Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

For most deep learning practitioners, sequence modeling is synonymous with recurrent networks. Yet recent results indicate that convolutional architectures can outperform recurrent networks on tasks such as audio synthesis and machine translation. Given a new sequence modeling task or dataset, which architecture should one use? We conduct a systematic evaluation of generic convolutional and recurrent architectures for sequence modeling. The models are evaluated across a broad range of standard tasks that are commonly used to benchmark recurrent networks. Our results indicate that a simple convolutional architecture outperforms canonical recurrent networks such as LSTMs across a diverse range of tasks and datasets, while demonstrating longer effective memory. We conclude that the common association between sequence modeling and recurrent networks should be reconsidered, and convolutional networks should be regarded as a natural starting point for sequence modeling tasks. To assist related work, we have made code available at this http URL .

An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

Electro-optic modulators translate high-speed electronic signals into the optical domain and are critical components in modern telecommunication networks1,2 and microwave-photonic systems3,4. They are also expected to be building blocks for emerging applications such as quantum photonics5,6 and non-reciprocal optics7,8. All of these applications require chip-scale electro-optic modulators that operate at voltages compatible with complementary metal–oxide–semiconductor (CMOS) technology, have ultra-high electro-optic bandwidths and feature very low optical losses. Integrated modulator platforms based on materials such as silicon, indium phosphide or polymers have not yet been able to meet these requirements simultaneously because of the intrinsic limitations of the materials used. On the other hand, lithium niobate electro-optic modulators, the workhorse of the optoelectronic industry for decades9, have been challenging to integrate on-chip because of difficulties in microstructuring lithium niobate. The current generation of lithium niobate modulators are bulky, expensive, limited in bandwidth and require high drive voltages, and thus are unable to reach the full potential of the material. Here we overcome these limitations and demonstrate monolithically integrated lithium niobate electro-optic modulators that feature a CMOS-compatible drive voltage, support data rates up to 210 gigabits per second and show an on-chip optical loss of less than 0.5 decibels. We achieve this by engineering the microwave and photonic circuits to achieve high electro-optical efficiencies, ultra-low optical losses and group-velocity matching simultaneously. Our scalable modulator devices could provide cost-effective, low-power and ultra-high-speed solutions for next-generation optical communication networks and microwave photonic systems. Furthermore, our approach could lead to large-scale ultra-low-loss photonic circuits that are reconfigurable on a picosecond timescale, enabling a wide range of quantum and classical applications5,10,11 including feed-forward photonic quantum computation. Chip-scale lithium niobate electro-optic modulators that rapidly convert electrical to optical signals and use CMOS-compatible voltages could prove useful in optical communication networks, microwave photonic systems and photonic computation.

Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages

Deep learning has been transforming our ability to execute advanced inference tasks using computers. Here we introduce a physical mechanism to perform machine learning by demonstrating an all-optical diffractive deep neural network (D2NN) architecture that can implement various functions following the deep learning-based design of passive diffractive layers that work collectively. We created 3D-printed D2NNs that implement classification of images of handwritten digits and fashion products, as well as the function of an imaging lens at a terahertz spectrum. Our all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can execute; will find applications in all-optical image analysis, feature detection, and object classification; and will also enable new camera designs and optical components that perform distinctive tasks using D2NNs.

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All-optical machine learning using diffractive deep neural networks

Artificial Neural Networks have dramatically improved performance for many machine learning tasks. We demonstrate a new architecture for a fully optical neural network that enables a computational speed enhancement of at least two orders of magnitude and three orders of magnitude in power efficiency over state-of-the-art electronics.

Deep learning with coherent nanophotonic circuits

Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. Here, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Band gaps with large Chern numbers of 2, 3, and 4 are present in the experimental results, which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations.

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.115.253901

Experimental Observation of Large Chern Numbers in Photonic Crystals.

Current experimental realizations of the quantum anomalous Hall phase in both electronic and photonic systems have been limited to a Chern number of one. In photonics, this corresponds to a single-mode one-way edge waveguide. Here, we predict quantum anomalous Hall phases in photonic crystals with large Chern numbers of 2, 3, and 4. These new topological phases were found by simultaneously gapping multiple Dirac and quadratic points. We demonstrate a continuously tunable power splitter as a possible application of multimode one-way waveguides. All our findings are readily realizable at microwave frequencies.

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Multimode One-Way Waveguides of Large Chern Numbers

Using unitary (instead of general) matrices in artificial neural networks (ANNs) is a promising way to solve the gradient explosion/vanishing problem, as well as to enable ANNs to learn long-term correlations in the data. This approach appears particularly promising for Recurrent Neural Networks (RNNs). In this work, we present a new architecture for implementing an Efficient Unitary Neural Network (EUNNs); its main advantages can be summarized as follows. Firstly, the representation capacity of the unitary space in an EUNN is fully tunable, ranging from a subspace of SU(N) to the entire unitary space. Secondly, the computational complexity for training an EUNN is merely O(1) per parameter. Finally, we test the performance of EUNNs on the standard copying task, the pixel-permuted MNIST digit recognition benchmark as well as the Speech Prediction Test (TIMIT). We find that our architecture significantly outperforms both other state-of-the-art unitary RNNs and the LSTM architecture, in terms of the final performance and/or the wall-clock training speed. EUNNs are thus promising alternatives to RNNs and LSTMs for a wide variety of applications.

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Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs

Cerenkov radiation is ubiquitous in a range of applications from nuclear reactors to biological imaging. New work shows that the quantum attributes of the charged particles result in important changes to the traditional Cerenkov theory.

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Scott Skirlo

Papers

Deep learning with coherent nanophotonic circuits

Experimental Observation of Large Chern Numbers in Photonic Crystals.

Multimode One-Way Waveguides of Large Chern Numbers

Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs

Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum