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Random fluctuations can lead to cooperative effects in complex systems. We here report the experimental observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system and uncover the potential role of synchronization for mixed-state quantum information science.

Silicon nitride (Si$_3$N$_4$) is an ever-maturing integrated platform for nonlinear optics. Yet, due to the absence of second-order ($\chi^{(2)}$) nonlinearity, Si$_3$N$_4$ is mostly considered for third-order ($\chi^{(3)}$) nonlinear interactions. Recently, this limitation was overcome by optical poling in both Si$_3$N$_4$ waveguides and microresonators via the photogalvanic effect, resulting in the inscription of quasi-phase-matched $\chi^{(2)}$ gratings. Here, we report cascaded nonlinear effects in a normal dispersion Si$_3$N$_4$ microresonator with combined $\chi^{(2)}$ and $\chi^{(3)}$ nonlinearities. We demonstrate that the photo-induced $\chi^{(2)}$ grating also provides phase-matching for the sum-frequency generation process, enabling the initiation and successive switching of primary combs at pump wavelength. Additionally, the doubly resonant pump and second-harmonic fields allow for cascaded third-harmonic generation, where a secondary optically written $\chi^{(2)}$ grating is identified. Finally, we reach a low-noise, broadband microcomb state evolved from the sum-frequency coupled primary comb. These results expand the scope of cascaded effects in $\chi^{(2)}$ and $\chi^{(3)}$ microresonators.

Arising from modulation instability, Turing rolls in optical Kerr microresonators have been used in the generation of optical frequency combs and the synthesis of microwave and terahertz frequencies. In this work, by applying electro-optic modulation on terahertz-frequency Turing rolls, we implement electro-optic frequency division with a microcomb to synthesize variable low-noise microwave signals. We also actively stabilize the terahertz oscillations to a microwave reference via intracavity power modulation, obtaining fractional frequency instabilities that are better than those of the free-running situation by up to six orders of magnitude. This study not only highlights the extraordinary spectral purity of Turing roll oscillations but also opens the way for bidirectional terahertz-to-microwave links with hybrid optical frequency comb techniques.

Low-noise lasers are of central importance in a wide variety of applications, including high spectral-efficiency coherent communication protocols, distributed fibre sensing, and long distance coherent LiDAR. In addition to low phase noise, frequency agility, that is, the ability to achieve high-bandwidth actuation of the laser frequency, is imperative for triangular chirping in frequency-modulated continuous-wave (FMCW) based ranging or any optical phase locking as routinely used in metrology. While integrated silicon-based lasers have experienced major advances and are now employed on a commercial scale in data centers, integrated lasers with sub-100 Hz-level intrinsic linewidth are based on optical feedback from photonic circuits that lack frequency agility. Here, we demonstrate a wafer-scale-manufacturing-compatible hybrid photonic integrated laser that exhibits ultralow intrinsic linewidth of 25 Hz while offering unsurpassed megahertz actuation bandwidth, with a tuning range larger than 1 GHz. Our approach uses ultralow-loss (1 dB/m) Si$_3$N$_4$ photonic microresonators, combined with aluminium nitride (AlN) or lead zirconium titanate (PZT) microelectromechanical systems (MEMS) based stress-optic actuation. Electrically driven low-phase noise lasing is attained by self-injection locking of an Indium Phosphide (InP) laser chip and only limited by fundamental thermo-refractive noise. By utilizing difference drive and apodization of the photonic chip, a flat actuation response up to 10 MHz is achieved. We leverage this capability to demonstrate a compact coherent LiDAR engine that can generate up to 800 kHz FMCW triangular optical chirp signals, requiring neither any active linearization nor predistortion compensation, and perform a 10 m optical ranging experiment, with a resolution of 12.5 cm.

