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Increasing the number of entangled entities is crucial for achieving exponential computational speedups and secure quantum networks. Despite recent progress in generating large-scale entanglement through continuous-variable (CV) cluster states, translating these technologies to photonic chips has been hindered by decoherence, limiting the number of entangled entities to 8. Here, we demonstrate 60-mode CVcluster states in a chip-based optical microresonator pumped by chromatic lasers. Resonantly-enhanced four-wave mixing processes establish entanglement between equidistant spectral quantum modes (qumodes), forming a quantum analogue of optical frequency combs. Decoherence is minimized to achieve unprecedented two-mode raw squeezing (>3 dB) from a chip. Using bichromatic and trichromatic pump lasers, we realize one- and two-dimensional cluster states with up to 60 qumodes. Our work provides a compact and scalable platform for constructing large-scale entangled quantum resources, which are appealing for performing computational and communicational tasks with quantum advantages.

Kerr microcombs generated in optical microresonators provide broadband light sources bridging optical and microwave signals. Their translation to thin-film lithium niobate unlocks second-order nonlinear optical interfaces such as electro-optic modulation and frequency doubling for completing comb functionalities. However, the strong Raman response of LiNbO$_3$ has complicated the formation of Kerr microcombs. Until now, dark pulse microcombs, requiring a double balance between Kerr nonlinearity and normal group velocity dispersion as well as gain and loss, have remained elusive in LiNbO$_3$ microresonators. Here, by incorporating dissipation engineering, we demonstrate dark pulse microcombs with 25 GHz repetition frequency and 200 nm span in a high-$Q$ LiNbO$_3$ microresonator. Resonances near the Raman-active wavelengths are strongly damped by controlling phase-matching conditions of a specially designed pulley coupler. The coherence and tunability of the dark pulse microcombs are also investigated. Our work provides a solution to realize high-power microcombs operating at microwave rates on LiNbO$_3$ chips, promising new opportunities for the monolithic integration of applications spanning communication to microwave photonics.

Optical frequency division relies on optical frequency combs to coherently translate ultra-stable optical frequency references to the microwave domain. This technology has enabled microwave synthesis with ultralow timing noise, but the required instruments are too bulky for real-world applications. Here, we develop a compact optical frequency division system using microresonator-based frequency references and comb generators. The soliton microcomb formed in an integrated Si$_3$N$_4$ microresonator is stabilized to two lasers referenced to an ultrahigh-$Q$ MgF$_2$ microresonator. Photodetection of the soliton pulse train produces 25 GHz microwaves with absolute phase noise of -141 dBc/Hz (547 zs Hz$^{-1/2}$) at 10 kHz offset frequency. The synthesized microwaves are tested as local oscillators in jammed communication channels, resulting in improved fidelity compared with those derived from electronic oscillators. Our work demonstrates unprecedented coherence in miniature microwave oscillators, providing key building blocks for next-generation timekeeping, navigation, and satellite communication systems., Comment: 8 pages, 7 figures and tables

Many key functionalities of optical frequency combs such as self-referencing and broad spectral access rely on coherent supercontinuum generation (SCG). While nanophotonic waveguides have emerged as a compact and power-efficient platform for SCG, their geometric degrees of freedom have not been fully utilized due to the underlying nonlinear and stochastic physics. Here, we introduce inverse design to unlock free-form waveguides for coherent SCG. The efficacy of our design is numerically and experimentally demonstrated on Si3N4 waveguides, producing flat and coherent spectra from visible to mid-infrared wavelengths. Our work has direct applications in developing chip-based broadband light sources for spectroscopy, metrology, and sensing across multiple spectral regimes.

Quantum diffusion of soliton microcombs has long been recognized as their fundamental noise limit. Here we surpass such limit by utilizing dispersive wave dynamics in multimode microresonators. Through the recoil force provided by these dispersive waves, the quantum diffusion can be suppressed to a much lower level that forms the ultimate fundamental noise limit of soliton microcombs. Our findings enable coherence engineering of soliton microcombs in the quantum-limited regime, providing critical guidelines for using soliton microcombs to synthesize ultralow-noise microwave and optical signals., Comment: 8 pages, 5 figures

