Classical to quantum transition of a driven nonlinear nanomechanical resonator

TL;DR

This paper investigates how nonlinear nanoresonators transition from classical to quantum behavior, providing theoretical predictions and signatures for experimental observation in nanoelectromechanical systems.

Contribution

It extends previous work by analyzing quantum transition signatures in nonlinear nanoresonators coupled to heat baths at various temperatures.

Findings

Numerical solutions reveal first quantum corrections to classical dynamics.

Nonlinearities enable probing quantum behavior with near-future technology.

Signatures of quantum transition are identified for experimental detection.

Abstract

Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold, and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale $\hbar\Omega$ becomes comparable to that of the ambient thermal energy $k_{B}T$. Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and test some of the basic principles of quantum mechanics. Here we expand and elaborate on our recent suggestion [PRL 99 (2007) 040404] to exploit the nonlinear nature of a nanoresonator in order to observe its transition into the quantum regime. We study this transition for an isolated resonator, as well as one that is coupled to a heat bath at either zero or finite temperature. We argue that by exploiting nonlinearities, quantum dynamics can be probed using technology that is almost within reach. Numerical solutions of the equations of motion display the first quantum corrections to classical dynamics that appear as the classical-to-quantum transition occurs. This provides practical signatures to look for in future experiments with NEMS resonators.