The past decade has witnessed major advances in the development of microresonator-based frequency combs (microcombs) that are broadband optical frequency combs with repetition rates in the millimeter-wave to microwave domain. Integrated microcombs can be manufactured using wafer-scale process and have been applied in numerous applications. Most of these advances are based on the harnessing of dissipative Kerr solitons (DKS) in optical microresonators with anomalous group velocity dispersion (GVD). However, microcombs can also be generated with normal GVD using dissipative localized structures that are referred to as "dark pulse", "switching wave" or "platicon". Importantly, as most materials feature intrinsic normal GVD, the requirement of dispersion engineering is significantly relaxed for platicon generation. Therefore while DKS microcombs require particular designs and fabrication processes, platicon microcombs can be readily built using standard CMOS-compatible platforms such as thin-film (i.e. typically below 300 nm) Si3N4. Yet laser self-injection locking that has been recently used to create highly compact integrated DKS microcomb modules has not been demonstrated for platicons. Here we report the first fully integrated platicon microcomb operating at a microwave-K-band repetition rate. Using laser self-injection locking of a DFB laser edge-coupled to a Si3N4 microresonator, platicons are electrically initiated and stably maintained, enabling a compact microcomb module without any complex control. We further characterize the phase noise of the platicon repetition rate and the pumping laser. The observation of self-injection-locked platicons facilitates future wide adoption of microcombs as a build-in block in standard photonic integrated architectures via commercial foundry service.

Silicon photonics enables wafer-scale integration of optical functionalities on chip. A silicon-based laser frequency combs could significantly expand the applications of silicon photonics, by providing integrated sources of mutually coherent laser lines for terabit-per-second transceivers, parallel coherent LiDAR, or photonics-assisted signal processing. Here, we report on heterogeneously integrated laser soliton microcombs combining both InP/Si semiconductor lasers and ultralow-loss silicon nitride microresonators on monolithic silicon substrate. Thousands of devices are produced from a single wafer using standard CMOS techniques. Using on-chip electrical control of the microcomb-laser relative optical phase, these devices can output single-soliton microcombs with 100 GHz repetition rate. Our approach paves the way for large-volume, low-cost manufacturing of chip-based frequency combs for next-generation high-capacity transceivers, datacenters, space and mobile platforms.

Solitons are shape preserving waveforms that are ubiquitous across nonlinear dynamical systems and fall into two separate classes, that of bright solitons, formed in the anomalous group velocity dispersion regime, and `dark solitons' in the normal dispersion regime. Both types of soliton have been observed in BEC, hydrodynamics, polaritons, and mode locked lasers, but have been particularly relevant to the generation of chipscale microresonator-based frequency combs (microcombs), used in numerous system level applications in timing, spectroscopy, and communications. For microcombs, both bright solitons, and alternatively dark pulses based on interlocking switching waves, have been studied. Yet, the existence of localized dissipative structures that fit between this dichotomy has been theoretically predicted, but proven experimentally elusive. Here we report the discovery of dissipative structures that embody a hybrid between switching waves and dissipative solitons, existing in the regime of (nearly) vanishing group velocity dispersion where third-order dispersion is dominant, hence termed as `zero-dispersion solitons'. These dissipative structures are formed via collapsing switching wave fronts, forming clusters of quantized solitonic sub-structures. The switching waves are formed directly via synchronous pulse-driving of a photonic chip-based Si3N4 microresonator. The resulting frequency comb spectrum is extremely broad in both the switching wave and zero-dispersion soliton regime, reaching 136 THz or 97% of an octave. Fourth-order dispersion engineering results in dual-dispersive wave formation, and a novel quasi-phase matched wave related to Faraday instability. This exotic unanticipated dissipative structure expands the domain of Kerr cavity physics to the regime near zero-dispersion and could present a superior alternative to conventional solitons for broadband comb generation., Comment: 11 pages, 6 figures. 1 video as supplementary information. 1 Supplementary Information Document

