Low fluctuations in a heated µ-resonator: first steps toward thermal noise engineering

The Fluctuation-Dissipation Theorem (FDT) is a cardinal tool of Statistical Physics. This relation yields to the Equipartition Principle, thanks to which we can link the fluctuations of an observable with the temperature of the system. In non-equilibrium situations however, such relations between fluctuations and response are not granted, and a higher noise is usually expected with respect to an equilibrium state. In this presentation, we show that the opposite phenomenon can also be experimentally observed: fluctuations smaller than in equilibrium!

In our experiment an atomic force microscope (AFM) µ-cantilever in vacuum is heated at its extremity with a laser. The heat flux sets the system in a Non-Equilibrium Steady State (NESS). We measure the thermal noise driven deflection d and quantify the amplitude of the fluctuations with an effective temperature T_eff extending the equipartition principle:

½ k_BT_eff = ½ k_n <d_n²>

with k_B the Boltzmann constant, k_n the mechanical mode stiffnesses and <d_n²> the mean square deflections. We observe a strong deficit of thermal noise with respect to the cantilever average temperature.

We will explain how a generalized FDT including the temperature field can account for these observations, when dissipation is not uniform. Further experimental evidence of the validity of this framework, down to cryogenic temperatures, will conclude the presentation. Our approach paves the way for thermal noise engineering: it can be used as a tool to probe the spatial distribution of dissipation, or on the contrary to tune the thermal noise amplitude and spectra by choosing an adequate damping field.