Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion.
ABSTRACT: Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime.
Project description:Cantilever electrostatically-actuated resonators show great promise in sensing and actuating applications. However, the electrostatic actuation suffers from high-voltage actuation requirements and high noise low-amplitude signal-outputs which limit its applications. Here, we introduce a mixed-frequency signal for a cantilever-based resonator that triggers its mechanical and electrical resonances simultaneously, to overcome these limitations. A single linear RLC circuit cannot completely capture the response of the resonator under double resonance excitation. Therefore, we develop a coupled mechanical and electrical mathematical linearized model at different operation frequencies and validate this model experimentally. The double-resonance excitation results in a 21 times amplification of the voltage across the resonator and 31 times amplitude amplification over classical excitation schemes. This intensive experimental study showed a great potential of double resonance excitation providing a high amplitude amplification and maintaining the linearity of the system when the parasitic capacitance is maintained low.
Project description:In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator's anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator's phase noise, as predicted by our model.
Project description:A major challenge in biology is that genetically identical cells in the same environment can display gene expression stochasticity (noise), which contributes to bet-hedging, drug tolerance, and cell-fate switching. The magnitude and timescales of stochastic fluctuations can depend on the gene regulatory network. Currently, it is unclear how gene expression noise of specific networks impacts the evolution of drug resistance in mammalian cells. Answering this question requires adjusting network noise independently from mean expression. Here, we develop positive and negative feedback-based synthetic gene circuits to decouple noise from the mean for Puromycin resistance gene expression in Chinese Hamster Ovary cells. In low Puromycin concentrations, the high-noise, positive-feedback network delays long-term adaptation, whereas it facilitates adaptation under high Puromycin concentration. Accordingly, the low-noise, negative-feedback circuit can maintain resistance by acquiring mutations while the positive-feedback circuit remains mutation-free and regains drug sensitivity. These findings may have profound implications for chemotherapeutic inefficiency and cancer relapse.
Project description:The dynamical backaction from a periodically driven optical cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Here we study experimentally and theoretically new aspects of the backaction and the discrete time-translation symmetry of a driven system using a micromechanical resonator with two nonlinearly coupled vibrational modes with strongly differing frequencies and decay rates. We find self-sustained oscillations in both the low- and high-frequency modes. Their frequencies and amplitudes are determined by the nonlinearity, which also leads to bistability and hysteresis. The phase fluctuations of the two modes show near-perfect anti-correlation, a consequence of the discrete time-translation symmetry. Concurrently, the phase of each mode undergoes anomalous diffusion. The phase variance follows a power law time dependence, with an exponent determined by the 1/f-type resonator frequency noise. Our findings enable compensating for the fluctuations using a feedback scheme to achieve stable frequency downconversion.
Project description:Near-field optical techniques exploit light-matter interactions at small length scales for mechanical sensing and actuation of nanomechanical structures. Here, we study the optical interaction between two mechanical oscillators--a plasmonic nanofocusing probe-tip supported by a low frequency cantilever, and a high frequency nanomechanical resonator--and leverage their interaction for local detection of mechanical vibrations. The plasmonic nanofocusing probe provides a confined optical source to enhance the interaction between the two oscillators. Dynamic perturbation of the optical cavity between the probe-tip and the resonator leads to nonlinear modulation of the scattered light intensity at the sum and difference of their frequencies. This double-frequency demodulation scheme is explored to suppress unwanted background and to detect mechanical vibrations with a minimum detectable displacement sensitivity of 0.45 pm/Hz(1/2), which is limited by shot noise and electrical noise. We explore the demodulation scheme for imaging the bending vibration mode shape of the resonator with a lateral spatial resolution of 20 nm. We also demonstrate the time-resolved aspect of the local optical interaction by recording the ring-down vibrations of the resonator at frequencies of up to 129 MHz. The near-field optical technique is promising for studying dynamic mechanical processes in individual nanostructures.
