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1. On the effect of linear feedback and parametric pumping on a resonator’s frequency stability

   https://doi.org/10.1088/1367-2630/abb1dd  

   Mohammadi, Zohreh; Heugel, Toni L; Miller, James M; Shin, Dongsuk D; Kwon, Hyun-Keun; Kenny, Thomas W; Chitra, Ramasubramanian; Zilberberg, Oded; Villanueva, Luis Guillermo (September 2020, New Journal of Physics)

   Abstract Resonant sensors based on micro- and nano-electro mechanical systems (M/NEMS) are ubiquitous in many sensing applications due to their outstanding performance capabilities, which are directly proportional to the quality factor ( Q ) of the devices. We address here a recurrent question in the field: do dynamical techniques that modify the effective Q (namely parametric pumping and direct drive velocity feedback) affect the performance of said sensors? We develop analytical models of both cases, while remaining in the linear regime, and introduce noise in the system from two separate sources: thermomechanical and amplifier (read-out) noise. We observe that parametric pumping enhances the quality factor in the amplitude response, but worsens it in the phase response on the resonator. In the case of feedback, we find that Q is enhanced in both cases. Then, we establish a solution for the noisy problem with direct drive and parametric pumping simultaneously. We also find that, in the case when thermomechanical noise dominates, no benefit can be obtained from either artificial Q -enhancement technique. However, in the case when amplifier noise dominates, we surprisingly observe that a significant advantage can only be achieved using parametric pumping in the squeezing region. 

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2. Highly Sensitive Readout Interface for Real-Time Differential Precision Measurements with Impedance Biosensors

   https://doi.org/10.3390/bios13010077  

   Neshani, Sara; Momeni, Kasra; Chen, Degang J.; Neihart, Nathan M. (January 2023, Biosensors)

   Field deployment is critical to developing numerous sensitive impedance transducers. Precise, cost-effective, and real-time readout units are being sought to interface these sensitive impedance transducers for various clinical or environmental applications. This paper presents a general readout method with a detailed design procedure for interfacing impedance transducers that generate small fractional changes in the impedance characteristics after detection. The emphasis of the design is obtaining a target response resolution considering the accuracy in real-time. An entire readout unit with amplification/filtering and real-time data acquisition and processing using a single microcontroller is proposed. Most important design parameters, such as the signal-to-noise ratio (SNR), common-mode-to-differential conversion, digitization configuration/speed, and the data processing method are discussed here. The studied process can be used as a general guideline to design custom readout units to interface with various developed transducers in the laboratory and verify the performance for field deployment and commercialization. A single frequency readout unit with a target 8-bit resolution to interface differentially placed transducers (e.g., bridge configuration) is designed and implemented. A single MCU is programmed for real-time data acquisition and sine fitting. The 8-bit resolution is achieved even at low SNR levels of roughly 7 dB by setting the component values and fitting algorithm parameters with the given methods. 

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3. Nonlinear coupling of closely spaced modes in atomically thin MoS2 nanoelectromechanical resonators

   https://doi.org/10.1038/s41378-024-00844-9  

   Yousuf, S_M_Enamul Hoque; Shaw, Steven W; Feng, Philip X-L (December 2024, Microsystems & Nanoengineering)

   Nanoelectromechanical systems (NEMS) incorporating atomic or molecular layer van der Waals materials can support multimode resonances and exotic nonlinear dynamics. Here we investigate nonlinear coupling of closely spaced modes in a bilayer (2L) molybdenum disulfide (MoS_2) nanoelectromechanical resonator. We model the response from a drumhead resonator using equations of two resonant modes with a dispersive coupling term to describe the vibration induced frequency shifts that result from the induced change in tension. We employ method of averaging to solve the equations of coupled modes and extract an expression for the nonlinear coupling coefficient (λ) in closed form. Undriven thermomechanical noise spectral measurements are used to calibrate the vibration amplitude of mode 2 (a_2) in the displacement domain. We drive mode 2 near its natural frequency and measure the shifted resonance frequency of mode 1 (f_1s) resulting from the dispersive coupling. Our model yields λ = 0.027 ± 0.005 pm^−2 · μs^−2 from thermomechanical noise measurement of mode 1. Our model also captures an anomalous frequency shift of the undriven mode 1 due to nonlinear coupling to the driven mode 2 mediated by large dynamic tension. This study provides a direct means to quantifying λ by measuring the thermomechanical noise in NEMS and will be valuable for understanding nonlinear mode coupling in emerging resonant systems. 

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4. Readout of a quantum processor with high dynamic range Josephson parametric amplifiers

   https://doi.org/10.1063/5.0127375  

   White, Theodore; Opremcak, Alex; Sterling, George; Korotkov, Alexander; Sank, Daniel; Acharya, Rajeev; Ansmann, Markus; Arute, Frank; Arya, Kunal; Bardin, Joseph C.; et al (January 2023, Applied Physics Letters)

   We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 Ω environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250–300 MHz with input saturation powers up to −95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimation of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Finally, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs. 

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5. Mode-dependent scaling of nonlinearity and linear dynamic range in a NEMS resonator

   https://doi.org/10.1063/5.0215566  

   Ma, M; Welles, N; Svitelskiy, O; Yanik, C; Kaya, I I; Hanay, M S; Paul, M R; Ekinci, K L (August 2024, Applied Physics Letters)

   Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of nanoelectromechanical systems' (NEMSs) resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. Here, we characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. We find that the modal Duffing constant increases as n4, while the critical amplitude for the onset of nonlinearity decreases as 1/n. The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further. 

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