Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators

Abstract

We propose a novel method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay between the parametric drive, external force and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the atto-newton range.

Quantum Transducer Using a Parametric Driven-Dissipative Phase Transition

“…This transition is the quantum manifestation of the classical parametric symmetry breaking studied in Refs. [26][27][28]. Here, we find that at low and intermediate photon numbers this switching persists as a sharp crossover.…”

“…1(b). The origin of this effect can be traced back to the bifurcation physics in the classical limit of the model [26][27][28].…”

Optically levitated nanoparticle as a model system for stochastic bistable dynamics

“…This could be implemented by electrically coupling a charged particle29 to an external field12 or via scattering force from a weakly focused beam and is the subject of future work. The unprecedented performances demonstrated could enable the realization of novel ultra-sensitive threshold sensors, capable of detecting tiny perturbations via a state change in the system, or other detection schemes based on nonlinear nanomechanical resonators34. Likewise, a high-Q parametrically driven Duffing resonator could boost the state-of-the-art in nanomechanical memory elements3031 introducing additional bits by simultaneous manipulation of the orthogonal oscillation modes32.…”

“…To overcome this limitation, modern nanotechnology requires new sensing schemes that take nonlinearities into account and even benefit from them2. Many of the proposed solutions operate inside an instability region34 or close to a bifurcation point56, where the system ideally becomes infinitely sensitive. Others exploit fluctuations of noisy environments to trigger stochastic resonances7 that amplify weak harmonic signals8910.…”

Direct and parametric synchronization of a graphene self-oscillator

“…23 The demonstrated phase oscillations are expected to occur naturally in entrained graphene oscillators, since they are easily driven into the nonlinear regime, 24 and their dependence on the drive strength and detuning with respect to the coupled reference oscillator may be used to further characterize the devices, or in applications that require the sensing of externally applied forces or masses. 25 In summary, the current work demonstrates that graphene self-oscillators can be synchronized to both a direct and a parametric external signal at low temperatures. It is shown that achieving entrainment can significantly reduce the width of the oscillation peak, thus allowing a reduction of oscillator frequency fluctuations to produce stable nanoscale oscillating motion.…”