Classical decoherence in a nanomechanical resonator

Abstract

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. 1 2 then leads to the definition of a pure dephasing rate G f [6].While the reported T 1 and T 2 for a particular qubit are often significantly different [7], such a difference in a nanomechanical resonator is still rare in the literature: usually mechanical systems seem to experience frequency fluctuations small compared to dissipation mechanisms, and do not exhibit visible spectral broadening due to dephasing [8][9][10][11]. Nonetheless, pure dephasing has been observed in [16][17][18]20]. But direct comparisons between time-domain (T 1 ) and frequency-domain (T 2 ) are still rare: thus, the second and main reason for the scarcity of experimental studies on mechanical decoherence is a lack of data combining these techniques. To our OPEN ACCESS RECEIVED

Nonlinear frequency transduction of nanomechanical Brownian motion

“…The gates, used in other works (e.g. [33]) are not connected in the present work. Keeping them floating or grounded is found to be equivalent.…”

“…This is the case of Ref. [33] for instance. Note that with an artificial telegraph frequency noise generated by a gate electrode, in Ref.…”

“…1 c). In the latter case, the fluctuations are slow enough so that the full range of frequency fluctuations can be explored by the x 0 n sine-wave response [33,49]: there is a large asymmetric broadening, which reflects the actual distribution of frequency fluctuations (bottom-right in Fig. 1 c).…”

“…In the "motional narrowing" limit, indeed the first order effect is a global frequency shift proportional to ∆x 2 n . On the other hand, in the "inhomogeneous broadening" range the main feature is the asymmetric broadening which is nothing but the image of the frequency distribution (inhomogeneity in time-domain, as opposed to positiondomain for NMR [33]). Further technical discussions of these two limits can be found in S.M.…”

“…But in the first place, it is also a fundamental research goal: the measured frequency noise in actual devices is much larger than all expectations [22,[24][25][26], demonstrating even non-linear features for carbon-based systems [27,28]. Thus, attempts have been made to model noise sources [29,30], or to create model experiments experimentally demonstrating the underlying mechanisms [19,31,33,34].…”