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 becomes comparable with that of the ambient thermal energy kBT. 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 (Katz et al 2007 Phys. Rev. Lett. 99 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.
Highlights
Two differences between the quantum and classical distributions are evident, namely, the strong interference pattern which exists in the Wigner function even in the steady state, and the infinitely fine structure which develops in the classical distribution
For the case of an isolated resonator—which is less relevant for experiment, yet still interesting theoretically—we have confirmed that the quantum and classical evolutions are essentially different, and that the transition from one picture to the other does not take place in a simple manner
The non-analytic nature of the limit h → 0 appears in the form of strong quantum interference patterns in the Wigner function, describing the quantum evolution, which are never suppressed in the absence of coupling to an environment
Summary
This special focus issue of the New Journal of Physics is motivated by the growing interest in the study of “Mechanical Systems at the Quantum Limit”. The question arises whether quantum-mechanically the resonator can be driven into a superposition of the two possible steady-states of motion, or at least tunnel or switch between them at temperatures that are sufficiently low for thermal switching to be suppressed, but not necessarily so low to satisfy the constraint kBT ≪ hΩ for observing full-fledged quantum mechanics To answer this question we perform two separate calculations on the same Duffing resonator, viewing it once as a quantummechanical object and once as a classical object. If the environment is measured, the reduced density matrix depends on the outcome of the measurements, and the evolution is said to be conditioned on the observation results, as described for example by Habib et al [61] This type of evolution can yield effectively classical trajectories, and is called the strong form of QCT. We shall analyze the latter case, which requires more advanced tools of quantum measurement theory, in a future publication
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