Dissipative Kerr solitons (DKSs) have been generated via injection locking of chipscale microresonators to continuous-wave (CW) III-V lasers. This advance has enabled fully integrated hybrid microcomb systems that operate in turnkey mode and can access microwave repetition rates. Yet, CW-driven DKS exhibits low energy conversion efficiency and high optical power threshold, especially when the repetition rate is within the microwave range that is convenient for direct detection with off-the-shelf electronics. Efficient DKS can be generated by spatiotemporally structured light (i.e., pulsed pumping), which to date however has required complex cascaded modulators for pulse synthesis. Here we demonstrate a photonic integrated approach to pulsed pumping. By actively switching the bias current of injection-locked III-V semiconductor lasers with switching frequencies in the X-band and K-band microwave ranges, we pump a crystalline and integrated microresonators with coherent picosecond laser pulses, achieving DKS generation with stable repetition rates and lowering the required average pumping power by one order of magnitude to a record-setting level of a few milliwatts. In addition, we unveil the critical role of the phase profile of the pumping pulses, and for the first time implement phase engineering on the pulsed pumping scheme by either accessing a multimode lasing regime in the gain-switching mode or applying external chirping to support robust single-soliton generation. Our work leverages the advantages of gain switching technique and pulse pumping technique, and establishes the merits of combining distinct compact frequency comb platforms that enhance the potential of energy-efficient chipscale microcombs.

Coherent ranging, also known as frequency-modulated continuous-wave (FMCW) laser based ranging (LIDAR) is currently developed for long range 3D distance and velocimetry in autonomous driving. Its principle is based on mapping distance to frequency, and to simultaneously measure the Doppler shift of reflected light using frequency chirped signals, similar to Sonar or Radar. Yet, despite these advantages, coherent ranging exhibits lower acquisition speed and requires precisely chirped and highly-coherent laser sources, hindering their widespread use and impeding Parallelization, compared to modern time-of-flight (TOF) ranging that use arrays of individual lasers. Here we demonstrate a novel massively parallel coherent LIDAR scheme using a photonic chip-based microcomb. By fast chirping the pump laser in the soliton existence range of a microcomb with amplitudes up to several GHz and sweep rate up to 10 MHz, the soliton pulse stream acquires a rapid change in the underlying carrier waveform, while retaining its pulse-to-pulse repetition rate. As a result, the chirp from a single narrow-linewidth pump laser is simultaneously transferred to all spectral comb teeth of the soliton at once, and allows for true parallelism in FMCW LIDAR. We demonstrate this approach by generating 30 distinct channels, demonstrating both parallel distance and velocity measurements at an equivalent rate of 3 Mpixel/s, with potential to improve sampling rates beyond 150 Mpixel/s and increase the image refresh rate of FMCW LIDAR up to two orders of magnitude without deterioration of eye safety. The present approach, when combined with photonic phase arrays based on nanophotonic gratings, provides a technological basis for compact, massively parallel and ultra-high frame rate coherent LIDAR systems., Comment: 18 pages, 12 Figures

Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The requirement on external driving lasers has been significantly relaxed with the demonstration of soliton formation via self-injection locking of the pump laser to the microresonator. Yet to date, the dynamics of this process has not been fully understood. Prior models of self-injection locking were not able to explain sufficiently large detunings, crucial for soliton formation. Here we develop a theoretical model of self-injection locking to a nonlinear microresonator (nonlinear self-injection locking) for the first time and show that self- and cross-phase modulation of the clockwise and counter-clockwise light enables soliton formation. Using an integrated soliton microcomb of directly detectable 30 GHz repetition rate, consisting of a DFB laser self-injection-locked to a Si3N4 microresonator chip, we study the soliton formation dynamics via self-injection locking, as well as the repetition rate evolution, experimentally. We reveal that Kerr nonlinearity in microresonator significantly modifies locking dynamics, making laser emission frequency red detuned. We propose and implement a novel technique for measurements of the nonlinear frequency tuning curve and concurrent observation of microcomb states switching in real time.