Project description:Optical tweezers based on optical radiation pressure are widely used to manipulate nanoscale to microscale particles. This study demonstrates direct measurement of the optical force gradient distribution acting on a polystyrene (PS) microsphere using a carbon nanotube (CNT) mechanical resonator, where a PS microsphere with 3??m diameter is welded at the CNT tip using laser heating. With the CNT mechanical resonator with PS microsphere, we measured the distribution of optical force gradient with resolution near the thermal noise limit of 0.02?pN/?m in vacuum, in which condition enables us to high accuracy measurement using the CNT mechanical resonator because of reduced mechanical damping from surrounding fluid. The obtained force gradient and the force gradient distribution agree well with theoretical values calculated using Lorenz-Mie theory.
Project description:We realize a simple and robust optomechanical system with a multitude of long-lived (Q >?107) mechanical modes in a phononic-bandgap shielded membrane resonator. An optical mode of a compact Fabry-Perot resonator detects these modes' motion with a measurement rate (96 kHz) that exceeds the mechanical decoherence rates already at moderate cryogenic temperatures (10 K). Reaching this quantum regime entails, inter alia, quantum measurement backaction exceeding thermal forces and thus strong optomechanical quantum correlations. In particular, we observe ponderomotive squeezing of the output light mediated by a multitude of mechanical resonator modes, with quantum noise suppression up to -2.4 dB (-3.6 dB if corrected for detection losses) and bandwidths ?90 kHz. The multimode nature of the membrane and Fabry-Perot resonators will allow multimode entanglement involving electromagnetic, mechanical, and spin degrees of freedom.
Project description:Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultralight resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultrasensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to ?150 nm. These advances in detection and fabrication allow us to reach [Formula: see text] displacement sensitivity. Thermal vibrations cooled cryogenically at 300 mK are detected with a signal-to-noise ratio as high as 17 dB. We demonstrate [Formula: see text] force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is an important step toward imaging individual nuclear spins and studying the coupling between mechanical vibrations and electrons in different quantum electron transport regimes.
Project description:We experimentally demonstrate and theoretically analyze high Q-factor (~107) capillary-based optical ring resonators for non-contact detection of air-coupled ultrasound. Noise equivalent pressures in air as low as 215?mPa/?Hz and 41?mPa/?Hz at 50?kHz and 800?kHz in air, respectively, are achieved. Furthermore, non-contact detection of air-coupled photoacoustic pulses optically generated from a 200?nm thick Chromium film is demonstrated. The interaction of an acoustic pulse and the mechanical mode of the ring resonator is also studied. Significant improvement in detection bandwidth is demonstrated by encapsulating the ring resonator in a damping medium. Our work will enable compact and sensitive ultrasound detection in many applications, such as air-coupled non-destructive ultrasound testing, photoacoustic imaging, and remote sensing. It will also provide a model system for fundamental study of the mechanical modes in the ring resonator.
Project description:The Lombard effect, an involuntary rise in call amplitude in response to masking ambient noise, represents one of the most efficient mechanisms to optimize signal-to-noise ratio. The Lombard effect occurs in birds and mammals, including humans, and is often associated with several other vocal changes, such as call frequency and duration. Most studies, however, have focused on noise-dependent changes in call amplitude. It is therefore still largely unknown how the adaptive changes in call amplitude relate to associated vocal changes such as frequency shifts, how the underlying mechanisms are linked, and if auditory feedback from the changing vocal output is needed. Here, we examined the Lombard effect and the associated changes in call frequency in a highly vocal mammal, echolocating horseshoe bats. We analyzed how bandpass-filtered noise (BFN; bandwidth 20 kHz) affected their echolocation behavior when BFN was centered on different frequencies within their hearing range. Call amplitudes increased only when BFN was centered on the dominant frequency component of the bats' calls. In contrast, call frequencies increased for all but one BFN center frequency tested. Both amplitude and frequency rises were extremely fast and occurred in the first call uttered after noise onset, suggesting that no auditory feedback was required. The different effects that varying the BFN center frequency had on amplitude and frequency rises indicate different neural circuits and/or mechanisms underlying these changes.