Vibrational spectroscopy is a ubiquitous technology that derives the species, constituents, and morphology of an object from its natural vibrations. However, the vibrational spectra of mesoscopic particles - including most biological cells - have remained hidden from existing technologies. These particles are expected to vibrate faintly at megahertz to gigahertz rates, imposing unpractical sensitivity and resolution for current optical and piezoelectric spectroscopy. Here we demonstrate the real-time measurement of natural vibrations of single mesoscopic particles using an optical microresonator, extending the reach of vibrational spectroscopy to a new spectral window. Conceptually, a spectrum of vibrational modes of the particles is stimulated photoacoustically, and correlated to a high-quality-factor optical resonance for the ultrasensitive readout. Experimentally, this scheme is testified by measuring mesoscopic particles with different constituents, sizes, and internal structures, showing an unprecedented signal-to-noise ratio of 50 dB and detection bandwidth over 1 GHz. This new technology is further applied for the biomechanical fingerprinting of single microbial cells with different species and living states. The present method opens up new avenues to study single-particle mechanical properties in vibrational degrees of freedom, and may find applications in photoacoustic sensing and imaging, cavity optomechanics and biomechanics., Comment: 15 pages, 10 figures

The frequency and orbital angular momentum (OAM) are independent physical properties of light that both offer unbounded degrees of freedom. However, creating, processing, and detecting high-dimensional OAM states have been a pivot and long-lasting task, as the complexity of the required optical systems scales up drastically with the OAM dimension. On the other hand, mature toolboxes -- such as optical frequency combs -- have been developed in the frequency domain for parallel measurements with excellent fidelity. Here we correlate the two dimensions into an equidistant comb structure on a photonic chip. Dissipative optical solitons formed in a nonlinear microresonator are emitted through the engraved angular gratings with each comb line carrying distinct OAM. Such one-to-one correspondence between the OAM and frequencies manifests state-of-the-art extinction ratios over 18.5 dB, enabling precision spectroscopy of optical vortices. The demonstrated vortex soliton microcombs provide coherent light sources that are multiplexed in the spatial and frequency domain, having the potential to establish a new modus operandi of high-dimensional structured light.

Microcombs are revolutionizing optoelectronics by providing parallelized, mutually coherent wavelength channels for time-frequency metrology and information processing. To implement this essential function in integrated photonic systems, it is desirable to drive microcombs directly with an on-chip laser in a simple and flexible way. However, two major difficulties are preventing this goal: 1) generating mode-locked comb states usually requires a significant amount of pump power and 2) the requirement to align laser and resonator frequency significantly complicates operation and limits the tunability of the comb lines. Here, we address these problems by using microresonators on an AlGaAs on-insulator platform to generate dark-pulse microcombs. This highly nonlinear platform dramatically relaxes fabrication requirements and leads to a record-low pump power of less than 1 mW for coherent comb generation. Dark-pulse microcombs facilitated by thermally-controlled avoided mode-crossings are accessed by direct DFB laser pumping. Without any feedback or control circuitries, the comb shows good coherence and stability. This approach also leads to an unprecedented wide chirping range of all the comb lines. Our work provides a route to realize power-efficient, simple and reconfigurable microcombs that can be seamlessly integrated with a wide range of photonic systems.

Optical microresonators with high quality ($Q$) factors are essential to a wide range of integrated photonic devices. Steady efforts have been directed towards increasing microresonator $Q$ factors across a variety of platforms. With success in reducing microfabrication process-related optical loss as a limitation of $Q$, the ultimate attainable $Q$, as determined solely by the constituent microresonator material absorption, has come into focus. Here, we report measurements of the material-limited $Q$ factors in several photonic material platforms. High-$Q$ microresonators are fabricated from thin films of SiO$_2$, Si$_3$N$_4$, Al$_{0.2}$Ga$_{0.8}$As and Ta$_2$O$_5$. By using cavity-enhanced photothermal spectroscopy, the material-limited $Q$ is determined. The method simultaneously measures the Kerr nonlinearity in each material and reveals how material nonlinearity and ultimate $Q$ vary in a complementary fashion across photonic materials. Besides guiding microresonator design and material development in four material platforms, the results help establish performance limits in future photonic integrated systems., Comment: Maodong Gao, Qi-Fan Yang and Qing-Xin Ji contributed equally to this work. 9 pages, 4 figures, 1 table

