Abstract A computer’s clock rate ultimately determines the minimum time between sequential operations or instructions. Despite exponential advances in electronic computer performance due to Moore’s Law and increasingly parallel system architectures, clock rates of conventional processors have remained stagnant at ~5 GHz for nearly two decades. This creates a significant challenge for applications requiring real-time processing or control of ultrafast information systems. Here, we break this barrier by proposing and experimentally demonstrating computing based on an all-optical recurrent neural network leveraging the ultrafast characteristics of linear and nonlinear optical operations while circumventing electronic bottlenecks. The all-optical computer realizes linear operations, nonlinear functions, and memory entirely in the optical domain with accuracy surpassing a purely linear model up to 80 GHz clock rates depending on the task. We experimentally demonstrate a prototypical task of noisy waveform classification as well as perform ultrafast in-situ analysis of the soliton states from integrated optical microresonators. We further illustrate the application of the architecture for generative artificial intelligence based on quantum fluctuations to generate images even in the absence of input optical signals. Our results highlight the potential of all-optical computing beyond what can be achieved with digital electronics by utilizing ultrafast linear, nonlinear, and memory functions and quantum fluctuations.

Sensors are indispensable tools of modern life that are ubiquitously used in diverse settings ranging from smartphones and autonomous vehicles to the healthcare industry and space technology. By interfacing multiple sensors that collectively interact with the signal to be measured, one can go beyond the signal-to-noise ratios (SNR) attainable by the individual constituting elements. Such techniques have also been implemented in the quantum regime, where a linear increase in the SNR has been achieved via using entangled states. Along similar lines, coupled non-Hermitian systems have provided yet additional degrees of freedom to obtain better sensors via higher-order exceptional points. Quite recently, a new class of non-Hermitian systems, known as non-Hermitian topological sensors (NTOS) has been theoretically proposed. Remarkably, the synergistic interplay between non-Hermiticity and topology is expected to bestow such sensors with an enhanced sensitivity that grows exponentially with the size of the sensor network. Here, we experimentally demonstrate NTOS using a network of photonic time-multiplexed resonators in the synthetic dimension represented by optical pulses. By judiciously programming the delay lines in such a network, we realize the archetypal Hatano-Nelson model for our non-Hermitian topological sensing scheme. Our experimentally measured sensitivities for different lattice sizes confirm the characteristic exponential enhancement of NTOS. We show that this peculiar response arises due to the combined synergy between non-Hermiticity and topology, something that is absent in Hermitian topological lattices. Our demonstration of NTOS paves the way for realizing sensors with unprecedented sensitivities.

A computer's clock rate ultimately determines the minimum time between sequential operations or instructions. Despite exponential advances in electronic computer performance owing to Moore's Law and increasingly parallel system architectures, computer clock rates have remained stagnant at ∼5 GHz for almost two decades. This poses an intractable problem for applications requiring real-time processing or control of ultrafast information systems. Here we break this barrier by proposing and experimentally demonstrating computing based on an end-to-end and all-optical recurrent neural network harnessing the ultrafast nature of linear and nonlinear optical operations while avoiding electronic operations. The all-optical computer realizes linear operations, nonlinear functions, and memory entirely in the optical domain with >100 GHz clock rates. We experimentally demonstrate a prototypical task of noisy waveform classification as well as perform ultrafast in-situ analysis of the soliton states from integrated optical microresonators. We further illustrate the application of the architecture for generative artificial intelligence based on quantum fluctuations to generate images even in the absence of input optical signals. Our results highlight the potential of all-optical computing beyond what can be achieved with digital electronics by utilizing ultrafast linear, nonlinear, and memory functions and quantum fluctuations.

Introducing elements into an optical cavity that modify the transverse spatial field structure can also impact the cavity spectral response. In particular, an intra-cavity spatial mode-converter is expected to induce modal runaway: unrestricted ladder-up in the modal order, concomitantly thwarting coherent field interference, thereby altogether suppressing the resonant response - a phenomenon that has yet to be observed in an optical cavity. Here we show that a single intra-cavity holographic phase mask placed in a compact free-standing planar Fabry-Pérot cavity renders the cavity spectral response resonance-free. By acting as a mode-converter on a basis of Laguerre-Gaussian (LG) modes, an incident broadband fundamental Gaussian mode exits the cavity in the form of a superposition of a large number of collinearly propagating broadband LG modes of fixed parity whose spectra coincide with that of the input. Crucially, the resonance-free spectral response is maintained while changing the cavity length by ~ 350%, raising the prospect of stable resonant optical sensors whose performance is impervious to length perturbations.

