Resonant nonlinear response of a nanomechanical system with broken symmetry

Year: 2021

Authors: Ochs J.S., Rastelli G., Seitner M., Dykman M.I., Weig E.M.

Autors Affiliation: Department of Physics, University of Konstanz, Konstanz, 78457, Germany; INO-CNR BEC Center, Dipartimento di Fisica, Universita di Trento, Povo, 38123, Italy; Michigan State University, East Lansing, 48824, MI, United States; Department of Electrical and Computer Engineering, Technical University of Munich, Munich, 80333, Germany

Abstract: We study the response of a weakly damped vibrational mode of a nanostring resonator to a moderately strong resonant driving force. Because of the geometry of the experiment, the studied flexural vibrations lack inversion symmetry. As we show, this leads to a nontrivial dependence of the vibration amplitude on the force parameters. For a comparatively weak force, the response has the familiar Duffing form, but for a somewhat stronger force, it becomes significantly different. Concurrently there emerge vibrations at twice the drive frequency, a signature of the broken symmetry. Their amplitude and phase allow us to establish the cubic nonlinearity of the potential of the mode as the mechanism responsible for both observations. The developed theory goes beyond the standard rotating-wave approximation. It quantitatively describes the experiment and allows us to determine the nonlinearity parameters.


Volume: 104 (15)      Pages from: 155434-1  to: 155434-13

More Information: We are grateful to H. Yamaguchi for the discussion of the mechanisms of overtone generation. J.S.O. and E.M.W. gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 425217212 -SFB 1432, the European Union´s Horizon 2020 Research and Innovation Programme under Grant Agreement No 732894 (FET Proactive HOT), and the German Federal Ministry of Education and Research (Contract No. 13N14777) within the European QuantERA cofund project QuaSeRT. M.I.D. acknowledges support from the National Science Foundation, Grants No. DMR-1806473 and No. CMMI 1661618. M.I.D. is a senior fellow of the Zukunftskolleg of the University of Konstanz; he is grateful for the warm hospitality at the University of Konstanz where this work was started.
KeyWords: nanomechanics, nonlinear resonators
DOI: 10.1103/PhysRevB.104.155434