Classical decoherence in a nanomechanical resonator

Decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to electromagnetic degrees of freedom. But decoherence can also be thought of in a purely classical context, as the loss of phase coherence in the classical phase space. Indeed the bridge between quantum and classical physics is under intense investigation, using, in particular, classical nanomechanical analogues of quantum phenomena. In the present work, by separating pure dephasing from dissipation, we quantitatively model the classical decoherence of a mechanical resonator: through the experimental control of frequency fluctuations, we engineer artificial dephasing. Building on the fruitful analogy introduced between spins/quantum bits and nanomechanical modes, we report on the methods available to define pure dephasing in these systems, while demonstrating the intrinsic almost-ideal properties of silicon nitride beams. These experimental and theoretical results, at the boundary between classical nanomechanics and quantum information fields, are prerequisite in the understanding of decoherence processes in mechanical devices, both classical and quantum. Introduction and background. Frequency noise in nano-mechanical systems (NEMS) is a topic intensely studied these last years, for both fundamental and practical reasons (references [ 13 – 23 ] of the paper): the frequency fluctuations can have an intrinsic origin linked to essential material properties, but they also limit the resolution of actual devices used as sensors. Recently, the Delft group proposed to analyze the effects of this noise on the dynamics of NEMS within a framework analogous to one of Nuclear Magnetic Resonance (NMR), or quantum bits (2014 Nat. Commun. 5 5819 ). Main results. Building on the analogy, in this paper we engineer frequency noise to study its impact on nano-resonators. We present a model experiment, with the full theory enabling the fit of data without free parameters. The effect of frequency noise is analogous to 'pure dephasing' in quantum bits, even though the device is a classical harmonic oscillator. As such, the analogy is very informative and interrogates the crossover between classical and quantum physics; it enters the class of 'classical analogues of quantum phenomena' studied in recent model nano-mechanical experiments (e.g. reference [ 10 ]). Wider implications. This is a broad topic that is of interest to many areas of science, far beyond NEMS and NMR. For the focused audience, we present the methods to quantitatively describe this 'classical pure dephasing' of NEMS, which can be used e.g. with carbon-based systems. As a conclusion, our results are a new tool for the understanding of classical decoherence in nano-resonators, and a pre-requisite for future experiments on quantum NEMS.