Vibrational high-harmonics and period-doubling bifurcation probed by time-resolved electron diffraction

Abstract

Nanoscale mechanical oscillators exhibit a plethora of nonlinear phenomena with promising applications for the sensing and clocking of processes down to atomic length scales. Oscillator dynamics are typically probed by electrical or optical means, providing only limited access to the spatial profile of the oscillator motion. Here, we introduce event-based convergent beam electron diffraction for the spatio-temporal mapping of nanoscale mechanical resonators in ultrafast transmission electron microscopy. Employing an optically driven silicon membrane resonator at various driving strengths, we gain access to nonlinear processes with increasing complexity, ranging from a simple Duffing behavior to nonlinear multimode coupling and period-doubling bifurcations. The time-resolved diffraction probing approach supports a spatial resolution down to a few nanometers and a temporal resolution of 5 ns and provides quantitative information on the local membrane bending. Because the diffraction signal responds to local displacement gradients, which become more pronounced as resonators shrink, this approach offers a route toward probing nonlinear nanomechanics at the atomic scale.