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

Abstract

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.

5 pages, minor changes

References in corpus (21)

• A tunable carbon nanotube electromechanical oscillator
• Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
• Circuit cavity electromechanics in the strong coupling regime
• Bidirectional and efficient conversion between microwave and optical light
• Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes
• State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime
• Measurement of the quantum zero-point motion of a nanomechanical resonator
• Strong coupling between single-electron tunneling and nano-mechanical motion
• Coherent phonon manipulation in coupled mechanical resonators
• Carbon Nanotubes as Nanoelectromechanical Systems
• Nonlinear modal interactions in clamped-clamped mechanical resonators
• Nonlinear Dynamics and Chaos in Two Coupled Nanomechanical Resonators
• Strong coupling between mechanical modes in a nanotube resonator
• Non-adiabatic dynamics of two strongly coupled nanomechanical resonator modes
• Classical to Quantum Transition of a Driven Nonlinear Nanomechanical Resonator
• Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
• Entropic Spectral Broadening in Carbon Nanotube Resonators
• Probing the charge of a quantum dot with a nanomechanical resonator
• Strong feedback and current noise in nanoelectromechanical systems
• Tension-induced non-linearities of flexural modes in nanomechanical resonators
• Nonlinear-dissipation-induced Entanglement of Coupled Nonlinear Oscillators