High-speed laser frequency actuation is critical in all applications employing lasers and frequency combs, and is prerequisite for phase locking, frequency stabilization and stability transfer among multiple optical carriers. Soliton microcombs have emerged as chip-scale, broadband and low-power-consumption frequency comb sources.Yet, integrated microcombs relying on thermal heaters for on-chip actuation all exhibit only kilohertz actuation bandwidth. Consequently, high-speed actuation and locking of microcombs have been attained only with off-chip bulk modulators. Here, we present high-speed microcomb actuation using integrated components. By monolithically integrating piezoelectric AlN actuators on ultralow-loss Si3N4 photonic circuits, we demonstrate voltage-controlled soliton tuning, modulation and stabilization. The integrated AlN actuators feature bi-directional tuning with high linearity and low hysteresis, operate with 300 nW power and exhibit flat actuation response up to megahertz frequency, significantly exceeding bulk piezo tuning bandwidth. We use this novel capability to demonstrate a microcomb engine for parallel FMCW LiDAR, via synchronously tuning the laser and microresonator. By applying a triangular sweep at the modulation rate matching the frequency spacing of HBAR modes, we exploit the resonant build-up of bulk acoustic energy to significantly lower the required driving to a CMOS voltage of only 7 Volts. Our approach endows soliton microcombs with integrated, ultralow-power-consumption, and fast actuation, significantly expanding the repertoire of technological applications.

Supercontinuum generation in optical fibers is one of the most dramatic nonlinear effects discovered, allowing short pulses to be converted into multi-octave spanning coherent spectra. However, generating supercontinua that are both coherent and broadband requires pulses that are simultaneously ultrashort with high peak power. This results in a reducing efficiency with increasing pulse repetition rate, that has hindered supercontinua at microwave line spacing, i.e. 10s of GHz. Soliton microcombs by contrast, can generate octave-spanning spectra, but with good conversion efficiency only at vastly higher repetition rates in the 100s of GHz. Here, we bridge this efficiency gap with resonant supercontinuum, allowing supercontinuum generation using input pulses with an ultra-low 6 picojoule energy, and duration of 1 picosecond, 10-fold longer than what is typical. By applying synchronous pulse-driving to a dispersion-engineered, low-loss Si$_3$N$_4$ photonic chip microresonator, we generate dissipative Kerr solitons with a strong dispersive wave, both bound to the input pulse. This creates a smooth, flattened 2,200 line frequency comb, with an electronically detectable repetition rate of 28 GHz, constituting the largest bandwidth-line-count product for any microcomb generated to date. Strikingly, we observe that solitons exist in a weakly bound state with the input pulse, stabilizing their repetition rate, but simultaneously allowing noise transfer from one to the other to be suppressed even for offset frequencies 100 times lower than the linear cavity decay rate. We demonstrate that this nonlinear filtering can be enhanced by pulse-driving asynchronously, in order to preserve the coherence of the comb. Taken together, our work establishes resonant supercontinuum as a promising route to broadband and coherent spectra.

High resolution and fast detection of molecular vibrational absorption is important for organic synthesis, pharmaceutical process and environmental monitoring, and is enabled by mid-infrared (mid-IR) laser frequency combs via dual-comb spectroscopy. Here, we demonstrate a novel and highly simplified approach to broadband mid-IR dual-comb spectroscopy via supercontinuum generation, achieved using unprecedented nanophotonic dispersion engineering that allows for flat-envelope, ultra-broadband mid-IR comb spectra. The mid-IR dual-comb has an instantaneous bandwidth covering the functional group region from 2800-3600 1/cm, comprising more than 100,000 comb lines, enabling parallel gas-phase detection with a high sensitivity, spectral resolution, and speed. In addition to the traditional functional groups, their isotopologues are also resolved in the supercontinuum based dual-comb spectroscopy. Our approach combines well established fiber laser combs, digital coherent data averaging, and integrated nonlinear photonics, each in itself a state-of-the-art technology, signalling the emergence of mid-IR dual-comb spectroscopy for use outside of the protected laboratory environment.

