Parallel convolutional processing using an integrated photonic tensor core.

With the proliferation of ultrahigh-speed mobile networks and internet-connected devices, along with the rise of artificial intelligence (AI)1, the world is generating exponentially increasing amounts of data that need to be processed in a fast and efficient way. Highly parallelized, fast and scalable hardware is therefore becoming progressively more important2. Here we demonstrate a computationally specific integrated photonic hardware accelerator (tensor core) that is capable of operating at speeds of trillions of multiply-accumulate operations per second (1012 MAC operations per second or tera-MACs per second). The tensor core can be considered as the optical analogue of an application-specific integrated circuit (ASIC). It achieves parallelized photonic in-memory computing using phase-change-material memory arrays and photonic chip-based optical frequency combs (soliton microcombs3). The computation is reduced to measuring the optical transmission of reconfigurable and non-resonant passive components and can operate at a bandwidth exceeding 14 gigahertz, limited only by the speed of the modulators and photodetectors. Given recent advances in hybrid integration of soliton microcombs at microwave line rates3-5, ultralow-loss silicon nitride waveguides6,7, and high-speed on-chip detectors and modulators, our approach provides a path towards full complementary metal-oxide-semiconductor (CMOS) wafer-scale integration of the photonic tensor core. Although we focus on convolutional processing, more generally our results indicate the potential of integrated photonics for parallel, fast, and efficient computational hardware in data-heavy AI applications such as autonomous driving, live video processing, and next-generation cloud computing services.

Measurement-based control of a mechanical oscillator at its thermal decoherence rate.

In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen successful applications of these protocols in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. However, stabilizing the quantum state of a tangibly massive object, such as a mechanical oscillator, remains very challenging: the main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, 4.3-megahertz nanomechanical oscillator in the timescale of its thermal decoherence, a basic requirement for real-time (Markovian) quantum feedback control tasks, such as ground-state preparation. The sensor is based on evanescent optomechanical coupling to a high-Q microcavity, and achieves an imprecision four orders of magnitude below that at the standard quantum limit for a weak continuous position measurement--a 100-fold improvement over previous reports--while maintaining an imprecision-back-action product that is within a factor of five of the Heisenberg uncertainty limit. As a demonstration of its utility, we use the measurement as an error signal with which to feedback cool the oscillator. Using radiation pressure as an actuator, the oscillator is cold damped with high efficiency: from a cryogenic-bath temperature of 4.4 kelvin to an effective value of 1.1 ± 0.1 millikelvin, corresponding to a mean phonon number of 5.3 ± 0.6 (that is, a ground-state probability of 16 per cent). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of mechanical oscillators as practical subjects for measurement-based quantum control.

Fractal-like Mechanical Resonators with a Soft-Clamped Fundamental Mode.

Self-similar structures occur naturally and have been employed to engineer exotic physical properties. We show that acoustic modes of a fractal-like system of tensioned strings can display increased mechanical quality factors due to the enhancement of dissipation dilution. We describe a realistic resonator design in which the quality factor of the fundamental mode is enhanced by as much as 2 orders of magnitude compared to a simple string with the same size and tension. Our findings can open new avenues in force sensing, cavity quantum optomechanics, and experiments with suspended test masses.

Highly efficient coupling of crystalline microresonators to integrated photonic waveguides.

Crystalline optical whispering gallery mode resonators made from alkaline earth fluorides can achieve exceptionally large optical finesse, and are used in a variety of applications, from frequency stabilization and narrow linewidth lasers, to low-noise microwave generation or soliton Kerr frequency combs. Here we demonstrate an efficient coupling method to resonators of these materials, which employs photonic integrated waveguides on a chip based on silicon nitride. By converting a mode from silicon nitride to a free-hanging silica waveguide on a silicon chip, coupling to a crystalline resonator is achieved with a high extinction, while preserving a quality factor exceeding 200 million. This compact, heterogeneous integration of ultra-high Q-factor crystalline resonators with photonic waveguides provides a proof of concept for wafer scale integration and robust, compact packaging for a wide range of applications.

From the Lugiato-Lefever equation to microresonator-based soliton Kerr frequency combs.

The model, that is usually called the Lugiato-Lefever equation (LLE), was introduced in 1987 with the aim of providing a paradigm for dissipative structure and pattern formation in nonlinear optics. This model, describing a driven, detuned and damped nonlinear Schroedinger equation, gives rise to dissipative spatial and temporal solitons. Recently, the rather idealized conditions, assumed in the LLE, have materialized in the form of continuous wave driven optical microresonators, with the discovery of temporal dissipative Kerr solitons (DKS). These experiments have revealed that the LLE is a perfect and exact description of Kerr frequency combs-first observed in 2007, i.e. 20 years after the original formulation of the LLE-and in particular describe soliton states. Observed to spontaneously form in Kerr frequency combs in crystalline microresonators in 2013, such DKS are preferred state of operation, offering coherent and broadband optical frequency combs, whose bandwidth can be extended exploiting soliton-induced broadening phenomena. Combined with the ability to miniaturize and integrate on-chip, microresonator-based soliton Kerr frequency combs have already found applications in self-referenced frequency combs, dual-comb spectroscopy, frequency synthesis, low noise microwave generation, laser frequency ranging, and astrophysical spectrometer calibration, and have the potential to make comb technology ubiquitous. As such, pattern formation in driven, dissipative nonlinear optical systems is becoming the central Physics of soliton micro-comb technology.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.

Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.

Soliton dual frequency combs in crystalline microresonators.

We present a novel compact dual-comb source based on a monolithic optical crystalline MgF2 multi-resonator stack. The coherent soliton combs generated in the two microresonators of the stack with the repetition rate of 12.1 GHz and difference of 1.62 MHz provided after heterodyning a 300 MHz wide radio frequency comb. An analogous system can be used for dual-comb spectroscopy, coherent LIDAR applications, and massively parallel optical communications.

Harmonization of chaos into a soliton in Kerr frequency combs.

Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresponding to the free spectral range of the microresonator, provides reliable convergence of an initially excited chaotic comb state to a single dissipative Kerr soliton (DKS) state. The efficiency of this approach depends on both frequency tuning speed and modulation depth. The relevance of the proposed method is confirmed experimentally in a MgF2 microresonator.

Higher order mode suppression in high-Q anomalous dispersion SiN microresonators for temporal dissipative Kerr soliton formation.

High-Q silicon nitride (SiN) microresonators enable optical Kerr frequency comb generation on a photonic chip and have recently been shown to support fully coherent combs based on temporal dissipative Kerr soliton formation. For bright soliton formation, it is necessary to operate SiN waveguides in the multimode regime in order to produce waveguide induced anomalous group velocity dispersion. However, this regime can lead to local disturbances of the dispersion due to avoided crossings caused by coupling between different mode families and, therefore, prevent the soliton formation. Here, we demonstrate that a single-mode "filtering" section inside high-Q resonators enables efficiently suppression of avoided crossings, while preserving high quality factors (Q∼10(6)). We verify the approach by demonstrating single soliton formation in SiN resonators with a filtering section.

Frequency combs and platicons in optical microresonators with normal GVD.

We predict the existence of a novel type of the flat-top dissipative solitonic pulses, "platicons", in microresonators with normal group velocity dispersion (GVD). We propose methods to generate these platicons from cw pump. Their duration may be altered significantly by tuning the pump frequency. The transformation of a discrete energy spectrum of dark solitons of the Lugiato-Lefever equation into a quasicontinuous spectrum of platicons is demonstrated. Generation of similar structures is also possible with bi-harmonic, phase/amplitude modulated pump or via laser injection locking.

All-optical stabilization of a soliton frequency comb in a crystalline microresonator.

We demonstrate the all-optical stabilization of a low-noise temporal soliton based microresonator based optical frequency comb in a crystalline resonator via a new technique to control the repetition rate. This is accomplished by thermally heating the microresonator with an additional probe laser coupled to an auxiliary optical resonator mode. The carrier-envelope offset frequency is controlled by stabilizing the pump laser frequency to a reference optical frequency comb. We analyze the stabilization by performing an out-of-loop comparison and measure the overlapping Allan deviation. This all-optical stabilization technique can prove useful as an actuator for self-referenced microresonator frequency combs.

Quantum-limited amplification and parametric instability in the reversed dissipation regime of cavity optomechanics.

Cavity optomechanical phenomena, such as cooling, amplification, or optomechanically induced transparency, emerge due to a strong imbalance in the dissipation rates of the parametrically coupled electromagnetic and mechanical resonators. Here we analyze the reversed dissipation regime where the mechanical energy relaxation rate exceeds the energy decay rate of the electromagnetic cavity. We demonstrate that this regime allows for mechanically induced amplification (or cooling) of the electromagnetic mode. Gain, bandwidth, and added noise of this electromagnetic amplifier are derived and compared to amplification in the normal dissipation regime. In addition, we analyze the parametric instability, i.e., optomechanical Brillouin lasing, and contrast it to conventional optomechanical phonon lasing. Finally, we propose an experimental scheme that realizes the reversed dissipation regime using parametric coupling and optomechanical cooling with a second electromagnetic mode enabling quantum-limited amplification. Recent advances in high-Q superconducting microwave resonators make the reversed dissipation regime experimentally realizable.

Mode spectrum and temporal soliton formation in optical microresonators.

The formation of temporal dissipative solitons in optical microresonators enables compact, high-repetition rate sources of ultrashort pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the microresonator mode spectrum on temporal soliton formation in a crystalline MgF2 microresonator. While an overall anomalous group velocity dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Avoided mode crossings induced by linear mode coupling in the resonator mode spectrum are found to prevent soliton formation when affecting resonator modes close to the pump laser frequency. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations. The presented results provide for the first time design criteria for the generation of temporal solitons in optical microresonators.

