Parametric Frequency Divider Based Ising Machines.

We report on a new class of Ising machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic-injection locking (SHIL), PFD IMs do not require strong injected continuous-wave signals or applied dc voltages. Therefore, they show a significantly lower power consumption per spin compared to SHIL-based IMs, making it feasible to accurately solve large-scale combinatorial optimization problems that are hard or even impossible to solve by using the current von Neumann computing architectures. Furthermore, using high quality factor resonators in the PFD design makes PFD IMs able to exhibit a nanowatt-level power per spin. Also, it remarkably allows a speedup of the phase synchronization among the PFDs, resulting in shorter time to solution and lower energy to solution despite the resonators' longer relaxation time. As a proof of concept, a 4-node PFD IM has been demonstrated. This IM correctly solves a set of Max-Cut problems while consuming just 600 nanowatts per spin. This power consumption is 2 orders of magnitude lower than the power per spin of state-of-the-art SHIL-based IMs operating at the same frequency.

Nonlinear Stiffness and Nonlinear Damping in Atomically Thin MoS2 Nanomechanical Resonators.

We report on experimental measurements and quantitative analyses of nonlinear dynamic characteristics in ultimately thin nanomechanical resonators built upon single-layer, bilayer, and trilayer (1L, 2L, and 3L) molybdenum disulfide (MoS2) vibrating drumhead membranes. This synergistic study with calibrated measurements and analytical modeling on observed nonlinear responses has led to the determination of nonlinear damping and stiffness coefficients at cubic and quintic orders for these two-dimensional (2D) resonators operating in the very high frequency (VHF) band (up to ∼90 MHz). We find that the quintic force can be ∼20% of the Duffing force at larger amplitudes, and thus, it generally cannot be ignored in a nonlinear dynamics analysis. This study provides the first quantification of nonlinear damping and frequency detuning characteristics in 2D semiconductor nanomechanical resonators and elucidates their origins and dependency on engineerable parameters, setting a foundation for future exploration and utilization of the rich nonlinear dynamics in 2D nanomechanical systems.

Five Low-Noise Stable Oscillators Referenced to the Same Multimode AlN/Si MEMS Resonator.

We report on the first experimental demonstration of five self-sustaining feedback oscillators referenced to a single multimode resonator, using piezoelectric aluminum nitride on silicon (AlN/Si) microelectromechanical systems (MEMS) technology. Integrated piezoelectric transduction enables efficient readout of five resonance modes of the same AlN/Si MEMS resonator, at 10, 30, 65, 95, and 233 MHz with quality ( Q ) factors of 18 600, 4350, 4230, 2630, and 2138, respectively, at room temperature. Five stable self-sustaining oscillators are built, each referenced to one of these high- Q modes, and their mode-dependent phase noise and frequency stability (Allan deviation) are measured and analyzed. The 10, 30, 65, 95, and 233 MHz oscillators exhibit low phase noise of -116, -100, -105, -106, and -92 dBc/Hz at 1 kHz offset frequency, respectively. The 65 MHz oscillator yields the Allan deviation of 4×10-9 and 2×10-7 at 1 and 1000 s averaging time, respectively. The 10 MHz oscillator's low phase noise holds strong promise for clock and timing applications. The five oscillators' overall promising performance suggests suitability for multimode resonant sensing and real-time frequency tracking. This work also elucidates mode dependency in oscillator noise and stability, one of the key attributes of mode-engineerable resonators.