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Logical and thermodynamical reversibility: optimized experimental implementation of the NOT operation

Salambô Dago and Ludovic Bellon, Phys. Rev. E 108, L022101

[Article] doi: 10.1103/PhysRevE.108.L022101
[Data set] doi: 10.5281/zenodo.8099300

The NOT operation is a reversible transformation acting on a 1-bit logical state, and should be achievable in a physically reversible manner at no energetic cost. We experimentally demonstrate a bit-flip protocol based on the momentum of an underdamped oscillator confined in a double well potential. The protocol is designed to be reversible in the ideal dissipationless case, and the thermodynamic work required is inversely proportional to the quality factor of the system. Our implementation demonstrates an energy dissipation significantly lower than the minimal cost of information processing in logically irreversible operations. It is moreover performed at high speed: a fully equilibrated final state is reached in only half a period of the oscillator. The results are supported by an analytical model that takes into account the presence of irreversibility. The Letter concludes with a discussion of optimization strategies.

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Accelerating the heat diffusion: Fast thermal relaxation of a microcantilever

Basile Pottier, Carlos Plata, Emmanuel Trizac, David Guéry-Odelin and Ludovic Bellon, Phys. Rev. Applied  19, 034072 (2023)

[Article] doi: 10.1103/PhysRevApplied.19.034072
[Data set] doi: 10.5281/zenodo.7669037

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 reach arbitrarily fast 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 to reach a thermal steady state significantly faster than the natural mechanical relaxation.

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

Alex Fontana and Ludovic Bellon, Physics. Rev. E 107, 034118 (2023)

[Article] doi: 10.1103/PhysRevE.107.034118
[Data set] doi: 10.5281/zenodo.7640707

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.

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Instrumentation pour la mesure diélectrique locale de films polymériques chargés de nanoparticules

Baptiste Ferrero, PhD Thesis, Université de Lyon (2023)

hal: tel-04056084

La dispersion d’oxydes métalliques au sein d’une matrice polymère permet de décupler la permittivité diélectrique de cette dernière tout en conservant ses propriétés mécaniques. Une compréhension fine des interactions entre les constituants est néanmoins nécessaire pour maîtriser la formulation et l’optimisation du matériau composite final.
Cette thèse porte sur la création d’un instrument permettant la caractérisation à l’échelle des nanoparticules de la réponse du matériau : un microscope à force atomique (AFM) pour réaliser une spectroscopie diélectrique locale. Cette méthode donnera accès à la dynamique microscopique des chaînes polymères en interaction avec les particules. L’instrument développé se distingue par sa grande précision, liée à une détection interférométrique de la déflexion de la sonde AFM et à un environnement très faible bruit, combinant cage de Faraday, chambre sourde et isolation des vibrations mécaniques. Une chambre à vide et un contrôle de température parachèvent la maîtrise des conditions de mesure.
Pour caractériser la précision et la fiabilité de la mesure interférométrique, une étude poussée des imperfections optiques est réalisée. Une méthode de calibration innovante permettant de passer outres ces imperfections est proposée. Elle améliore notablement la linéarité de la mesure par rapport aux méthodes traditionnelles des interféromètres à quadrature de phase. Pour finir, une preuve de principe de la mesure diélectrique locale est réalisée sur un échantillon de PVdF-HFP chargé de particules de BaTiO3. Elle démontre le potentiel de la méthode pour la cartographie des propriétés diélectriques à l’échelle de particules de 50 nm de diamètre.

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Harmonic calibration of quadrature phase interferometry

Baptiste Ferrero and Ludovic Bellon, EPL 139, 55002 (2022)

[Article] doi: 10.1209/0295-5075/ac8761
[Data set] doi:10.5281/zenodo.6801118

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.

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Stochastic thermodynamics: driving of micro-oscillators applied to the study and the optimisation of information processing

Salambô Dago, PhD Thesis, Université de Lyon (2022)

hal: tel-03771837

This thesis extends by theoretical and experimental studies our understanding of the dynamics of systems ruled by thermal fluctuations in order to better control them and, in particular, use them as 1-bit logic gates. This work falls within the framework of out-of-equilibrium statistical physics and of thermodynamics of information based on stochastic thermodynamics. In this respect, we study the minimal work required to perform irreversible operations on 1-bit of information ([RESET] to 0 or 1), or reversible ones ([NOT] operation), and we aim to optimise the energetic cost and the speed of these processes. Our strategy to enhance the processing efficiency and speed consists in using as 1-bit memory a low dissipation micro-mechanical oscillator, therefore evolving at much smaller time-scales than the over-damped test systems used to date (colloidal particles in solution). The feedback control designed to create a virtual energy potential in which evolves the micro-resonator is a major step forward in coding and handling the 1-bit information: it represents the fastest and most energy-efficient device among those which perform logic operations at the thermal energy scale. We furthermore provide a solid theoretical basis, validated by experimental and numerical simulation results, to model energy exchanges. Taken as a whole, this work results in the theoretical prediction of the energetic cost of any logical operation and opens perspectives for information processing optimisation in term of reliability, speed and energy saving.

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

Salambô Dago, Jorge Pereda, Sergio Ciliberto and Ludovic Bellon, J. Stat. Mech. 2022, 053209 (2022)

[Article] doi: 10.1088/1742-5468/ac6d62
[Erratum] doi: 10.1088/1742-5468/acd697
[Dataset] doi: 10.5281/zenodo.6497247

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 (evolving at much smaller time scale than its overdamped counterpart), in order to build a tunable virtual double-well potential. To properly describe the system behavior in the feedback trap, we express the commutation 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 commutation 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.

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

Salambô Dago and Ludovic Bellon, Phys. Rev. Lett. 128, 070604 (2022)
[Article] doi: 10.1103/PhysRevLett.128.070604
[Dataset] doi: 10.5281/zenodo.4807408

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 kBTeffln2, where Teff is a weighted average of the actual temperature of the memory during the process.

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PDF of position and speed during a fast erasure process: comparison between a numerical simulation and the ansatz we propose – See article Supp. Mat for details.
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Force microscopy cantilevers locally heated in a fluid: Temperature fields and effects on the dynamics

Basile Pottier and Ludovic Bellon, Journal of Applied Physics 130, 124502 (2021)

[Article] doi:10.1063/5.0060911
[Data set] doi:10.5281/zenodo.5346796

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.

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

Alex Fontana, Richard Pedurand, Vincent Dolique, Ghaouti Hansali, Ludovic Bellon, Physical Review E 103, 062125 (2021)

[Article] doi: 10.1103/PhysRevE.103.062125
[Data set] doi: 10.5281/zenodo.4696489

 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.

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