Jizhao Zang

We introduce and explore a Kerr soliton Ising machine with all-to-all connectivity and up to tripartite (cubic) interactions, unlocking efficient approaches for combinatorial optimization. The machine is an ensemble of solitons in a Kerr resonator, where a programmable optoelectronic feedback circuit generates amplitude mixing terms involving up to three arbitrary soliton spins in the system Hamiltonian. This capability offers a key advantage for solving canonical NP-complete problems like Boolean satisfiability (SAT) with three literal clauses, substantially reducing the spin overhead compared to quadratic-only Ising mappings. To explore our cubic Ising machine, we solve randomly generated 3-SAT instances of 250 variables and 1000 clauses, approaching the intrinsic satisfiability threshold. Our results highlight Kerr solitons as a flexible and energy-efficient analog computing substrate, with the potential to address challenges in combinatorial optimization, artificial intelligence, and machine learning.

The challenge of scaling digital computing motivates innovation, especially through the evolution of physical systems that mimic neural networks and combinatorial optimization problems. Light is a hyperefficient information carrier, and if efficient interactions with it could be uncovered, then direct information processing would become far more feasible. We harness an ensemble of hundreds of Kerr microresonator solitons and implement an analog feedback network to create an Ising machine with fully programmable all-to-all interactions. By increasing the feedback for self, on-diagonal interactions, each soliton exhibits a universal spin-like bifurcation, and using this palette of interactions, we solve the canonical Boolean satisfiability problem (SAT). The combination of uniform soliton interactions and the compatibility of our Ising machine with high-speed data interconnects enables rapid and precise solutions of complex SAT problems. The well-established theoretical properties of Kerr solitons bound the trade-off of optical power and time use by the machine at ~0.15 milliwatts per soliton and 1 microsecond for a single feedback step. We performed >10,000 trials on more than 100 randomly generated SAT instances to evaluate the Ising machine, demonstrating the potential to exceed the performance of benchmark digital SAT solvers. Our work highlights the convergence of optical nonlinearity, ultralow loss photonics, and optoelectronic circuits for computation-acceleration tasks.

The photonics landscape encompasses a wide scope of material platforms, each optimized for specific functionalities, yet no platform meets the demands of all current and evolving photonic applications. Although combining integrated-photonics materials enhances overall capability, such as unifying nonlinear optics, low-loss passive devices and electro-optics, material and process compatibility remains a major challenge. Here we introduce full-wafer, monolithic 3D integration of tantalum pentoxide (Ta₂O₅, hereafter tantala¹) photonics directly onto a patterned substrate, demonstrated here with thin-film lithium niobate². Tantala's unique properties, importantly room-temperature deposition, moderate-temperature annealing and low residual stress in thick films optimized for phase matching, make it well suited for monolithic 3D integration without compromising substrate performance or compatibility. We demonstrate low-loss, high-quality-factor microresonators and nanophotonics in tantala, robust quasi-phase-matching in poled lithium niobate waveguides³, and efficient 3D interlayer routing. These capabilities enable us to demonstrate a rich palette of nonlinear frequency conversion processes, including χ⁽³⁾ four-wave mixing for supercontinuum generation, optical parametric oscillation and dark-pulse microcomb generation in tantala microresonators and photonic crystal resonators, χ⁽²⁾ second-harmonic generation in periodically poled lithium niobate, and combinations thereof.

Microcomb-based sources formed by placing an integrated demultiplexer with an ultra-low power consumption after an efficient optical frequency comb play a key role in many large-scale optical links for data centers and AI systems. Here, we demonstrate a multi-wavelength multi-port source based on a Kerr microcomb followed by a monolithically-integrated demultiplexer, which autonomously locks to and tracks the comb lines. Mach-Zehnder interferometer- and ring resonator-based wavelength demultiplexers, implemented using capacitive optical phase shifters with a zero static power consumption, and a soliton microcomb, with a 200 GHz mode-spacing and 53% efficiency, are implemented. Using a single control unit for the sequential control of all phase shifters, a total demultiplexer power consumption of 2.4 mW is achieved, which corresponds to a record demultiplexer energy consumption of 10fJ/b and 2.5fJ/b for an 8-channel and 32-channel systems at a data-rate of 32 Gb/s/channel, respectively, significantly improving the demultiplexer energy efficiency compared to the thermally-tuned state-of-the-art systems.