The process of soliton Cherenkov radiation (also known as dispersive wave emission) in microresonator frequency combs plays a critical role in generating broadband and coherent microcomb spectra. Here, we report the observation of symmetry breaking in the group velocity of counter-propagating dissipative Kerr solitons, induced by polychromatic soliton Cherenkov radiation. Results show that in the presence of higher-order dispersion, the temporal arrangement of a multi-soliton state affects its group velocity, an effect which originates from the interference between multiple radiative tails emitted by individual solitons. Experimentally, we bidirectionally pump a microresonator with laser fields of equal power and frequency, and observe lifting of the degeneracy between the repetition rates of the counter-propagating solitons. The observation of symmetry breaking despite symmetric pumping conditions not only shines new light on the impact of dispersive waves on dissipative Kerr soliton dynamics, but also introduces a novel approach to develop coherent dual-comb spectrometers based on microcombs., Comment: 11 pages, 10 figures

Dissipative Kerr solitons in optical microresonators provide a unifying framework for nonlinear optical physics with photonic-integrated technologies and have recently been employed in a wide range of applications from coherent communications to astrophysical spectrometer calibration. Dissipative Kerr solitons can form a rich variety of stable states, ranging from breathers to multiple-soliton formations, among which, the recently discovered soliton crystals stand out. They represent temporally-ordered ensembles of soliton pulses, which can be regularly arranged by a modulation of the continuous-wave intracavity driving field. To date, however, the dynamics of soliton crystals remains mainly unexplored. Moreover, the vast majority of the reported crystals contained defects - missing or shifted pulses, breaking the symmetry of these states, and no procedure to avoid such defects was suggested. Here we explore the dynamical properties of soliton crystals and discover that often-neglected chaotic operating regimes of the driven optical microresonator are the key to their understanding. In contrast to prior work, we prove the viability of deterministic generation of $\mathrm{perfect}$ soliton crystal states, which correspond to a stable, defect-free lattice of optical pulses inside the cavity. We discover the existence of critical pump power, below which the stochastic process of soliton excitation suddenly becomes deterministic enabling faultless, device-independent access to perfect soliton crystals. Furthermore, we demonstrate the switching of soliton crystal states and prove that it is also tightly linked to the pump power and is only possible in the regime of transient chaos. Finally, we report a number of other dynamical phenomena experimentally observed in soliton crystals including the formation of breathers, transitions between soliton crystals, their melting, and recrystallization.

Optical soliton molecules are bound states of solitons that arise from the balance between attractive and repulsive effects. Having been observed in systems ranging from optical fibers to mode-locked lasers, they provide insights into the fundamental interactions between solitons and the underlying dynamics of the nonlinear systems. Here, we enter the multistability regime of a Kerr microresonator to generate superpositions of distinct soliton states that are pumped at the same optical resonance, and report the discovery of heteronuclear dissipative Kerr soliton molecules. Ultrafast electrooptical sampling reveals the tightly short-range bound nature of such soliton molecules, despite comprising dissipative Kerr solitons of dissimilar amplitudes, durations and carrier frequencies. Besides the significance they hold in resolving soliton dynamics in complex nonlinear systems, such heteronuclear soliton molecules yield coherent frequency combs whose unusual mode structure may find applications in metrology and spectroscopy.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap, to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons follows the external drive at long time scales, but exhibits an unexpected suppression of the fast timing jitter. Counter-intuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long-time-scale stability of the Kerr frequency comb repetition rate is improved by more than 4 orders of magnitude as a result of locking to the external microwave signal, the soliton stream shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

We demonstrate thermometry with a resolution of 80 $\mathrm{nK} / \sqrt{\mathrm{Hz}}$ using an isotropic crystalline whispering-gallery mode resonator based on a dichroic dual-mode technique. We simultaneously excite two modes that have a mode frequency ratio very close to two ($\pm0.3$ppm). The wavelength- and temperature-dependence of the refractive index means that the frequency difference between these modes is an ultra-sensitive proxy of the resonator temperature. This approach to temperature sensing automatically suppresses sensitivity to thermal expansion and vibrationally induced changes of the resonator. We also demonstrate active suppression of temperature fluctuations in the resonator by controlling the intensity of the driving laser. The residual temperature fluctuations are shown to be below the limits set by fundamental thermodynamic fluctuations of the resonator material.