Silicon nitride (SiN) waveguides with ultra-low optical loss enable integrated photonic applications including low noise, narrow linewidth lasers, chip-scale nonlinear photonics, and microwave photonics. Lasers are key components to SiN photonic integrated circuits (PICs), but are difficult to fully integrate with low-index SiN waveguides due to their large mismatch with the high-index III-V gain materials. The recent demonstration of multilayer heterogeneous integration provides a practical solution and enabled the first-generation of lasers fully integrated with SiN waveguides. However a laser with high device yield and high output power at telecommunication wavelengths, where photonics applications are clustered, is still missing, hindered by large mode transition loss, nonoptimized cavity design, and a complicated fabrication process. Here, we report high-performance lasers on SiN with tens of milliwatts output through the SiN waveguide and sub-kHz fundamental linewidth, addressing all of the aforementioned issues. We also show Hertz-level linewidth lasers are achievable with the developed integration techniques. These lasers, together with high-$Q$ SiN resonators, mark a milestone towards a fully-integrated low-noise silicon nitride photonics platform. This laser should find potential applications in LIDAR, microwave photonics and coherent optical communications., Comment: 8 pages, 3 figures

Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning optical communications, metrology and sensing provide unrivalled performance. To transfer these capabilities from the laboratory to the real world, a key missing ingredient is a mass-produced integrated laser with superior coherence. Here, we bridge conventional semiconductor lasers and coherent optical systems using CMOS-foundry-fabricated microresonators with record high $Q$ factor over 260 million and finesse over 42,000. Five orders-of-magnitude noise reduction in the pump laser is demonstrated, and for the first time, fundamental noise below 1 Hz$^2$ Hz$^{-1}$ is achieved in an electrically-pumped integrated laser. Moreover, the same configuration is shown to relieve dispersion requirements for microcomb generation that have handicapped certain nonlinear platforms. The simultaneous realization of record-high $Q$ factor, highly coherent lasers and frequency combs using foundry-based technologies paves the way for volume manufacturing of a wide range of coherent optical systems., Comment: 19 pages, 11 figures

Coherently-pumped (Kerr) solitons in an ideal optical microcavity are expected to undergo random quantum motion that determines fundamental performance limits in applications of soliton microcombs. Here, this diffusive motion and its impact on Kerr soliton timing jitter is studied experimentally. Typically hidden below technical noise contributions, the quantum limit is discerned by measuring counter-propagating solitons. Their relative motion features only weak interactions and also presents excellent common mode suppression of technical noise. This is in strong contrast to co-propagating solitons which are found to have relative timing jitter well below the quantum limit of a single soliton on account of strong mutual motion correlation. Good agreement is found between theory and experiment. The results establish the fundamental limits to timing jitter in soliton microcombs and provide new insights on multi-soliton physics

While soliton microcombs offer the potential for integration of powerful frequency metrology and precision spectroscopy systems, their operation requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components. Moreover, CMOS-rate microcombs, required in nearly all comb systems, have resisted integration because of their power requirements. Here, a regime for turnkey operation of soliton microcombs co-integrated with a pump laser is demonstrated and theoretically explained. Significantly, a new operating point is shown to appear from which solitons are generated through binary turn-on and turn-off of the pump laser, thereby eliminating all photonic/electronic control circuitry. These features are combined with high-Q $Si_3N_4$ resonators to fully integrate into a butterfly package microcombs with CMOS frequencies as low as 15 GHz, offering compelling advantages for high-volume production., Comment: Boqiang Shen, Lin Chang, Junqiu Liu, Heming Wang and Qi-Fan Yang contributed equally to this work

For its many useful properties, including second and third-order optical nonlinearity as well as electro-optic control, lithium niobate is considered an important potential microcomb material. Here, a soliton microcomb is demonstrated in a monolithic high-Q lithium niobate resonator. Besides the demonstration of soliton mode locking, the photorefractive effect enables mode locking to self-start and soliton switching to occur bi-directionally. Second-harmonic generation of the soliton spectrum is also observed, an essential step for comb self-referencing. The Raman shock time constant of lithium niobate is also determined by measurement of soliton self-frequency-shift. Besides the considerable technical simplification provided by a self-starting soliton system, these demonstrations, together with the electro-optic and piezoelectric properties of lithium niobate, open the door to a multi-functional microcomb providing f-2f generation and fast electrical control of optical frequency and repetition rate, all of which are critical in applications including time keeping, frequency synthesis/division, spectroscopy and signal generation.

Acquisition of laser frequency with high resolution under continuous and abrupt tuning conditions is important for sensing, spectroscopy and communications. Here, a single microresonator provides rapid and broad-band measurement of frequencies across the optical C-band with a relative frequency precision comparable to conventional dual frequency comb systems. Dual-locked counter-propagating solitons having slightly different repetition rates are used to implement a Vernier spectrometer. Laser tuning rates as high as 10 THz/s, broadly step-tuned lasers, multi-line laser spectra and also molecular absorption lines are characterized using the device. Besides providing a considerable technical simplification through the dual-locked solitons and enhanced capability for measurement of arbitrarily tuned sources, this work reveals possibilities for chip-scale spectrometers that greatly exceed the performance of table-top grating and interferometer-based devices.

