Dynamics of coupled vibration modes in a quantum non-linear mechanical resonator

G. Labadze, M. Dukalski, Ya M. Blanter*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
22 Downloads (Pure)


We investigate the behaviour of two non-linearly coupled flexural modes of a doubly clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven mode is reminiscent of that of a parametrically driven linear oscillator: it exhibits a threshold behavior, with the amplitude of this mode below the threshold being exactly zero. Quantum-mechanically, we were able to access the dynamics of this mode below the classical parametric threshold. We show that whereas the mean displacement of this mode is still zero, the mean squared displacement is finite and at the threshold corresponds to the occupation number of 1/2. This finite displacement of the non-driven mode can serve as an experimentally verifiable quantum signature of quantum motion.

Original languageEnglish
Pages (from-to)181-186
Number of pages6
JournalPhysica E: Low-Dimensional Systems and Nanostructures
Publication statusPublished - 2016

Bibliographical note

Accepted Author Manuscript


  • Nano- and opto-mechanics
  • Non-linear systems
  • Parametric resonance
  • Quantum effects


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