Optical frequency comb generation from a monolithic microresonator.

Optical frequency combs provide equidistant frequency markers in the infrared, visible and ultraviolet, and can be used to link an unknown optical frequency to a radio or microwave frequency reference. Since their inception, frequency combs have triggered substantial advances in optical frequency metrology and precision measurements and in applications such as broadband laser-based gas sensing and molecular fingerprinting. Early work generated frequency combs by intra-cavity phase modulation; subsequently, frequency combs have been generated using the comb-like mode structure of mode-locked lasers, whose repetition rate and carrier envelope phase can be stabilized. Here we report a substantially different approach to comb generation, in which equally spaced frequency markers are produced by the interaction between a continuous-wave pump laser of a known frequency with the modes of a monolithic ultra-high-Q microresonator via the Kerr nonlinearity. The intrinsically broadband nature of parametric gain makes it possible to generate discrete comb modes over a 500-nm-wide span (approximately 70 THz) around 1,550 nm without relying on any external spectral broadening. Optical-heterodyne-based measurements reveal that cascaded parametric interactions give rise to an optical frequency comb, overcoming passive cavity dispersion. The uniformity of the mode spacing has been verified to within a relative experimental precision of 7.3 x 10(-18). In contrast to femtosecond mode-locked lasers, this work represents a step towards a monolithic optical frequency comb generator, allowing considerable reduction in size, complexity and power consumption. Moreover, the approach can operate at previously unattainable repetition rates, exceeding 100 GHz, which are useful in applications where access to individual comb modes is required, such as optical waveform synthesis, high capacity telecommunications or astrophysical spectrometer calibration.

Dual-mode temperature compensation technique for laser stabilization to a crystalline whispering gallery mode resonator.

Frequency stabilization of a diode laser locked to a whispering gallery mode (WGM) reference resonator made of a MgF2 single crystal is demonstrated. The strong thermal dependence of the difference frequency between two orthogonally polarized TE an TM modes (dual-mode frequency) of the optically anisotropic crystal material allows sensitive measurement of the resonator's temperature within the optical mode volume. This dual-mode signal was used as feedback for self-referenced temperature stabilization to nanokelvin precision, resulting in frequency stability of 0.3 MHz/h at 972 nm, which was measured by comparing with an independent ultrastable laser.

Observation of strong coupling between one atom and a monolithic microresonator.

Over the past decade, strong interactions of light and matter at the single-photon level have enabled a wide set of scientific advances in quantum optics and quantum information science. This work has been performed principally within the setting of cavity quantum electrodynamics with diverse physical systems, including single atoms in Fabry-Perot resonators, quantum dots coupled to micropillars and photonic bandgap cavities and Cooper pairs interacting with superconducting resonators. Experiments with single, localized atoms have been at the forefront of these advances with the use of optical resonators in high-finesse Fabry-Perot configurations. As a result of the extreme technical challenges involved in further improving the multilayer dielectric mirror coatings of these resonators and in scaling to large numbers of devices, there has been increased interest in the development of alternative microcavity systems. Here we show strong coupling between individual caesium atoms and the fields of a high-quality toroidal microresonator. From observations of transit events for single atoms falling through the resonator's evanescent field, we determine the coherent coupling rate for interactions near the surface of the resonator. We develop a theoretical model to quantify our observations, demonstrating that strong coupling is achieved, with the rate of coherent coupling exceeding the dissipative rates of the atom and the cavity. Our work opens the way for investigations of optical processes with single atoms and photons in lithographically fabricated microresonators. Applications include the implementation of quantum networks, scalable quantum logic with photons, and quantum information processing on atom chips.

Hierarchical tensile structures with ultralow mechanical dissipation.

Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitride nanomechanical resonators and realize binary tree-shaped resonators with room temperature quality factors as high as 7.8 × 108 at 107 kHz frequency (1.1 × 109 at T = 6 K). The resonators' thermal-noise-limited force sensitivities reach 740 zN/Hz1/2 at room temperature and 90 zN/Hz1/2 at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. Moreover, we demonstrate hierarchically structured, ultralow dissipation membranes suitable for interferometric position measurements in Fabry-Pérot cavities. Hierarchical nanomechanical resonators open new avenues in force sensing, signal transduction and quantum optomechanics, where low dissipation is paramount and operation with the fundamental mode is often advantageous.

Octave spanning tunable frequency comb from a microresonator.

We report the generation of an octave-spanning optical frequency comb in a continuous wave laser pumped microresonator. The generated comb spectrum covers the wavelength range from 990 to 2170 nm without relying on additional external broadening. Continuous tunability of the generated frequency comb over more than an entire free spectral range is demonstrated. Moreover, the linewidth of individual optical comb components and its relation to the pump laser phase noise is studied. The ability to derive octave-spanning spectra from microresonator comb generators represents a key step towards f-2f self-referencing of microresonator-based optical frequency combs.

Optomechanical coupling in a two-dimensional photonic crystal defect cavity.

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of ~3(λ/n)³. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.