainty quantification in SSL methods with limited computational or memory overhead. We demonstrate that BaM-SSL mitigates confirmation bias in SOTA SSL methods across standard vision benchmarks of CIFAR-10, CIFAR-100, giving up to 16% improvement in test accuracy on the CIFAR-100 with 400 labels benchmark. Furthermore, we also demonstrate their effectiveness in additional realistic and challenging problems, such as class-imbalanced datasets and in photonics science.

Light and matter can now interact in a regime where their coupling is stronger than their bare energies. This deep-strong coupling (DSC) regime of quantum electrodynamics promises to challenge many conventional assumptions about the physics of light and matter. Here we show how light-matter interactions in this regime give rise to electromagnetic nonlinearities dramatically different from those of naturally existing materials. Excitations in the DSC regime act as photons with a linear energy spectrum up to a critical excitation number, after which the system suddenly becomes strongly anharmonic, thus acting as an effective intensity-dependent nonlinearity of an extremely high order. We show that this behavior allows for N-photon blockade (with N≫ 1), enabling qualitatively new kinds of quantum light sources. For example, this nonlinearity forms the basis for a new type of gain medium, which when integrated …

Surface plasmon polariton (SPP) lasers have so far relied on metallic substrates. Here, we report a three-dimensional (3D) plasmonic particle laser using gold coating on lead halide perovskite crystals as small as 620 nm in size. Upon optical pumping, SPP modes are strongly confined along the particle edges with high Purcell enhancement in room conditions. Lasing of metal-coated plasmonic laser particles in live cells is demonstrated.

Weyl fermions are hypothetical chiral particles that can also manifest as excitations near three-dimensional band crossing points in lattice systems. These quasiparticles are subject to the Nielsen-Ninomiya" no-go" theorem when placed on a lattice, requiring the total chirality across the Brillouin zone to vanish. This constraint results from the topology of the (orientable) manifold on which they exist. Here, we ask to what extent the concepts of topology and chirality of Weyl points remain well-defined when the underlying manifold is non-orientable. We show that the usual notion of chirality becomes ambiguous in this setting, allowing for systems with a non-zero total chirality. Furthermore, we discover that Weyl points on non-orientable manifolds carry an additional topological invariant which satisfies a different no-go theorem. We implement such Weyl points by imposing a non-symmorphic symmetry in the …

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.

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 …

Expanding the repertoire of two dimensional materials is of fundamental importance for the viability of optoelectronic and plasmonic properties beyond those achievable by canonical low dimensional materials such as graphene. Herein, we explore the landscape of carbon substitutional defects in hexagonal boron nitride and explicate their electronic, phononic, and plasmonic properties through the use of Density Functional Theory. We report the structural stability of our candidate materials, their band structures as a function of electronic doping, as well as their TM polarized plasmonic dispersions, confinements, and losses. We show that a simple analytical model explains doping induced changes in the spectra of optical excitations in our materials to a high level of accuracy. Our work also indicates that this new class of plasmonic materials allows for tunable plasmonic excitations in the infrared with confinements …

Convolutional neural networks (CNNs), well-known for their translational invariance property on translational man-ifolds, are not guaranteed to generalize to images on other types of manifolds. Existing works extending CNNs' translational invariance property are limited to linear transformations such as rotation. We propose a novel framework, the Manifold Transfer Network, with an embedded inductive bias for any specified nonlinear manifold. Our model maps a nonlinear transformation to a linear translation on a translational manifold, making it suitable for a CNN to learn and predict. We design such a map through the solutions of a particular class of partial differential equations. We empirically apply our method to the domain of radial lens distortion rectification. In our experiments on the CelebA dataset we demonstrate superior performance of our model compared to conventional baselines.

Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on the careful analysis of their bands and mode profiles, but recent theoretical advances have revealed new and powerful insights into the connection between band symmetry, connectivity, and topology. Here we propose a combined global and local optimization framework that integrates a flexible symmetry-constrained level-set parametrization with standard gradient-free optimization algorithms to optimize topological photonic crystals, a problem setting where the objective function may be highly nonconvex and noncontinuous. Our framework can be applied to any symmetry-identifiable band topology, and we demonstrate its applicability to several prominent kinds of three-dimensional band topologies, namely, Γ-enforced nodal lines, Weyl …

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space with respect to the particle number, a direct simulation is intractable. While representing quantum states with tensor networks and neural networks are the two state-of-the-art methods for approximate simulations, each has its own limitations in terms of expressivity and optimization. To address these challenges, we develop a novel architecture, Autoregressive Neural TensorNet (ANTN), which bridges tensor networks and autoregressive neural networks. We show that Autoregressive Neural TensorNet parameterizes normalized wavefunctions with exact sampling, generalizes the expressivity of tensor networks and autoregressive neural networks, and inherits a variety of symmetries from autoregressive neural networks. We demonstrate our approach on the 2D - Heisenberg model with different systems sizes and coupling parameters, outperforming both tensor networks and autoregressive neural networks. Our work opens up new opportunities for both scientific simulations and machine learning applications.

Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and quantum communications. Nevertheless, a wide variety of important quantum light states are currently challenging to deterministically generate at optical frequencies. In part, this is due to a relatively small number of schemes that prepare target quantum states given nonlinear interactions. Here, we present an especially simple concept for deterministically generating and stabilizing important quantum states of light, using only simple third-order optical nonlinearities and engineered dissipation. We show how by considering either a nonlinear cavity with frequency-dependent outcoupling, or a chain of nonlinear waveguides, one can "filter" out all but a periodic ladder of photon number components of a density matrix. As examples of this phenomenon, we show cavities which can stabilize squeezed states, as well as produce "photon-number-comb" states. Moreover, in these types of filter cavities, Glauber coherent states will deterministically evolve into Schrodinger cat states of a desired order. We discuss potential realizations in quantum nonlinear optics. More broadly, we expect that combining the techniques introduced here with additional "phase-sensitive" nonlinearities (such as second-order nonlinearity) should enable passive stabilization and generation of a wider variety of states than shown here.

We present a method to produce entangled photon pairs in the extreme ultraviolet (EUV) and X-ray regime, using a new highly nonperturbative nonlinear optical process which we term “high harmonic down conversion”(HHDC).

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 …

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks. Our code is available at https://github. com/clott3/multi-sym-ensem

Recent experiments have revealed ultrastrong coupling between light and matter as a promising avenue for modifying material properties, such as electrical transport, chemical reaction rates, and even superconductivity. Here, we explore (ultra) strong coupling as a means for manipulating the optical response of metamaterials based on ensembles of constituent units individually in the ultrastrong-coupling regime. We develop a framework based on linear response for quantum electrodynamical systems to study how light-matter coupling affects the optical response. We begin by applying this framework to find the optical response of a two-level emitter coupled to a single cavity mode, which could be seen as a “meta-atom” of a metamaterial built from repeated units of this system. We find optical behavior ranging from that of a simple two-level system (Lorentz-oscillator) to effectively transparent, as the coupling goes …

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by symmetry, this problem cannot be addressed directly with conventional band-symmetry analysis due to the existence of a photonic polarization vortex at zero frequency. We develop an approach for overcoming the associated symmetry singularity by incorporating fictitious, auxiliary longitudinal modes. Our strategy also enables us to extend recent developments in symmetry-based topological analysis to the fundamental gap of three-dimensional photonic crystals. Exploiting this, we systematically study the topology of the minimal fundamental gaps. This reveals the existence of topological gap obstructions that push the fundamental gap higher than what a conventional …

In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we demonstrate the use of a machine learning system to aid the discovery of symbolic models that capture nonlinear and dynamical relationships in social science datasets. By extending neuro-symbolic methods to find compact functions and differential equations in noisy and longitudinal data, we show that our system can be used to discover interpretable models from real-world data in economics and sociology. Augmenting existing workflows with symbolic regression can help uncover novel relationships and explore counterfactual models during the scientific process. We propose that this AI-assisted framework can bridge parametric and non-parametric models commonly employed in social science research by systematically exploring the space of nonlinear models and enabling fine-grained control over expressivity and interpretability.

The Hofstadter model exemplifies a large class of physical systems characterized by particles hopping on a lattice immersed in a gauge field. Recent advancements on various synthetic platforms have enabled highly controllable simulations of such systems with tailored gauge fields featuring complex spatial textures. These synthetic gauge fields could introduce synthetic symmetries that do not appear in electronic materials. Here, in an SU (2) non-Abelian Hofstadter model, we theoretically show the emergence of multiple nonsymmorphic chiral symmetries, which combine an internal unitary antisymmetry with fractional spatial translation. Depending on the values of the gauge fields, the nonsymmorphic chiral symmetries can exhibit non-Abelian algebra and protect Kramers quartet states in the bulk band structure, creating general fourfold degeneracy at all momenta. These nonsymmorphic chiral symmetries protect …

Bayesian optimization (BO) is a popular algorithm for global optimization of expensive black-box functions (eg experiments or derivative-free numerical simulations that are costly or time-consuming), but there are many domains where the function is not completely black-box. For example, the data may have some known structure or symmetries, and the data generation process can yield useful intermediate or auxiliary information. However, the surrogate models typically used in BO, Gaussian Processes (GPs), scale poorly with dataset size and dimensionality and struggle to adapt to specific domains. Here, we propose using a class of deep learning models called Bayesian Neural Networks (BNNs) as the surrogate function, as their representation power and flexibility to handle structured data and exploit auxiliary information enable BO to be applied to complex problems. We demonstrate BO on a number of realistic …

I will present our recent work on determining where the fundamental, or first, photonic band gap can be opened in three-dimensional photonic crystals with spatial and time-reversal symmetry. In particular, I will present a symmetry-based framework for determining the minimum possible band connectivity below the fundamental photonic gap across every space group, as well as the determination of any associated symmetry-identifiable topology. By systematically examining the topology of all possible minimum-connectivity configurations, we find a new, uniquely photonic topological effect, Γ-enforced topology, that obstructs symmetry-allowed gap-openings by requiring the presence of topological nodal lines.

We present a method for angle and wavelength sensing for underdetermined imaging systems by performing end-to-end nanophotonic inverse design with a compressed sensing backend.

We demonstrate how Implosion Fabrication, a new three-dimensional nanofabrication technique, enables the realization of three-dimensional photonic devices at optical wavelengths. We realize two- and three-dimensional optical crystals of hydrogel-embedded silver meta-atoms.

Finding efficient optimization methods plays an important role for quantum optimization and quantum machine learning on near-term quantum computers. While backpropagation on classical computers is computationally efficient, obtaining gradients on quantum computers is not, because the computational complexity scales linearly with the number of parameters and measurements. In this paper, we connect Koopman operator theory, which has been successful in predicting nonlinear dynamics, with natural gradient methods in quantum optimization. We propose a data-driven approach using Koopman operator learning to accelerate quantum optimization and quantum machine learning. We develop two new families of methods: the sliding window dynamic mode decomposition (DMD) and the neural DMD for efficiently updating parameters on quantum computers. We show that our methods can predict gradient dynamics on quantum computers and accelerate the quantum variational eigensolver used in quantum optimization, as well as quantum machine learning. We further implement the learning algorithms on a real quantum computer and demonstrate their practical effectiveness.

Utilizing surface plasmon polaritons (SPPs) is one of the most promising ways to miniaturize lasers into subwavelength-scale. Despite its potential, it has been challenging to make a plasmonic laser having a sub-micrometer scale in all three dimensions due to large cavity loss. Here, we demonstrate single-particle lasing around 540 nm with full-submicron, cesium lead bromide perovskite (CsPbBr 3) crystals atop polymer-coated gold substrates at room temperature. With a large number (~ 100) of devices, we systematically study the lasing action of plasmonic test and photonic control groups. The achieved smallest plasmonic laser was 0.56 μm× 0.58 μm× 0.32 μm in size, ten-fold smaller than that of our smallest photonic laser. Key elements to efficient plasmonic lasing are identified as enhanced optical gain by the Purcell effect, long carrier diffusivity, a large spontaneous emission factor, and a high group index …

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (e.g., the object can be described by a small number of nonzero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework effectively optimizes metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select …

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 …

Here, we introduce a mechanism of “sharp nonlinear gain” that strongly suppresses quantum fluctuations of lasers. This effect can lead to orders-of-magnitude suppression of intensity fluctuations in real lasers, as well as macroscopic sub-Poissonian light.

We present a new gain concept based on time-modulated quantum systems. We show "Floquet lasers" incorporating this gain enable phenomena such as single-threshold coherent multimode lasing and even lasing without traditional population inversion.

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. Achieving this kind of interpretable system identification is even more difficult for partially observed systems. We propose a machine learning framework for discovering the governing equations of a dynamical system using only partial observations, combining an encoder for state reconstruction with a sparse symbolic model. The entire architecture is trained end-to-end by matching the higher-order symbolic time derivatives of the sparse symbolic model with finite difference estimates from the data. Our tests show that this method can successfully reconstruct the full system state and identify the equations of motion governing the underlying dynamics for a variety of ordinary differential …

Fast gradient-based optimization algorithms have become increasingly essential for the computationally efficient training of machine learning models. One technique is to multiply the gradient by a preconditioner matrix to produce a step, but it is unclear what the best preconditioner matrix is. This paper introduces a novel machine learning optimizer called LODO, which tries to online meta-learn the best preconditioner during optimization. Specifically, our optimizer merges Learning to Optimize (L2O) techniques with quasi-Newton methods to learn preconditioners parameterized as neural networks; they are more flexible than preconditioners in other quasi-Newton methods. Unlike other L2O methods, LODO does not require any meta-training on a training task distribution, and instead learns to optimize on the fly while optimizing on the test task, adapting to the local characteristics of the loss landscape while traversing it. Theoretically, we show that our optimizer approximates the inverse Hessian in noisy loss landscapes and is capable of representing a wide range of inverse Hessians. We experimentally verify that our algorithm can optimize in noisy settings, and show that simpler alternatives for representing the inverse Hessians worsen performance. Lastly, we use our optimizer to train a semi-realistic deep neural network with 95k parameters at speeds comparable to those of standard neural network optimizers.

