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Abstract Deep learning has become a widespread tool in both science and industry. However, continued progress is hampered by the rapid growth in energy costs of ever-larger deep neural networks. Optical neural networks provide a potential means to solve the energy-cost problem faced by deep learning. Here, we experimentally demonstrate an optical neural network based on optical dot products that achieves 99% accuracy on handwritten-digit classification using ~3.1 detected photons per weight multiplication and ~90% accuracy using ~0.66 photons (~2.5 × 10 −19  J of optical energy) per weight multiplication. The fundamental principle enabling our sub-photon-per-multiplication demonstration—noise reduction from the accumulation of scalar multiplications in dot-product sums—is applicable to many different optical-neural-network architectures. Our work shows that optical neural networks can achieve accurate results using extremely low optical energies. 

The overall goal of photonics research is to understand and control light in new and richer ways to facilitate new and richer applications. Many major developments to this end have relied on nonlinear optical techniques, such as lasing, mode-locking, and parametric downconversion, to enable applications based on the interactions of coherent light with matter. These processes often involve nonlinear interactions between photonic and material degrees of freedom spanning multiple spatiotemporal scales. While great progress has been made with relatively simple optimizations, such as maximizing single-mode coherence or peak intensity alone, the ultimate achievement of coherent light engineering is complete, multidimensional control of light–light and light–matter interactions through tailored construction of complex optical fields and systems that exploit all of light’s degrees of freedom. This capability is now within sight, due to advances in telecommunications, computing, algorithms, and modeling. Control of highly multimode optical fields and processes also facilitates quantitative and qualitative advances in optical imaging, sensing, communication, and information processing since these applications directly depend on our ability to detect, encode, and manipulate information in as many optical degrees of freedom as possible. Today, these applications are increasingly being enhanced or enabled by both multimode engineering and nonlinearity. Here, we provide a brief overview of multimode nonlinear photonics, focusing primarily on spatiotemporal nonlinear wave propagation and, in particular, on promising future directions and routes to applications. We conclude with an overview of emerging processes and methodologies that will enable complex, coherent nonlinear photonic devices with many degrees of freedom.

 

Abstract Deep-learning models have become pervasive tools in science and engineering. However, their energy requirements now increasingly limit their scalability 1 . Deep-learning accelerators 2–9 aim to perform deep learning energy-efficiently, usually targeting the inference phase and often by exploiting physical substrates beyond conventional electronics. Approaches so far 10–22 have been unable to apply the backpropagation algorithm to train unconventional novel hardware in situ. The advantages of backpropagation have made it the de facto training method for large-scale neural networks, so this deficiency constitutes a major impediment. Here we introduce a hybrid in situ–in silico algorithm, called physics-aware training, that applies backpropagation to train controllable physical systems. Just as deep learning realizes computations with deep neural networks made from layers of mathematical functions, our approach allows us to train deep physical neural networks made from layers of controllable physical systems, even when the physical layers lack any mathematical isomorphism to conventional artificial neural network layers. To demonstrate the universality of our approach, we train diverse physical neural networks based on optics, mechanics and electronics to experimentally perform audio and image classification tasks. Physics-aware training combines the scalability of backpropagation with the automatic mitigation of imperfections and noise achievable with in situ algorithms. Physical neural networks have the potential to perform machine learning faster and more energy-efficiently than conventional electronic processors and, more broadly, can endow physical systems with automatically designed physical functionalities, for example, for robotics 23–26 , materials 27–29 and smart sensors 30–32 . 

We study the emergence of non-Gaussian quantum features in pulsed squeezed light generation with a mesoscopic number (i.e., dozens to hundreds) of pump photons. Due to the strong optical nonlinearities necessarily involved in this regime, squeezing occurs alongside significant pump depletion, compromising the predictions made by conventional semiclassical models for squeezing. Furthermore, nonlinear interactions among multiple frequency modes render the system dynamics exponentially intractable in naïve quantum models, requiring a more sophisticated modeling framework. To this end, we construct a nonlinear Gaussian approximation to the squeezing dynamics, defining a “Gaussian interaction frame” in which non-Gaussian quantum dynamics can be isolated and concisely described using a few dominant (i.e., principal) supermodes. Numerical simulations of our model reveal non-Gaussian distortions of squeezing in the mesoscopic regime, largely associated with signal-pump entanglement. We argue that state of the art in nonlinear nanophotonics is quickly approaching this regime, providing an all-optical platform for experimental studies of the semiclassical-to-quantum transition in a rich paradigm of coherent, multimode nonlinear dynamics. Mesoscopic pulsed squeezing, thus, provides an intriguing case study of the rapid rise in dynamic complexity associated with semiclassical-to-quantum crossover, which we view as a correlate of the emergence of new information processing capacities in the quantum regime.

 

Ultrashort pulses propagating in nonlinear nanophotonic waveguides can simultaneously leverage both temporal and spatial field confinement, promising a route towards single-photon nonlinearities in an all-photonic platform. In this multimode quantum regime, however, faithful numerical simulations of pulse dynamics naïvely require a representation of the state in an exponentially large Hilbert space. Here, we employ a time-domain, matrix product state (MPS) representation to enable efficient simulations by exploiting the entanglement structure of the system. To extract physical insight from these simulations, we develop an algorithm to unravel the MPS quantum state into constituent temporal supermodes, enabling, e.g., access to the phase-space portraits of arbitrary pulse waveforms. As a demonstration, we perform exact numerical simulations of a Kerr soliton in the quantum regime. We observe the development of non-classical Wigner-function negativity in the solitonic mode as well as quantum corrections to the semiclassical dynamics of the pulse. A similar analysis of${\mathrm{\chi <\#comment/>}}^{(2)}$simultons reveals a unique entanglement structure between the fundamental and second harmonics. Our approach is also readily compatible with quantum trajectory theory, allowing full quantum treatment of propagation loss and decoherence. We expect this work to establish the MPS technique as part of a unified engineering framework for the emerging field of broadband quantum photonics.