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.

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.

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.

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)'.

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.

Elastic strain engineering for ultralow mechanical dissipation.

Extreme stresses can be produced in nanoscale structures; this feature has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. We show how nanoscale stress can be used to realize exceptionally low mechanical dissipation when combined with "soft-clamping"-a form of phononic engineering. Specifically, using a nonuniform phononic crystal pattern, we colocalize the strain and flexural motion of a free-standing silicon nitride nanobeam. Ringdown measurements at room temperature reveal string-like vibrational modes with quality (Q) factors as high as 800 million and Q × frequency exceeding 1015 hertz. These results illustrate a promising route for engineering ultracoherent nanomechanical devices.

Ultrafast optical ranging using microresonator soliton frequency combs.

Light detection and ranging is widely used in science and industry. Over the past decade, optical frequency combs were shown to offer advantages in optical ranging, enabling fast distance acquisition with high accuracy. Driven by emerging high-volume applications such as industrial sensing, drone navigation, or autonomous driving, there is now a growing demand for compact ranging systems. Here, we show that soliton Kerr comb generation in integrated silicon nitride microresonators provides a route to high-performance chip-scale ranging systems. We demonstrate dual-comb distance measurements with Allan deviations down to 12 nanometers at averaging times of 13 microseconds along with ultrafast ranging at acquisition rates of 100 megahertz, allowing for in-flight sampling of gun projectiles moving at 150 meters per second. Combining integrated soliton-comb ranging systems with chip-scale nanophotonic phased arrays could enable compact ultrafast ranging systems for emerging mass applications.

Breathing dissipative solitons in optical microresonators.

Dissipative solitons are self-localised structures resulting from the double balance of dispersion by nonlinearity and dissipation by a driving force arising in numerous systems. In Kerr-nonlinear optical resonators, temporal solitons permit the formation of light pulses in the cavity and the generation of coherent optical frequency combs. Apart from shape-invariant stationary solitons, these systems can support breathing dissipative solitons exhibiting a periodic oscillatory behaviour. Here, we generate and study single and multiple breathing solitons in coherently driven microresonators. We present a deterministic route to induce soliton breathing, allowing a detailed exploration of the breathing dynamics in two microresonator platforms. We measure the relation between the breathing frequency and two control parameters-pump laser power and effective-detuning-and observe transitions to higher periodicity, irregular oscillations and switching, in agreement with numerical predictions. Using a fast detection, we directly observe the spatiotemporal dynamics of individual solitons, which provides evidence of breather synchronisation.Dissipative Kerr solitons enable optical frequency comb generation in microresonators, but these solitons can undergo a breathing transition which impacts the stability of such microcombs. Here, Lucas et al. deterministically induce soliton breathing and directly observe the spatiotemporal dynamics.

Nonreciprocal reconfigurable microwave optomechanical circuit.

Nonreciprocal microwave devices are ubiquitous in radar and radio communication and indispensable in the readout chains of superconducting quantum circuits. Since they commonly rely on ferrite materials requiring large magnetic fields that make them bulky and lossy, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using the Josephson nonlinearity. Here, we realize reconfigurable nonreciprocal transmission between two microwave modes using purely optomechanical interactions in a superconducting electromechanical circuit. The scheme relies on the interference in two mechanical modes that mediate coupling between the microwave cavities and requires no magnetic field. We analyse the isolation, transmission and the noise properties of this nonreciprocal circuit. Finally, we show how quantum-limited circulators can be realized with the same principle. All-optomechanically mediated nonreciprocity demonstrated here can also be extended to directional amplifiers, and it forms the basis towards realizing topological states of light and sound.Nonreciprocal optical devices traditionally rely on magnetic fields and magnetic-free approaches are rather recent. Here, Bernier et al. propose and demonstrate a purely optomechanical circulator with reconfigurable transmission without the need for direct coupling between input and output modes.

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.

Mid-infrared ultra-high-Q resonators based on fluoride crystalline materials.

The unavailability of highly transparent materials in the mid-infrared has been the main limitation in the development of ultra-sensitive molecular sensors or cavity-based spectroscopy applications. Whispering gallery mode microresonators have attained ultra-high-quality (Q) factor resonances in the near-infrared and visible. Here we report ultra-high Q factors in the mid-infrared using polished alkaline earth metal fluoride crystals. Using an uncoated chalcogenide tapered fibre as a high-ideality coupler in the mid-infrared, we study via cavity ringdown technique the losses of BaF2, CaF2, MgF2 and SrF2 microresonators. We show that MgF2 is limited by multiphonon absorption by studying the temperature dependence of the Q factor. In contrast, in SrF2 and BaF2 the lower multiphonon absorption leads to ultra-high Q factors at 4.5 µm. These values correspond to an optical finesse of , the highest value achieved for any type of mid-infrared resonator to date.

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.

Photonic chip-based optical frequency comb using soliton Cherenkov radiation.

Optical solitons are propagating pulses of light that retain their shape because nonlinearity and dispersion balance each other. In the presence of higher-order dispersion, optical solitons can emit dispersive waves via the process of soliton Cherenkov radiation. This process underlies supercontinuum generation and is of critical importance in frequency metrology. Using a continuous wave-pumped, dispersion-engineered, integrated silicon nitride microresonator, we generated continuously circulating temporal dissipative Kerr solitons. The presence of higher-order dispersion led to the emission of red-shifted soliton Cherenkov radiation. The output corresponds to a fully coherent optical frequency comb that spans two-thirds of an octave and whose phase we were able to stabilize to the sub-Hertz level. By preserving coherence over a broad spectral bandwidth, our device offers the opportunity to develop compact on-chip frequency combs for frequency metrology or spectroscopy.

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.

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.

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.

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.

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.