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Thermo-optical bistability in silicon micro-cantilevers

Basile Pottier and Ludovic Bellon, SciPost Phys. 10, 120 (2021)

[Article] doi: 10.21468/SciPostPhys.10.5.120
[Data set] doi: 10.5281/zenodo.4703793

We report a thermo-optical bistability observed in silicon micro-cantilevers irradiated by a laser beam with mW powers: reflectivity, transmissivity, absorption, and temperature can change by a factor of two between two stable states for the same input power. The temperature dependency of the absorption at the origin of the bistability results from interferences between internal reflections in the cantilever thickness, acting as a lossy Fabry-Pérot cavity. A theoretical model describing the thermo-optical coupling is presented. The experimental results obtained for silicon cantilevers irradiated in vacuum at two different visible wavelengths are in quantitative agreement with the predictions of this model.

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Resonance frequency shift of silicon cantilevers heated from 300 K up to the melting point

Basile Pottier, Felipe Aguilar, Mickaël Geitner, Francisco Melo, Ludovic Bellon, Journal of Applied Physics 129, 184503 (2021) – Editor’s Pick

[Article] doi: 10.1063/5.0040733
[Data set] doi: 10.5281/zenodo.4629591

When heated, micro-resonators present a shift of their resonance frequencies. We study specifically silicon cantilevers heated locally by laser absorption, and evaluate theoretically and experimentally their temperature profile and its interplay with the mechanical resonances. We include both elasticity and geometry temperature dependency, showing that the latter can account for 20% of the observed shift for the first flexural mode. The temperature profile description takes into account thermal clamping conditions, radiation at high temperature, and lower conductivity than bulk silicon due to phonon confinement. Thanks to a space-power equivalence in the heat equation, scanning the heating point along the cantilever directly reveals the temperature profile. Finally, frequency shift measurement can be used to infer the temperature field with a few percent precision.

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Information and thermodynamics: fast and precise approach to Landauer’s bound in an underdamped micro-mechanical oscillator

 Salambô Dago, Jorge Pereda, Nicolas Barros, Sergio Ciliberto, and
 Ludovic Bellon, Phys. Rev. Lett. 126, 170601 (2021)

[Article] doi: 10.1103/PhysRevLett.126.170601
[Data set] doi:10.5281/zenodo.4626559

The Landauer principle states that at least kBT ln 2 of energy is required to erase a 1-bit memory, with kBT the thermal energy of the system. We study the effects of inertia on this bound using as one-bit memory an underdamped micro-mechanical oscillator confined in a double-well potential created by a feedback loop. The potential barrier is precisely tunable in the few kBT range. We measure, within the stochastic thermodynamic framework, the work and the heat of the erasure protocol. We demonstrate experimentally and theoretically that, in this underdamped system, the Landauer bound is reached with a 1 % uncertainty, with protocols as short as 100 ms.

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The left panel displays the position of the wells and of the threshold between them as a function of time, with two experimental trajectories superposed. The right panel shows the trajectories as small dots moving inside the potential while the information (their initial position) is erased.
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Engineered Swift Equilibration of brownian particles: consequences of hydrodynamic coupling

S. Dago, B. Besga , R. Mothe, D. Guéry-Odelin, E. Trizac , A. Petrosyan, L. Bellon, S. Ciliberto, SciPost Phys. 9, 064 (2020)

[Article] doi: 10.21468/SciPostPhys.9.5.064
[Data set] doi:10.5281/zenodo.4242922

We present a detailed theoretical and experimental analysis of Engineered Swift Equilibration (ESE) protocols applied to two hydrodynamically coupled colloids in optical traps. The second particle disturbs slightly (10% at most) the response to an ESE compression applied to a single particle. This effect is quantitatively explained by a model of hydrodynamic coupling. Then we design a coupled ESE protocol for the two particles, allowing the perfect control of one target particle while the second is enslaved to the first. The calibration errors and the limitations of the model are finally discussed in detail.

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Large colloidal probes for atomic force microscopy: Fabrication and calibration issues

Matteo Chighizola, Luca Puricelli, Ludovic Bellon, Alessandro Podestà, Journal of Molecular Recognition  e2849 (2020)

doi: 10.1002/jmr.2879

Atomic force microscopy (AFM) is a powerful tool to investigate interaction forces at the micro and nanoscale. Cantilever stiffness, dimensions and geometry of the tip can be chosen according to the requirements of the specific application, in terms of spatial resolution and force sensitivity. Colloidal probes (CPs), obtained by attaching a spherical particle to a tipless (TL) cantilever, offer several advantages for accurate force measurements: tunable and well-characterisable radius; higher averaging capa- bilities (at the expense of spatial resolution) and sensitivity to weak interactions; a well-defined interaction geometry (sphere on flat), which allows accurate and reliable data fitting by means of analytical models. The dynamics of standard AFM probes has been widely investigated, and protocols have been developed for the calibration of the cantilever spring constant. Nevertheless, the dynamics of CPs, and in particular of large CPs, with radius well above 10 μm and mass comparable, or larger, than the cantilever mass, is at present still poorly characterized. Here we describe the fabrica- tion and calibration of (large) CPs. We describe and discuss the peculiar dynamical behaviour of CPs, and present an alternative protocol for the accurate calibration of the spring constant.

