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

TL;DR

This paper explores the classical and quantum dynamics of two coupled vibrational modes in a nanomechanical resonator, revealing quantum signatures such as finite displacement below classical thresholds.

Contribution

It provides the first analysis of quantum behavior of a non-driven mode below the classical parametric threshold in a coupled nanomechanical system.

Findings

Classical mode exhibits threshold behavior similar to a parametric oscillator.

Quantum mode has zero mean displacement but finite mean squared displacement below threshold.

Quantum signature identified as finite displacement at occupation number 1/2.

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.