arXiv subjects

Ludovic Bellon

Publications and source records attributed to Ludovic Bellon.

At least 37 records · Page 2Linked to original sources

arXiv2023

Accelerating the heat diffusion: fast thermal relaxation of a microcantilever

In most systems, thermal diffusion is intrinsically slow with respect to mechanical relaxation. We devise here a generic approach to accelerate the relaxation of the temperature field of a 1D object, in order to beat the mechanical time scales. This approach is applied to a micro-meter sized silicon cantilever, locally heated by a laser beam. A tailored driving protocol for the laser power is derived to quickly reach the thermal stationary state. The model is implemented experimentally yielding a significant acceleration of the thermal relaxation, up to a factor 30. An excellent agreement with the theoretical predictions is reported. This strategy allows a thermal steady state to be reached significantly faster than the natural mechanical relaxation.

physics.app-ph↗

arXiv2023

Linking fluctuation and dissipation in spatially extended out-of-equilibrium systems

For systems in equilibrium at a temperature $T$, thermal noise and energy damping are related to $T$ through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out of equilibrium steady state: a microcantilever subject to a constant heat flux. The resulting thermal profile in this spatially extended system interplays with the local energy dissipation field to prescribe the amplitude of mechanical fluctuations. Using three samples with different damping profiles (localized or distributed), we probe this approach and experimentally demonstrate the link between fluctuations and dissipation. The thermal noise can therefore be predicted a priori from the measurement of the dissipation as a function of the maximum temperature of the micro-oscillator.

cond-mat.stat-mech↗

arXiv2022

Harmonic calibration of quadrature phase interferometry

The two output signals of quadrature phase interferometers allow to benefit both from the high sensitivity of interferometry (working inside a fringe) and from an extended input range (counting fringes). Their calibration to reach a linear output is traditionally performed using Heydemann's correction, which involves fitting one output versus the other by an ellipse. Here we present two alternative methods based on the linear response of the measurement to a sinusoidal input in time, which enables a direct calibration with an excellent linearity. A ten fold improvement with respect to the usual technique is demonstrated on an optical interferometer measuring the deflection of scanning force microscopy cantilevers.

physics.ins-det↗

arXiv2022

Virtual double-well potential for an underdamped oscillator created by a feedback loop

Virtual potentials are a very elegant, precise and flexible tool to manipulate small systems and explore fundamental questions in stochastic thermodynamics. In particular double-well potentials have applications in information processing, such as the demonstration of Landauer's principle. Nevertheless, virtual double-well potentials had never been implemented in underdamped systems. In this article, we detail how to face the experimental challenge of creating a feedback loop for an underdamped system (exploring its potential energy landscape much faster than its over-damped counterpart), in order to build a tunable virtual double-well potential. To properly describe the system behavior in the feedback trap, we express the switching time in the double-well for all barrier heights, combining for the first time Kramer's description, valid at high barriers, with an adjusted model for lower ones. We show that a small hysteresis or delay of the feedback loop in the switches between the two wells results in a modified velocity distribution, interpreted as a cooling of the kinetic temperature of the system. We successfully address all issues to create experimentally a virtual potential that is statistically indistinguishable from a physical one, with a tunable barrier height and energy step between the two wells.

cond-mat.stat-mech↗

arXiv2022

Dynamics of information erasure and extension of Landauer's bound to fast processes

Using a double-well potential as a physical memory, we study with experiments and numerical simulations the energy exchanges during erasure processes, and model quantitatively the cost of fast operation. Within the stochastic thermodynamics framework we find the origins of the overhead to Landauer's Bound required for fast operations: in the overdamped regime this term mainly comes from the dissipation, while in the underdamped regime it stems from the heating of the memory. Indeed, the system is thermalized with its environment at all time during quasi-static protocols, but for fast ones, the inefficient heat transfer to the thermostat is delayed with respect to the work influx, resulting in a transient temperature rise. The warming, quantitatively described by a comprehensive statistical physics description of the erasure process, is noticeable on both the kinetic and potential energy: they no longer comply with equipartition. The mean work and heat to erase the information therefore increase accordingly. They are both bounded by an effective Landauer's limit $k_B T_{eff} \ln{2}$, where $T_{eff}$ is a weighted average of the actual temperature of the memory during the process.

cond-mat.stat-mech↗

arXiv2021

Force microscopy cantilevers locally heated in a fluid: temperature fields and effects on the dynamics

Atomic force microscopy cantilevers are often, intentionally or not, heated at their extremity. We describe a model to compute the resulting temperature field in the cantilever and in the surrounding fluid on a wide temperature range. In air and for common geometries, the heat fluxes in the cantilever and to the environment are of comparable magnitude. We then infer how the fluid-structure interaction is modified due to heating, and predict the induced changes in the dynamics of the system. In particular, we describe how the resonance frequencies of the cantilever shift with a temperature increase due to two competing processes: softening of the cantilever, and decrease of the fluid inertial effects. Our models are illustrated by experiments on a set of cantilevers spanning the relevant geometries to explore the relative importance of both effects.