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Thermal fluctuations in an out-of-equilibrium system

Alex Fontana, , PhD Thesis, Université de Lyon (2020)

hal: tel-03325266

The goal of this thesis is a theoretical and experimental study of the non-equilibrium prop- erties of thermal noise, with the purpose of understanding whether we can extend certain statistical physics tools to non-equilibrium systems. In particular, we show how we can ex- tend the Fluctuation-Dissipation Theorem (FDT) to systems subjected to a stationary spatial temperature profile, thus in a Non-Equilibrium Steady State (NESS). Since thermal fluctua- tions cannot be described by a single temperature through the Equipartition Theorem, we show how they are then prescribed by the temperature profile weighted by the local me- chanical dissipation.

We test this prediction in various silicon micro-cantilevers, creating a strong temperature difference of hundreds of degrees between the base and the tip. In one experiment in par- ticular, the base is held at cryogenic temperatures, thus placing the cantilever as far from equilibrium as physically possible. We then measure the thermal fluctuations of the sample alongside their dissipation, showing how these two quantities are perfectly construed by our theoretical framework. The same is also verified for a macroscopic aluminum oscillator. A careful analysis of the statistical properties of thermal noise finally demonstrates that our results are robust, and a sorting algorithm of the experimental data is proposed. A simple method to estimate the uncertainties of the measurements is finally given.

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Calibrated force measurement in Atomic Force Microscopy using the Transient Fluctuation Theorem

Samuel Albert, Aubin Archambault, Artyom Petrosyan, Caroline Crauste-Thibierge, Ludovic Bellon, Sergio Ciliberto, EPL 131, 10008 (2020)

doi: 10.1209/0295-5075/131/10008

The Transient Fluctuation Theorem is used to calibrate an Atomic Force Microscope by measuring the fluctuations of the work performed by a time dependent force applied between a colloïdal probe and the surface. From this measure one can easily extract the value of the interaction force and the relevant parameters of the cantilever. The results of this analysis are compared with those obtained by standard calibration methods. 

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Extended equipartition in a mechanical system subject to a heat flow: the case of localised dissipation

Alex Fontana, Richard Pedurand, Ludovic Bellon, J. Stat. Mech. 073206 (2020)

doi:10.1088/1742-5468/ab97b1

Statistical physics in equilibrium grants us one of its most powerful tools: the equipartition principle. It states that the degrees of freedom of a mechanical system act as a thermometer: temperature is equal to the mean variance of their oscillations divided by their stiffness. However, when a non-equilibrium state is considered, this principle is no longer valid. In our experiment, we study the fluctuations of a micro-cantilever subject to a strong heat flow, which creates a highly non-uniform local temperature. We measure independently the temperature profile of the object and the temperature yielded from the mechanical thermometers, thus testing the validity of the equipartition principle out of equilibrium. We demonstrate how the fluctuations of the most energetic degrees of freedom are equivalent to the temperature at the base of the cantilever, even when the average temperature is several hundreds of degrees higher. We then present a model based on the localised mechanical dissipation in the system to account for our results, which correspond to mechanical losses localised at the clamping position.

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Instrumentation for Thermal Noise Spectroscopy

Richard Pedurand, PhD Thesis, Université de Lyon (2019)

hal: tel-02612035

La résolution des interféromètres gravitationnels est limitée par le mouvement Brownien – ou bruit thermique – de leurs miroirs dans la partie centrale de leur bande de détection, entre 10Hz et 1kHz. La répartition en fréquence de ce bruit thermique est dictée par les mécanismes de dissipation d’énergie mécanique à l’origine de cette vibration aléatoire, en accord avec le théorème fluctuation-dissipation. Cette dissipation provient principalement des revêtements optiques déposés sur les miroirs pour leur donner leur réflectivité. Dans le but de réduire le bruit thermique, une nouvelle génération de détecteurs d’ondes gravitationnelles employant des miroirs refroidis à température cryogénique a été proposée. Le développement de nouveaux matériaux optiques en couche mince à faible dissipation mécanique, opérant à la fois à température ambiante et température cryogénique, demande donc de nouveaux outils expérimentaux. L’objet principal de cette thèse est la construction d’un nouvel instrument, le CryoQPDI, qui consiste en l’association d’un interféromètre haute résolution et d’un cryostat basé sur un refroidisseur pulse tube. Il est capable de mesurer directement le mouvement Brownien d’un microlevier entre 300K et 7K. En combinant des mesures effectuées sur un microlevier avant et après le dépôt d’une couche mince, il est possible de caractériser la dissipation mécanique interne de cette couche mince. Cet instrument participera ainsi à l’optimisation des revêtements optiques des futurs interféromètres gravitationnels, dans le but de minimiser les nuisances dues au bruit thermique

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