Frequency modulated self-oscillation and phase inertia in a synchronized nanowire mechanical resonator

Abstract

Synchronization has been reported for a wide range of self-oscillating systems. However, even though it has been predicted theoretically for several decades, the experimental realization of phase self-oscillation, sometimes called phase trapping, in the high driving regime has been studied only recently. We explored in detail the phase dynamics in a synchronized field emission SiC nanoelectromechanical system with intrinsic feedback. A richer variety of phase behavior has been unambiguously identified, implying phase modulation and inertia. This synchronization regime is expected to have implications for the comprehension of the dynamics of interacting self-oscillating networks and for the generation of frequency modulated signals at the nanoscale.S Online supplementary data available from stacks.iop.org/njp/16/083009/ mmedia

Quantum-coherent phase oscillations in synchronization

“…(3), leading to a second-order differential equation of the phase, δφ + Γδφ + Ω 2 δφ = 0 . Here, δφ = φ − φ ss describes phase deviations from the steady-state phase φ ss and [25,28]. Before we discuss results from our effective quantum model, we briefly review the relevant features of the corresponding classical "phase diagram" of synchronization, Fig.…”

Direct and parametric synchronization of a graphene self-oscillator

“…A more detailed picture of the oscillator phase is obtained by plotting the displacement signal on a slow (microseconds) time scale and a fast (nanoseconds) time scale. 3,10 Figure 2(a) shows such a plot for the freely running oscillator, where the phase diffuses after a few hundred microseconds. 16 In contrast, when the reference signal is applied (panel (b)), the phase is coherent during the measurement ($ 1 ms).…”

“…These oscillations are known as phase inertia. 10 To extract the frequency of the phase oscillations, a Lorentzian function is fitted to the PSD of the phase, as shown in the inset in Fig. 4(a).…”

“…Indeed, their strong nonlinearity, tunability, and convenient time scales make detailed experimental studies of synchronization possible, including the observation of features such as phase slipping, phase locking, phase inertia, and phase oscillation. 4,[7][8][9][10] Compared to top-down fabricated NEMS devices, graphene nanomechanical systems offer enhanced nonlinear response due to their extreme aspect ratio. This enables new experimental studies of parametric synchronization and phaseoscillation dynamics, which are the topics of this letter.…”

A Kuramoto Network in a Single Nonlinear Microelectromechanical Device

“…The ability to synchronize librators to an externally injected tone has yet to be explored, let alone the ability to mutually synchronize coupled librators and establish a network. This is not necessarily as straightforward as synchronization of oscillators [34][35][36][37][38], since the librators are centered around varying frequencies (the modal frequencies) with no special frequency ratios. And the synchronization is to take place via the quasi-dc strain tuning around a quasi-dc frequency ω quasi−dc as shown schematically in Figs.…”