cond-mat.stat-mech↗

arXiv2021

Thermal noise of a cryo-cooled silicon cantilever locally heated up to its melting point

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.

cond-mat.stat-mech↗

arXiv2021

Silicon cantilevers locally heated from 300K up to the melting point: temperature profile measurement from their resonances frequency shift

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 present a enhanced version of our earlier model [F. Aguilar Sandoval et al., J. Appl. Phys. 117, 234503 (2015)] including 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.

cond-mat.mtrl-sci↗

arXiv2021

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

The Landauer principle states that at least $k_B T \ln 2$ of energy is required to erase a 1-bit memory, with $k_B T$ 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 $k_B T$ 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.

cond-mat.stat-mech↗

arXiv2021

Thermo-optical bistability in silicon micro-cantilevers

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.

physics.optics↗

arXiv2020

Engineered Swift Equilibration of brownian particles: consequences of hydrodynamic coupling

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.

cond-mat.stat-mech↗

arXiv2020

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

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 collo{ï}dal 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. a) present adress: ISIS, Univ.

cond-mat.mes-hall↗

arXiv2020

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

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.

cond-mat.stat-mech↗

arXiv2019

Extended Nyquist formula for a resistance subject to a heat flow

The Nyquist formula quantifies the thermal noise driven fluctuations of voltage across a resistance in equilibrium. We deal here with the case of a resistance driven out of equilibrium by putting it in contact with two thermostats at different temperatures. We reach a non-equilibrium steady state where a heat flux is flowing through the resistance. Our measurements demonstrate anyway that a simple extension of the Nyquist formula to the non uniform temperature field describes with an excellent precision the thermal noise. For a metallic ohmic material, the fluctuations are actually equivalent to those of a resistance in equilibrium with a single thermostat at the mean temperature between the hot and cold sources.

cond-mat.stat-mech↗

arXiv2017

Low thermal fluctuations in a system heated out of equilibrium

We study the mechanical fluctuations of a micrometer sized silicon cantilever subjected to a strong heat flow, thus having a highly non-uniform local temperature. In this non-equilibrium steady state, we show that fluctuations are equivalent to the thermal noise of a cantilever at equilibrium around room temperature, while its mean local temperature is several hundred of degrees higher. Changing the mechanical dissipation by adding a coating to the cantilever, we recover the expected rise of fluctuations with the mean temperature. Our work demonstrates that inhomogeneous dissipation mechanisms can decouple the amplitude of thermal fluctuations from the average temperature. This property could be useful to understand out-of-equilibrium fluctuating systems, or to engineer low noise instruments.

cond-mat.stat-mech↗

arXiv2017

Dynamic stiffness of the contact between a carbon nanotube and a flat substrate in a peeling geometry

We study the physics of adhesion and the contact mechanics at the nanoscale with a peeling experiment of a carbon nanotube on a flat substrate. Using an interferometric atomic force microscope and an extended force modulation protocol, we investigate the frequency response of the stiffness of the nano-contact from DC to 20 kHz. We show that this dynamic stiffness is only weakly frequency dependent, increasing by a factor 2 when the frequency grows by 3 orders of magnitude. Such behavior may be the signature of amorphous relaxations during the mechanical solicitation at the nano-scale.

cond-mat.mtrl-sci↗

arXiv2017

"Noiseless" thermal noise measurement of atomic force microscopy cantilevers

When measuring quadratic values representative of random fluctuations, such as the thermal noise of Atomic Force Microscopy (AFM) cantilevers, the background measurement noise cannot be averaged to zero. We present a signal processing method that allows to get rid of this limitation using the ubiquitous optical beam deflection sensor of standard AFMs. We demonstrate a two orders of magnitude enhancement of the signal to noise ratio in our experiment, allowing the calibration of stiff cantilevers or easy identification of higher order modes from thermal noise measurements.

physics.ins-det↗

arXiv2015

High Resolution Viscosity Measurement by Thermal Noise Detection

An interferometric method is implemented in order to accurately assess the thermal fluctuations of a micro-cantilever sensor in liquid environments. The power spectrum density (PSD) of thermal fluctuations together with Sader's model of the cantilever allow for the indirect measurement of the liquid viscosity with good accuracy. The good quality of the deflection signal and the characteristic low noise of the instrument allow for the detection and corrections of drawbacks due to both the cantilever shape irregularities and the uncertainties on the position of the laser spot at the fluctuating end of the cantilever. Variation of viscosity below 0.03 mPa$\cdot$s was detected with the alternative to achieve measurements with a volume as low as 50 $μ$L.

cond-mat.soft↗