Over the past decade, artificial intelligence (AI) has led to disruptive advancements in fundamental sciences and everyday technologies. Among various machine learning algorithms, deep neural networks have become instrumental in revealing complex patterns in large datasets with key applications in computer vision, natural language processing, and predictive analytics. On-chip photonic neural networks offer a promising platform that leverage high bandwidths and low propagation losses associated with optical signals to perform analog computations for deep learning. However, nanophotonic circuits are yet to achieve the required linear and nonlinear operations simultaneously in an all-optical and ultrafast fashion. Here, we report an ultrafast nanophotonic neuromorphic processor using an optical parametric oscillator (OPO) fabricated on thin-film lithium niobate (TFLN). The input data is used to modulate the optical pulses synchronously pumping the OPO. The consequent signal pulses generated by the OPO are coupled to one another via the nonlinear delayed dynamics of the OPO, thus forming the internal nodes of a deep recurrent neural network. We use such a nonlinearly coupled OPO network for chaotic time series prediction, nonlinear error correction in a noisy communication channel, as well as noisy waveform classification and achieve accuracies exceeding 93 an operating clock rate of 10 GHz. Our OPO network is capable of achieving sub-nanosecond latencies, a timescale comparable to a single clock cycle in state-of-the-art digital electronic processors. By circumventing the need for optical-electronic-optical (OEO) conversions, our ultrafast nanophotonic neural network paves the way for the next generation of compact all-optical neuromorphic processors with ultralow latencies and high energy efficiencies.

Arrays of nonlinear resonators offer a fertile ground for a wide range of complex phenomena and opportunities for advanced photonic sensing and computing. Recently, significant attention has focused on studying coupled resonators in special-purpose configurations either on chips or in table-top experiments. However, a path to realizing a large-scale programmable network of nonlinear photonic resonators remains elusive because of the challenges associated with simultaneously achieving strong nonlinearity, independent operation of the resonators, and programmability of the couplings. In this work, we break these barriers by realizing large-scale, time-multiplexed optical parametric oscillators (OPOs) on a single lithium niobate nanophotonic chip. We show independent operation of 70 identical OPOs in an ultrafast nanophotonic circuit. The OPOs exhibit an ultra-low threshold of a few picojoules, substantially surpassing the strength of nonlinearity of other platforms. Using our ultrafast nanophotonic circuit, a network of N OPOs with programmable all-to-all couplings requires only a few additional components. The time-multiplexed nanophotonic OPOs can enable myriad applications, including ultrafast classical and quantum information processing.

We experimentally demonstrate a recurrent optical neural network based on a nanophotonic optical parametric oscillator fabricated on thin-film lithium niobate. Our demonstration paves the way for realizing optical neural networks exhibiting ultra-low la-tencies.

Rapid advancements in deep learning over the past decade have fueled an insatiable demand for efficient and scalable hardware. Photonics offers a promising solution by leveraging the unique properties of light. However, conventional neural network architectures, which typically require dense programmable connections, pose several practical challenges for photonic realizations. To overcome these limitations, we propose and experimentally demonstrate Photonic Neural Cellular Automata (PNCA) for photonic deep learning with sparse connectivity. PNCA harnesses the speed and interconnectivity of photonics, as well as the self-organizing nature of cellular automata through local interactions to achieve robust, reliable, and efficient processing. We utilize linear light interference and parametric nonlinear optics for all-optical computations in a time-multiplexed photonic network to experimentally perform self-organized image classification. We demonstrate binary classification of images in the fashion-MNIST dataset using as few as 3 programmable photonic parameters, achieving an experimental accuracy of 98.0% with the ability to also recognize out-of-distribution data. The proposed PNCA approach can be adapted to a wide range of existing photonic hardware and provides a compelling alternative to conventional photonic neural networks by maximizing the advantages of light-based computing whilst mitigating their practical challenges. Our results showcase the potential of PNCA in advancing photonic deep learning and highlights a path for next-generation photonic computers.

We experimentally demonstrate an end-to-end all-optical recurrent neural net-work utilizing short laser pulses and ultrafast χ(2) nonlinear optics to unlock unprecedented computational clock rates and massively parallel information processing for time-series classification and prediction tasks.