Solitons are self-sustained wavepackets that occur in many physical systems. Their recent demonstration in optical microresonators has provided a new platform for study of nonlinear optical physics with practical implications for miniaturization of time standards, spectroscopy tools and frequency metrology systems. However, despite its importance to understanding of soliton physics as well as development of new applications, imaging the rich dynamical behaviour of solitons in microcavities has not been possible. These phenomena require a difficult combination of high-temporal-resolution and long-record-length in order to capture the evolving trajectories of closely-spaced microcavity solitons. Here, an imaging method is demonstrated that visualizes soliton motion with sub-picosecond resolution over arbitrary time spans. A wide range of complex soliton transient behaviors are characterized in the temporal or spectral domain, including soliton formation, collisions, spectral breathing and soliton decay. This method can serve as a universal visualization tool for understanding complex soliton physics in microcavities., Comment: Xu Yi and Qi-Fan Yang contributed equally to this work

An external-cavity diode laser is reported with ultralow noise, high power coupled to a fiber, and fast tunability. These characteristics enable the generation of an optical frequency comb in a silica micro-resonator with a single-soliton state. Neither an optical modulator nor an amplifier was used in the experiment. This demonstration greatly simplifies the soliton generation setup and represents a significant step forward to a fully integrated soliton comb system., Comment: 7 pages, 5 figures

Laser linewidth is of central importance in spectroscopy, frequency metrology and all applications of lasers requiring high coherence. It is also of fundamental importance, because the Schawlow-Townes laser linewidth limit is of quantum origin. Recently, a theory of stimulated Brillouin laser (SBL) linewidth has been reported. While the SBL linewidth formula exhibits power and optical Q factor dependences that are identical to the Schawlow-Townes formula, a source of noise not present in two-level lasers, phonon occupancy of the Brillouin mechanical mode, is predicted to be the dominant SBL linewidth contribution. Moreover, the quantum-limit of the SBL linewidth is predicted to be twice the Schawlow-Townes limit on account of phonon participation. To help confirm this theory the SBL fundamental linewidth is measured at cryogenic temperatures in a silica microresonator. Its temperature dependence and the SBL linewidth theory are combined to predict the number of thermo-mechanical quanta at three temperatures. The result agrees with the Bose-Einstein phonon occupancy of the microwave-rate Brillouin mode in support of the SBL linewidth theory prediction.

Frequency combs have applications that extend from the ultra-violet into the mid-infrared bands. Microcombs, a miniature and often semiconductor-chip-based device, can potentially access most of these applications, but are currently more limited in spectral reach. Here, we demonstrate mode-locked silica microcombs with emission near the edge of the visible spectrum. By using both geometrical and mode-hybridization dispersion control, devices are engineered for soliton generation while also maintaining optical $Q$ factors as high as 80 million. Electronics-bandwidth-compatible (20 GHz) soliton mode locking is achieved with low pumping powers (parametric oscillation threshold powers as low as 5.4 mW). These are the shortest wavelength soliton microcombs demonstrated to date and could be used in miniature optical clocks. The results should also extend to visible and potentially ultra-violet bands., Comment: Seung Hoon Lee, Dong Yoon Oh, Qi-Fan Yang, Boqiang Shen and Heming Wang contributed equally to this work

Solitons occur in many physical systems when a nonlinearity compensates wave dispersion. Their recent formation in microresonators opens a new research direction for nonlinear optical physics and provides a platform for miniaturization of spectroscopy and frequency metrology systems. These microresonator solitons orbit around a closed waveguide path and produce a repetitive output pulse stream at a rate set by the round-trip time. In this work counter-propagating solitons that simultaneously orbit in an opposing sense (clockwise/counter-clockwise) are studied. Despite sharing the same spatial mode family, their round-trip times can be precisely and independently controlled. Furthermore, a state is possible in which both the relative optical phase and relative repetition rates of the distinct soliton streams are locked. This state allows a single resonator to produce dual-soliton frequency-comb streams having different repetition rates, but with high relative coherence useful in both spectroscopy and laser ranging systems., Comment: Qi-Fan Yang and Xu Yi contributed equally to this work