Fock states are the most fundamental quantum states of light, as they are eigenstates of the electromagnetic field Hamiltonian. They underlie numerous quantum information protocols and could allow next-generation sensors with vastly improved sensitivity far bypassing the shot noise limit. However, the current state of the art is limited to weakly intensity-squeezed light and few-photon Fock states. Here, we propose applying the phenomenon of nonlinear dispersive loss to semiconductor laser platforms, harnessing their strong nonlinearities and convenient integration with on-chip photonics to create lasers with strong intensity noise squeezing, paving the way to applications including enhanced-sensitivity biosensors to on-chip quantum computing.

Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex dynamical systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build efficient, stable predictive models. Many current approaches for discovering conservation laws rely on fine-grained time measurements and dynamical information. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach, combining the Wasserstein metric from optimal transport with diffusion maps, to determine all the conserved quantities that vary across trajectories sampled from a dynamical system. We test this new approach on a variety of physical systems and demonstrate that our manifold learning method is able to both identify the number of conserved quantities and …

An integrated optical beam steering device includes a planar dielectric lens that collimates beams from different inputs in different directions within the lens plane. It also includes an output coupler, such as a grating or photonic crystal, that guides the collimated beams in different directions out of the lens plane. A switch matrix controls which input port is illuminated and hence the in-plane propagation direction of the collimated beam. And a tunable light source changes the wavelength to control the angle at which the collimated beam leaves the plane of the substrate. The device is very efficient, in part because the input port (and thus in-plane propagation direction) can be changed by actuating only log 2 N of the N switches in the switch matrix. It can also be much simpler, smaller, and cheaper because it needs fewer control lines than a conventional optical phased array with the same resolution.

We develop a general framework to enhance and control X-ray scintillation by embedding nanophotonic structures into scintillators. We demonstrate 10-fold scintillation enhancement in a conventional scintillator, showing the potential of our technique for X-ray imaging.

We show in both theory and experiment that flatband photonic resonances can control and boost free-electron radiation, as validated by enhancement, band, and polarization-shaping measurements.

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 …

Large non-Gaussian states of light are a highly coveted resource in quantum science and technology. An important example of such states are n-photon states of light (Fock states), which, besides being the most fundamental states of the quantized radiation field, are theoretically believed to be valuable for many tasks including metrology, communication, simulation, quantum state generation, and information processing. However, the deterministic creation of even approximate large-number Fock states at optical frequencies is a long-standing open problem. Here, we present a fundamental new effect in nonlinear photonic systems, called n-photon bound states in the continuum, which can be applied to deterministically create large Fock states, as well as very highly intensity-squeezed states of light. The effect is one in which destructive interference gives a certain quantum state of light an infinite lifetime, despite …

State-of-the-art (SOTA) semi-supervised learning (SSL) methods have been highly successful in leveraging a mix of labeled and unlabeled data by combining techniques of consistency regularization and pseudo-labeling. During pseudo-labeling, the model's predictions on unlabeled data are used for training and thus, model calibration is important in mitigating confirmation bias. Yet, many SOTA methods are optimized for model performance, with little focus directed to improve model calibration. In this work, we empirically demonstrate that model calibration is strongly correlated with model performance and propose to improve calibration via approximate Bayesian techniques. We introduce a family of new SSL models that optimizes for calibration and demonstrate their effectiveness across standard vision benchmarks of CIFAR-10, CIFAR-100 and ImageNet, giving up to 15.9% improvement in test accuracy. Furthermore, we also demonstrate their effectiveness in additional realistic and challenging problems, such as class-imbalanced datasets and in photonics science.

