Fluctuations, nonlinear dynamics, and their interplay in nanomechanical resonators

Orateur : Olivier MAILLET (PhD, Néel)

Owing to tremendous progresses in nanofabrication over the last three decades, mechanical resonators have reached the nanometer scale. On the one hand, these nanomechanical systems can be thought of as very sensitive force probes down to the attonewton range, while realizations of the quantum ground state of a macroscopic mechanical degree of freedom have highlighted their potential as model systems for fundamental physics. One common feature of interest for both applied and fundamental purposes is their intrinsic nonlinearity, which is known to be important in some configurations such as doubly clamped nanobeams. This nonlinearity is of geometrical origin : as the mechanical motion grows bigger compared to the structure size, additional stress is generated in the beam, resulting in a change of the mechanical eigenfrequencies. This nonlinear behavior allows one to dispersively couple two mechanical modes, while being at the same time a good implementation of an anharmonic, so-called Duffing oscillator for a single mode. Simultaneously, a mechanical mode dissipatively coupled to a thermal bath experiences a stochastic Langevin force, resulting in fluctuations of its position. In this talk we will describe our measurements of nanofabricated nano-electro-mechanical systems (NEMS) with submicronic cross-dimensions down to helium temperatures in vacuum. A careful calibration scheme enabled us to know forces and displacements in real units with no free parameters. By feeding one mechanical mode with a white force noise we were able to artificially heat it to an effective temperature of our choice while keeping the whole structure in ideal measurement conditions. This way, the generic situation where one driven and detected cold mode is nonlinearly and dispersively coupled to a “hot” out-of-equilibrium mode with large thermal fluctuations could be experimentally addressed. We will describe how the combination of nonlinearities and thermal fluctuations resulted in complex dynamics arising from fluctuations of the mechanical eigenfrequency. Our results could be explained by a no-free-parameter model in the case of intermode coupling. We then addressed the cas e of intramode coupling, where the driven response of a mode is nonlinearly coupled to its own Brownian motion. In particular, we found this situation to be qualitatively and quantitatively different from the intermode case. Finally we will discuss some of the implications regarding e.g. the stability of oscillators or the extension of this study to the quantum regime.

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