Optical microcavities are essential in numerous technologies and scientific disciplines. However, their application in many areas relies exclusively upon discrete microcavities in order to satisfy challenging combinations of ultra-low-loss performance (high cavity-Q-factor) and cavity design requirements. Indeed, finding a microfabrication bridge connecting ultra-high-Q device functions with micro and nanophotonic circuits has been a long-term priority of the microcavity field. Here, an integrated ridge resonator having a record Q factor over 200 million is presented. Its ultra-low-loss and flexible cavity design brings performance that has been the exclusive domain of discrete silica and crytalline microcavity devices to integrated systems. Two distinctly different devices are demonstrated: soliton sources with electronic repetition rates and high-coherence Brillouin lasers. This multi-device capability and performance from a single integrated cavity platform represents a critical advance for future nanophotonic circuits and systems., Comment: (1) Added Fig.4 to show high-coherence Brillouin lasing using the integrated resonator; (2) Added system illustrations (Fig. 1a); (3) Changed title of paper to reflect demonstrations of both low-repetition-rate soliton mode locking and Brillouin laser using the integrated resonator; (4) Fig. 6 added in Methods to describe resonator-to-waveguide phase-matching control; (5) Other minor changes

Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton is shown to induce bistable behavior in the spectral and temporal properties of the soliton. Also, an operating point of enhanced repetition-rate stability is predicted and observed. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications., Comment: Xu Yi, Qi-Fan Yang and Xueyue Zhang contributed equally to this work

Rapid characterization of optical and vibrational spectra with high resolution can identify species in cluttered environments and is important for assays and early alerts. In this regard, dual-comb spectroscopy has emerged as a powerful approach to acquire nearly instantaneous Raman and optical spectra with unprecedented resolution. Spectra are generated directly in the electrical domain and avoid bulky mechanical spectrometers. Recently, a miniature soliton-based comb has emerged that can potentially transfer the dual-comb method to a chip platform. Unlike earlier microcombs, these new devices achieve high-coherence, pulsed mode locking. They generate broad, reproducible spectral envelopes, which is essential for dual-comb spectroscopy. Here, dual-comb spectroscopy is demonstrated using these devices. This work shows the potential for integrated, high signal-to-noise spectroscopy with fast acquisition rates., Comment: 7 pages, 4 figures

Solitons are wavepackets that resist dispersion through a self-induced potential well. They are studied in many fields, but are especially well known in optics on account of the relative ease of their formation and control in optical fiber waveguides. Besides their many interesting properties, solitons are important to optical continuum generation, in mode-locked lasers and have been considered as a natural way to convey data over great distances. Recently, solitons have been realized in microcavities thereby bringing the power of microfabrication methods to future applications. This work reports a soliton not previously observed in optical systems, the Stokes soliton. The Stokes soliton forms and regenerates by optimizing its Raman interaction in space and time within an optical-potential well shared with another soliton. The Stokes and the initial soliton belong to distinct transverse mode families and benefit from a form of soliton trapping that is new to microcavities and soliton lasers in general. The discovery of a new optical soliton can impact work in other areas of photonics including nonlinear optics and spectroscopy., Comment: Qi-Fan Yang and Xu Yi contributed equally to this work

The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One example is dispersive wave generation, the optical analog of Cherenkov radiation. These waves have an essential role in fiber spectral broadeners that are routinely used in spectrocopy and metrology. Dispersive waves form when a soliton pulse begins to radiate power as a result of higher-order dispersion. Recently, dispersive wave generation in microcavities has been reported by phase matching the waves to dissipative Kerr cavity (DKC) solitons. Here, it is shown that spatial mode interactions within a microcavity can also be used to induce dispersive waves. These interactions are normally avoided altogether in DKC soliton generation. The soliton self frequency shift is also shown to induce fine tuning control of the dispersive wave frequency. Both this mechanism and spatial mode interactions provide a new method to spectrally control these important waves., Comment: Qi-Fan Yang and Xu Yi contributed equally to this work

Because they coherently link radio/microwave-rate electrical signals with optical-rate signals derived from lasers and atomic transitions, frequency combs are having a remarkably broad impact on science and technology. Integrating these systems on a photonic chip would revolutionize instrumentation, time keeping, spectroscopy, navigation and potentially create new mass-market applications. A key element of such a system-on-a-chip will be a mode-locked comb that can be self-referenced. The recent demonstration of soliton pulses from a microresonator has placed this goal within reach. However, to provide the requisite link between microwave and optical rate signals soliton generation must occur within the bandwidth of electronic devices. So far this is possible in crytalline devices, but not chip-based devices. Here, a monolithic comb that generates electronic-rate soliton pulses is demonstrated., Comment: Xu Yi, Qi-Fan Yang, Ki Youl Yang contributed equally to this work