Mode-locked lasers play a key role in modern science and technology. Not only do they lay the foundation for ultrafast optics and play a central role in nonlinear optics, but also they have important applications in imaging, telecommunications, sensing, and computing. While substantial efforts have focused on mode-locking the spectral modes of lasers, relatively little attention has been paid to mode-locking their temporal modes. However, temporal mode-locking presents ample opportunities to develop new technologies and to study the intersection of nonlinear, non-Hermitian, and topological phenomena, which, in recent years, has been a priority for the field of topological physics. Here, we theoretically predict and experimentally realize topological temporal mode-locking in a laser cavity with time-delayed intracavity couplings. These couplings introduce non-Hermitian point-gap topology into the temporal modes of our laser and conspire with an effective nonlocal nonlinearity to generate mode-locked temporal structures in our laser cavity, whose form can be tailored by suitably engineering the underlying couplings. We harness this approach to realize a nonlinearity-driven non-Hermitian skin effect, and we show that the topological temporal modes of our laser are robust against disorder-induced localization. The flexibility and programmability of our topological temporal mode-locking scheme reveals new opportunities to study nonlinear and non-Hermitian topological phenomena in mode-locked photonic resonators and could enable new applications of mode-locked lasers to sensing and optical computing.

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

The convoluted nonlinear behaviors of heavily multimode photonic structures have been recently the focus of considerable attention. The sheer complexity associated with such multimode systems, allows them to display a host of phenomena that are otherwise impossible in few-mode settings. At the same time, however, it introduces a set of fundamental challenges in terms of comprehending and harnessing their response. Here, we develop an optical thermodynamic approach capable of describing the thermalization dynamics in large scale nonlinear photonic tight-binding networks. For this specific system, an optical Sackur-Tetrode equation is obtained that explicitly provides the optical temperature and chemical potential of the photon gas. Processes like isentropic expansion/compression, Joule expansion, as well as aspects associated with beam cleaning/cooling and thermal conduction effects in such chain networks are discussed. Our results can be used to describe in an effortless manner the exceedingly complex dynamics of highly multimoded nonlinear bosonic systems.

We experimentally demonstrate enhanced sensitivities within non-Hermitian topological lattices realized in a dissipatively-coupled network of time-multiplexed resonators. Our demonstration paves the way for realizing optical sensors with unprecedented sensitivities using notions of non-Hermiticity and topology.

Neural networks based on Cellular Automata (CA) have recently yielded more robust, reliable, and parameter-efficient machine learning models. We experimentally demonstrate the first photonic implementation of CA which successfully performs image classification on the Fashion-MNIST dataset.

We theoretically investigate a Thouless pumping scheme in the 1D topological Su-Schrieffer-Heeger (SSH) model for single and multiple band-gaps systems when implemented in a discrete nematic liquid crystal arrangement. For an electrically controlled SSH waveguide array, we numerically demonstrate edge-to-edge light transport at low power levels. On the other hand, at higher powers, the transport is frustrated by light-induced nonlinear defect states, giving rise to robust all-optical switching.

We demonstrate Bloch oscillations in a dissipatively-coupled network of time-multiplexed resonators, and experimentally measure the topological invariants in open systems. This reveals the complex interplay between topology and dissipation with potential applications in quantum/classical photonics.

We experimentally realize a topological actively mode-locked laser by coupling the pulses with intracavity delay lines. Our work reveals a new regime of nonlinear topological photonics and has potential applications to short-pulse lasers.

The chaotic evolution resulting from the interplay between topology and nonlinearity in photonic systems generally forbids the sustainability of optical currents. Here, we systematically explore the nonlinear evolution dynamics in topological photonic lattices within the framework of optical thermodynamics. By considering an archetypical two-dimensional Haldane photonic lattice, we discover several prethermal states beyond the topological phase transition point and a stable global equilibrium response, associated with a specific optical temperature and chemical potential. Along these lines, we provide a consistent thermodynamic methodology for both controlling and maximizing the unidirectional power flow in the topological edge states. This can be achieved by either employing cross-phase interactions between two subsystems or by exploiting self-heating effects in disordered or Floquet topological lattices. Our results indicate that photonic topological systems can in fact support robust photon transport processes even under the extreme complexity introduced by nonlinearity, an important feature for contemporary topological applications in photonics.

We present experimental evidence of a 64th order exceptional point realized on a time-multiplexed photonic resonator network. Our highly scalable implementation uses a unidirectionally coupled one-dimensional lattice to achieve higher order exceptional points that are robust to variation in nearest neighbor couplings. Moreover, the non-reciprocal couplings of our network allow for the possibility to exceed the signal to noise limits that restrict other exceptional point implementations.