The vision of building computational hardware for problem optimization has spurred large efforts in the physics community. In particular, networks of Kerr parametric oscillators (KPOs) are envisioned as simulators for finding the ground states of Ising Hamiltonians. It was shown, however, that KPO networks can feature large numbers of unexpected solutions that are difficult to sample with the existing deterministic (i.e., adiabatic) protocols. In this work, we experimentally realize a system of two classical coupled KPOs, and we find good agreement with the predicted mapping to Ising states. We then introduce a protocol based on stochastic sampling of the system, and we show how the resulting probability distribution can be used to identify the ground state of the corresponding Ising Hamiltonian. This method is akin to a Monte Carlo sampling of multiple out-of-equilibrium stationary states and is less prone to become trapped in local minima than deterministic protocols.

Encapsulated bulk mode microresonators in the megahertz range are used in commercial timekeeping and sensing applications but their performance is limited by the current state of the art of readout methods. We demonstrate a readout using dispersive coupling between a high-Q encapsulated bulk mode micromechanical resonator and a lumped element microwave resonator that is implemented with commercially available components and standard printed circuit board fabrication methods and operates at room temperature and pressure. A frequency domain measurement of the microwave readout system yields a displacement resolution of $522 \, \mathrm{fm/\sqrt{Hz}}$, which demonstrates an improvement over the state of the art of displacement measurement in bulk-mode encapsulated microresonators. This approach can be readily implemented in cryogenic measurements, allowing for future work characterizing the thermomechanical noise of encapsulated bulk mode resonators at cryogenic temperatures.

We study the influence of clamping loss, electrical damping, and transduction nonlinearity on the measured nonlinear dissipation in encapsulated microme-chanical wheel resonators. Our measurements suggest that nonlinear dissipation may arise from the same phonon scattering origins as thermoelastic dissipation in flexural mode resonators ranging in size from carbon nanotubes to guitar strings. These results point to future investigations of thermal bath engineering to probe the origins of nonlinear dissipation in micro- and nanomechanical resonators.

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. In the presence of noise, the system switches between two states via a fluctuating trajectory in phase space, instead of following a straight path. The presence of such fluctuating trajectories makes it hard to establish a precise count or even a useful definition, of the “lifetime” of the state. Addressing this issue, we compare several rate counting methods that allow to estimate a lifetime for the levels. In particular, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels' lifetime. Our work provides a basis for characterizing KPO networks for simulated annealing where an accurate determination of the state lifetime is of fundamental importance.

In this work we experimentally investigate the influence of parametric amplification and parametric suppression on the frequency stability of micromechanical resonators. We isolate the influence of phase slope tuning from changes in the vibrational amplitude and find that parametric suppression improves the frequency stability in the thermal noise regime by over threefold, while parametric amplification degrades the frequency stability by nearly a factor of two.

The Kerr Parametric Oscillator (KPO) is a nonlinear resonator system that is often described as a synthetic two-level system. We reveal that activated switches between these levels follow a fluctuating and curving trajectory in phase space. Such fluctuations make it hard to establish a precise count, or even a useful definition, of the "lifetime" of the levels. Addressing this issue, we compare several methods to overcome this systemic noise, and estimate a lifetime for the levels. Moreover, we establish that a peak in the Allan variance of fluctuations can also be used to determine the levels' lifetime. Our work provides a basis for characterizing KPO networks for simulated annealing.

We observe significant temperature hysteresis in the resonant frequency and quality factor of silicon piezoresistive microcantilevers from room temperature down to 40 K. The hysteresis becomes increasingly pronounced as the support beam length is reduced from 100 μm to 30 μm, leading to over a twenty-fold difference in Q values between the temperature sweep downwards and upwards for the 30 μm support beam device. Our work suggests that temperature hysteresis is an important consideration for thermal-piezoresistive oscillators and other microelectromechanical resonators that require multiple anchor points.

Sensitive capacitive transduction of micromechanical resonators can contribute significant electrical dissipation, which degrades the quality factor of the eigenmodes. We theoretically and experimentally demonstrate a scheme for isolating the electrical damping of a mechanical resonator due to Ohmic dissipation in the readout amplifier. The quality factor suppression arising from the amplifier is strongly dependent on the amplifier feedback resistance and parasitic capacitance. By studying the thermomechanical displacement noise spectrum of a doubly clamped micromechanical beam, we confirm that electrical dissipation tunes the actual, not effective, quality factor. Electrical dissipation is an important consideration in the design of sensitive capacitive displacement transducers, which are a key component in resonant sensors and oscillators.

We present a Lamé mode resonator whose limiting damping mechanism depends on its anchor geometry. The device is anchor-limited when the anchors are stiffer and is Akhiezer-limited with more compliant anchors. This result is determined by observing the temperature dependence of the quality factor (Q) for devices with different lateral dimensions and different anchor designs. The total measured Q increases by an order of magnitude with the more compliant anchors and reaches a room temperature fxQ product of $\boldsymbol {2.2\times 10^{13}}$ . We studied the relationship between the device design and the anchor design and the measured Q(T) results to identify the contributions from different dissipation mechanisms. This investigation provides insight into how anchor design affects anchor damping. [2020-0195]

Provides corrections to a reference in the above named paper.

In this paper, we demonstrate a dual frequency oven-controlled MEMS resonator that can be designed to have an output frequency of 1.27 Mhz or 13 Mhz depending on the crystal orientation of the device. Both modes operate based on closed-loop thermal compensation that can offer PPB (parts-per-billion) level temperature stability over a wide temperature range using low power and exhibit strong shock robustness. As the device is rotated 45- degrees with respect to the $< 100>$ plane of the wafer, the two modes used in oven control exhibit a unique temperature coefficient of frequency (tcF) reversal that allows selection of the output frequency for timing reference applications. The stiffer inplane mode has better temperature stability and shock resistance whereas the plate-bending mode offers ease of drive. Both devices retain stability performance after multiple 12,000g level shocks. [2020-0143]

In this work we present measurements of drive-induced negative nonlinear dissipation present in doubly clamped microbeams fabricated in a hermetically sealed package. We characterize the amplitude-frequency nonlinearity and nonlinear dissipation present in this system under direct drive. The negative nature of the nonlinear dissipation is observed when measuring either the directly- or parametrically-actuated response. By comparing to the free ringdown response, we confirm that the nonlinear dissipation is induced by driving the resonator. Drive-induced nonlinear damping is an important consideration for resonant sensors and oscillators operated at large amplitudes. [2020-0140]

We use parametric suppression for signal amplification in a phase-modulated microelectromechanical (MEM) charge detector. Simultaneously driving and parametrically pumping a MEM resonator with the appropriate relative phase increases the phase slope near the resonant frequency. We use this to increase the sensitivity of a MEM electrometer more than tenfold.

The thermomechanical motion imposes the fundamental noise limit in room-temperature resonant sensors and oscillators. Due to the inherently low sensitivity of capacitive transduction in microelectromechanical (MEM) resonators, its effects are often masked by noise in the subsequent amplifier and measurement stages. In this work, we demonstrate a capacitive transduction scheme for measuring kHz-MHz frequency MEM resonators across 1 $\mu \text{m}$ capacitive gaps with 99.8 thermomechanical-noise-limited resolution. We delineate the transimpedance gain and noise of our custom off-chip differential transimpedance amplifier setup. The thermomechanical noise spectrum can provide estimates of the resonant frequency, quality factor, and electromechanical transduction factor comparable to the commonly used driven response, without the downsides of capacitive feedthrough or nonlinearity. [2019-0115]