Thermal noise of a cryocooled silicon cantilever locally heated up to its melting point

Abstract

The Fluctuation-Dissipation Theorem (FDT) is a powerful tool to estimate the thermal noise of physical systems in equilibrium. In general however, thermal equilibrium is an approximation, or cannot be assumed at all. A more general formulation of the FDT is then needed to describe the behavior of the fluctuations. In our experiment we study a micro-cantilever brought out-ofequilibrium by a strong heat flux generated by the absorption of the light of a laser. While the base is kept at cryogenic temperatures, the tip is heated up to the melting point, thus creating the highest temperature difference the system can sustain. We independently estimate the temperature profile of the cantilever and its mechanical fluctuations, as well as its dissipation. We then demonstrate how the thermal fluctuations of all the observed degrees of freedom, though increasing with the heat flux, are much lower than what is expected from the average temperature of the system. We interpret these results thanks to a minimal extension of the FDT: this dearth of thermal noise arises from a dissipation shared between clamping losses and distributed damping.

On the link between mechanics and thermal properties: mechanothermics

“…for which 2U 0 sin(ωt) factorizes out in equations ( 11)- (13). Similarly form equation ( 17) one obtains:…”

“…This situation should be possible to demonstrate experimentally, using high-order modes, with not too large quality factors. The marginal situation ω {η} ̸ = ω {η ′ } should however be commented, for practical reasons: this is the situation encountered with the modes that are easily at reach for the experimentalist [11][12][13]22]. In this case, the model leads to:…”

“…In this case, measured properties (local temperature along the beam, mode spectrum) do depend on the heat flow imposed in the structure. The situation is thus much more complex than for the in-equilibrium case (where everything is defined through the single parameter T), and heat flows are usually extremely large in the experimental realizations, which adds another degree of complexity [13]. New thermodynamics concepts that describe the steady-state have to be developed beyond standard equipartition and fluctuation-dissipation theorems [11,13].…”

Mesoscopic Quantum Thermo-mechanics: a new frontier of experimental physics

“…Ideally, under small thermal gradients ensuring that it represents only a (vanishingly) small perturbation of the equilibrium condition [31]. Such experiments can be performed with the monitoring of mechanical modes' effective temperatures while a heat current is imposed, similarly to what is done using cantilevers subject to lasers [112]. From the mode temperature's knowledge, one can built a thermal model of the system at hand.…”

“…From the mode temperature's knowledge, one can built a thermal model of the system at hand. This can also be performed with systems (strongly) out-of-equilibrium, and requires then a completely new conceptual approach (a generalized version of the fluctuation-dissipation theorem) [112]; this is not in the scope of our discussion here. In principle, this could be adapted to the microwave/microKelvin platform we describe here, down to the quantum regime.…”