Control of nonlinear interactions in microresonators enhances access to classical and quantum field states across nearly limitless bandwidth. A recent innovation has been to leverage coherent scattering of the intraresonator pump field as a control of group-velocity dispersion and nonlinear frequency shifts, which are precursors for the dynamical evolution of new field states. Yet, since nonlinear-resonator phenomena are intrinsically multimode and exhibit complex modelocking, here we demonstrate a new approach to controlling nonlinear interactions with bandgap modes completely separate from the pump laser. We explore this bandgap-detuned excitation regime through generation of benchmark optical parametric oscillators (OPOs) and soliton microcombs. Indeed, we show that mode-locked states are phase matched more effectively in the bandgap-detuned regime in which we directly control the modal Kerr shift with the bandgaps without perturbing the pump field. In particular, bandgap-detuned excitation enables an arbitrary, mode-by-mode control of the backscattering rate as a versatile tool for mode-locked state engineering. Our experiments leverage nanophotonic resonators for phase matching of OPOs and solitons, leading to control over threshold power, conversion efficiency, and emission direction that enable application advances in high-capacity signaling and computing, signal generation, and quantum sensing.

Access to electrical signals across the millimeter-wave (mmW) and terahertz (THz) bands offers breakthroughs for high-performance applications. Despite generations of revolutionary development, integrated electronics are challenging to operate beyond 100 GHz. Therefore, new technologies that generate wideband and tunable electronic signals would advance wireless communication, high-resolution imaging and scanning, spectroscopy, and network formation. Photonic approaches have been demonstrated for electronic signal generation, but at the cost of increased size and power consumption. Here, we describe a chip-scale, universal mmW frequency synthesizer, which uses integrated nonlinear photonics and high-speed photodetection to exploit the nearly limitless bandwidth of light. We use a photonic-integrated circuit to generate dual, microresonator-soliton frequency combs whose interferogram is fundamentally composed of harmonic signals spanning the mmW and THz bands. By phase coherence of the dual comb, we precisely stabilize and synthesize the interferogram to generate any output frequency from DC to >1000 GHz. Across this entire range, the synthesizer exhibits exceptional absolute fractional frequency accuracy and precision, characterized by an Allan deviation of 3*10^(-12) in 1 s measurements. We use a modified uni-traveling-carrier (MUTC) photodiode with an operating frequency range to 500 GHz to convert the interferogram to an electrical signal, generating continuously tunable tones across the entire mmW band. The synthesizer phase noise at a reference frequency of 150 GHz is -83 dBc/Hz at 100 kHz offset, which exceeds the intrinsic performance of state-of-the-art CMOS electronics. Our work harnesses the coherence, bandwidth, and integration of photonics to universally extend the frequency range of current, advanced-node CMOS microwave electronics to the mmW and THz bands.

We demonstrate ultra-broadband optoelectronic mixing of frequency combs that provides phase-coherent detection of a repetition frequency up to 500 GHz, using a high-speed modified uni-traveling carrier (MUTC) photodiode. Nonlinear photo-electron effects in the photodiode itself enable harmonic generation and down-mixing process of combs with widely different repetition frequencies. Specifically, we generate two 25 GHz frequency combs and use an optical filter to explore coherent down-mixing to the baseband of comb spectral components across microwave, millimeter-wave, and terahertz (THz) frequencies. The exceptional noise performance of the optoelectronic mixer enables the phase-coherent measurement of millimeter-wave and THz frequency combs with an Allan deviation of 10⁻¹³/τ for a measurement time of τ. We further investigate the dependence of conversion loss on the reverse bias voltage and photocurrent. The experimental results indicate that we can minimize the conversion loss by operating the photodiode at an optimal voltage and maximum available photocurrent. Our work provides a solution for millimeter-wave and THz frequency-comb measurements and facilitates fully stabilized frequency combs with microresonators.

We explore an AIM Photonics silicon nitride platform to fabricate photonic-crystal resonators (PhCRs) for generating optical parametric oscillators (OPOs) and soliton microcombs. Our approach leverages the scalability and fine feature size of silicon nitride processing on large-scale silicon wafers to achieve low-loss, high-Q microresonators, functionalized by nanoscale photonic-crystal structures. We demonstrate an intrinsic microresonator quality factor up to 1.2 × 10⁷ with complete foundry fabrication on 300 mm silicon, a 700 nm thick silicon nitride device layer, and inclusion of complex nanophotonics. These features enable a host of nonlinear nanophotonic sources on the platform, including OPOs, microcombs, parametric amplifiers, squeezed-light generators, and single-photon sources. By fine-tuning the photonic-crystal design parameters, we achieve broad tunability in the frequency of the OPO output, spanning a significant portion of the near-infrared. Additionally, we observe the formation of soliton frequency combs, enabled by the precise dispersion engineering of the microresonators. These results highlight the potential of widely accessible, photolithographically patterned, silicon nitride photonics to enable wide access to and complex integration of frequency comb sources, with applications in spectroscopy, metrology, and communications.