Scott B. Papp

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.

Choice of material is ubiquitous in integrated photonics to design device properties, whereas changing material composition is much less common. With phase matching as an additional objective, constraints in depositing and patterning thin films limit the use of integrated nonlinear photonics to only select materials. Here, we explore an amorphous metal oxide mixture of titania (TiO ₂ ) and tantala (Ta ₂ O ₅ ) in which material composition is a tool to enhance and customize photonics properties. In particular, the inclusion of titania reduces the oxygen-defect density in a tantala film, while maintaining a comparable Kerr nonlinear index. With ion-beam sputtering at room temperature, we deposit a thick, ultralow-loss titania-tantala film, and we nanopattern it to create microresonator frequency combs. Titania-tantala microresonators offer lower loss, higher index of refraction, and reduced optical absorption and photorefractive effects. Specifically, the titania-tantala mixture enables microresonator quality factor up to 10 ⁷ and a direct factor of 1.7 reduction in optical absorption. This, along with its large transparency window, high nonlinearity, and low processing temperature requirement, positions titania-tantala as a leading material for integrated nonlinear photonics. Our work demonstrates that composition in metal-oxide mixtures is a design parameter alongside the nanofabrication process and photonics design for integrated nonlinear photonics.

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.

We propose advancing photonic in-memory computing through three-dimensional photonic-electronic integrated circuits using phase-change materials (PCM) and AlGaAs-CMOS technology. These circuits offer high precision (greater than 12 bits), scalability (greater than 1024 by 1024), and massive parallelism (greater than 1 million operations) across the wavelength, spatial, and temporal domains at ultra-low power (less than 1 watt per PetaOPS). Monolithically integrated hybrid PCM-AlGaAs memory resonators handle coarse-precision iterations (greater than 5-bit most significant bit precision) through reversible PCM phase transitions. Electro-optic memristive tuning enables fine-precision updates (greater than 8-bit least significant bit precision), resulting in over 12-bit precision for in-memory computing. The use of low-loss PCM (less than 0.01 dB per cm) and electro-optical tuning yields memristive optical resonators with high Q-factors (greater than 1 million), low insertion loss, and low tuning power. A W by W photonic tensor core composed of PCM-AlGaAs memresonators performs general matrix multiplication (GEMM) across W wavelengths from optical frequency combs, with minimal crosstalk and loss. Hierarchical scaling in the wavelength domain (K) and spatial domain (L) enables this system to address high-dimensional (N) scientific partial differential equation (PDE) problems in a single constant-time operation, compared to the conventional quadratic-time (N squared) computational complexity.

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.