Sources of photons with controllable quantum properties such as entanglement and squeezing are desired for applications in quantum information, metrology and sensing. However, fine-grained control over these properties is hard to achieve, especially for two-photon sources. Here we propose a mechanism for the controlled generation of entangled and squeezed photon pairs using superluminal or accelerating modulations of the refractive index in a medium or both. By leveraging time-changing dielectric media, where quantum vacuum fluctuations of the electromagnetic field can be converted into photon pairs, we show that energy and momentum conservation in multimode systems give rise to frequency and angle correlations of photon pairs controlled by the trajectory of index modulation. In our examples, these radiation effects are two-photon analogues of Cherenkov and synchrotron radiation by moving …

A photonic parallel network can be used to sample combinatorially hard distributions of Ising problems. The photonic parallel network, also called a photonic processor, finds the ground state of a general Ising problem and can probe critical behaviors of universality classes and their critical exponents. In addition to the attractive features of photonic networks—passivity, parallelization, high-speed and low-power—the photonic processor exploits dynamic noise that occurs during the detection process to find ground states more efficiently.

Fuel-combustion-based thermophotovoltaic (TPV) systems are emerging as a viable power source for small, portable generators for a spectrum of applications such as UAVs, robotic platforms, and sensors. In TPV systems, an emitter heated to above 1000 K emits radiation that is then converted to electricity by a low bandgap photovoltaic cell. One promising class of TPV emitters are two-dimensional photonic crystals (PhCs) made of tantalum, which have shown high-temperature stability at 1150–1250K over hundreds of hours [1], [2] and have been implemented in a prototype system with 4.4% fuel-to-electricity efficiency [1]. Tantalum PhCs filled and capped with hafnium oxide can enable even higher optical performance with in-band emissivities of 0.8–0.9. However, two key features are difficult to realize simultaneously: a uniformly filled cavity and a thin capping layer of hafnium oxide [3], [4]. Here, we present a …

We present a new type of dissipation unique to nonlinear optical systems. We show how this phenomenon enables a new type of laser that deterministically creates macroscopic Fock states of light at optical frequencies.

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 …

Efficient optimization methods play a crucial role for quantum optimization and machine learning on near-term quantum computers. Unlike classical computers, obtaining gradients on quantum computers is costly with sample complexity scaling with the number of parameters and measurements. In this paper, we connect the natural gradient method in quantum optimization with Koopman operator theory, which provides a powerful framework for predicting nonlinear dynamics. We propose a data-driven approach for accelerating quantum optimization and machine learning via Koopman operator learning. To predict parameter updates on quantum computers, we develop new methods including the sliding window dynamic mode decomposition (DMD) and the neural-network-based DMD. We apply our methods both on simulations and real quantum hardware. We demonstrate efficient prediction and acceleration of gradient optimization on the variational quantum eigensolver and quantum machine learning.

I will present some of our recent results in the field of photonics, including novel phenomena in topology, and free electron sources of light.

Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, with the potential to replace bulky optical components. A central stepping stone toward realizing this promise is the demonstration of multifunctionality under several constraints (e.g., at multiple incident wavelengths and/or angles) in a single device, an achievement being hampered by design limitations inherent to single-layer planar geometries. Here, we propose a framework for the inverse design of multilayer metaoptics via topology optimization, showing that even few-wavelength thick devices can achieve high-efficiency multifunctionality, such as multiangle light concentration and plan-achromaticity. We embody our framework in multiple closely spaced patterned layers of a low-index polymer, with fabrication constraints specific to this platform enforced in the optimization process. We …

We propose DiffCSE, an unsupervised contrastive learning framework for learning sentence embeddings. DiffCSE learns sentence embeddings that are sensitive to the difference between the original sentence and an edited sentence, where the edited sentence is obtained by stochastically masking out the original sentence and then sampling from a masked language model. We show that DiffSCE is an instance of equivariant contrastive learning (Dangovski et al., 2021), which generalizes contrastive learning and learns representations that are insensitive to certain types of augmentations and sensitive to other "harmful" types of augmentations. Our experiments show that DiffCSE achieves state-of-the-art results among unsupervised sentence representation learning methods, outperforming unsupervised SimCSE by 2.3 absolute points on semantic textual similarity tasks.

We introduce end-to-end inverse design in which a nanophotonics frontend is optimized in conjunction with a computational-imaging backend to minimize reconstruction errors. We present several nanophotonics designs for depth, spectral and polarization imaging.

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.

Meteorological applications such as precipitation nowcasting, synthetic radar generation, statistical downscaling and others have benefited from deep learning (DL) approaches, however several challenges remain for widespread adaptation of these complex models in operational systems. One of these challenges is adequate generalizability; deep learning models trained from datasets collected in specific contexts should not be expected to perform as well when applied to different contexts required by large operational systems. One obvious mitigation for this is to collect massive amounts of training data that cover all expected meteorological contexts, however this is not only costly and difficult to manage, but is also not possible in many parts of the globe where certain sensing platforms are sparse. In this paper, we describe an application of transfer learning to perform domain transfer for deep learning models …