Thermal noise calibration of functionalized cantilevers for force microscopy: effects of the colloidal probe position

Aubin Archambault, Caroline Crauste-Thibierge and Ludovic Bellon, J. Appl. Phys. 135, 094502 (2024)

Article: doi: 10.1063/5.0189480
Dataset:  doi: 10.5281/zenodo.10102664
Software : doi: 10.5281/zenodo.10103601

Colloidal probes are often used in force microscopy when the geometry of the tip-sample interaction should be well controlled. Their calibration requires the understanding of their mechanical response, which is very sensitive to the details of the force sensor consisting of a cantilever and the attached colloid. We present analytical models to describe the dynamics of the cantilever and its load positioned anywhere along its length. The thermal noise calibration of such probes is then studied from a practical point of view, leading to correction coefficients that can be applied in standard force microscope calibration routines. Experimental measurements of resonance frequencies and thermal noise profiles of raw and loaded cantilevers demonstrate the validity of the approach.

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Multimode characterization of an optical beam deflection setup

Alex Fontana and Ludovic Bellon, submitted to Phys. Rev. App. (2024)

arXiv: 2402.04887

Optical beam deflection is a popular method to measure the deformation of micro-mechanical devices. As it measures mostly a local slope, its sensitivity depends on the location and size of the optical spot. We present a method to evaluate precisely these parameters, using the relative amplitude of the thermal noise induced vibrations. With a case study of a micro-cantilever, we demonstrate the accuracy of the approach, as well as its ability to fully characterize the sensitivity of the detector, and the parameters (mass,
stiffness) of the resonator.

Experimental study of information engines at the mesoscopic scale

Aubin Archambault, PhD Thesis, Université de Lyon (2023)

The usual laws of thermodynamics are robust and can be applied to large range of macroscopic systems. However, when thermal fluctuations are on the same scale as the studied phenomena, these laws only describe the average behaviour. While it is impossible to macroscopicaly extract work from thermal fluctuations, this limit can be overcome by adapting the protocols based on the outcome of a measurement. This thesis presents an experimental realisation of information engine, monothermal cycles whose evolution is determined by the result of a measurement on the system. We show that it is then possible to extract energy from thermal fluctuations, and optimise the engine to maximise the work extraction in different regimes. These measurements are used to test recent theoretical works and explore the underdamped regime, usually harder to study. They also highlight specific effects of this underdamped regime. Two supplementary works are presented. The first presents two model for the description of the flexural modes of micro-cantilevers loaded with massive spheres. These models are completed by experiments, made possible by the development of microfabrication process. The second presents the development of force measurement device, adapted to forces in the range of the piconewton. This device is used to measure Casimir forces, up to a distance of 30nm.

Role of a capping layer on the crystalline structure of Sn thin films grown at cryogenic temperatures on InSb substrates

A.-H. Chen, C.P. Dempsey, M. Pendharkar, A. Sharma, B. Zhang, S. Tan, L. Bellon, S.M. Frolov, C.J. Palmstrom, E. Bellet-Amalric, and M. Hocevar, Nanotechnology 35 075702

[Article] doi: 10.1088/1361-6528/ad079e
[Data set] doi: 10.5281/zenodo.7581136

Metal deposition with cryogenic cooling is a common technique in the condensed matter community for producing ultra-thin epitaxial superconducting layers on semiconductors. However, a significant challenge arises when these films return to room temperature, as they tend to undergo dewetting. This issue can be mitigated by capping the films with an amorphous layer. In this study, we investigate the influence of different in situ fabricated caps on the structural characteristics of Sn thin films deposited at 80 K on InSb substrates. Regardless of the type of capping, we consistently observe that the films remain smooth upon returning to room temperature and exhibit epitaxy on InSb in the cubic Sn (α-Sn) phase. Notably, we identify a correlation between alumina capping using an electron beam evaporator and an increased presence of tetragonal Sn (β-Sn) grains. This suggests that heating from the alumina source may induce a partial phase transition in the Sn layer. The existence of the β-Sn phase induces superconducting behavior of the films by percolation effect. This study highlights the potential for tailoring the structural properties of cryogenic Sn thin films through in situ capping. This development opens avenues for precise control in the production of superconducting Sn films, facilitating their integration into quantum computing platforms.

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Reliability and operation cost of underdamped memories during cyclic erasures

Salambô Dago, Sergio Ciliberto, Ludovic Bellon, Adv. Phys. Res. 2023 2300074 (2023)

[Article] doi: 10.1002/apxr.202300074
[Dataset] doi: 10.5281/zenodo.8307734

The reliability of fast repeated erasures is studied experimentally and theoretically in a 1-bit underdamped memory. The bit is encoded by the position of a micro-mechanical oscillator whose motion is confined in a double well potential. To contain the energetic cost of fast erasures, we use a resonator with high quality factor Q: the erasure work W is close to Landauer’s bound, even at high speed. The drawback is the rise of the system’s temperature T due to a weak coupling to the environment. Repeated erasures without letting the memory thermalize between operations result in a continuous warming, potentially leading to a thermal noise overcoming the barrier between the potential wells. In such case, the reset operation can fail to reach the targeted logical state. The reliability is characterized by the success rate Rsi after i successive operations. W, T and Rsi are studied experimentally as a function of the erasure speed. Above a velocity threshold, T soars while Rsi collapses: the reliability of too fast erasures is low. These experimental results are fully justified by two complementary models. We demonstrate that Q≃10 is optimal to contain energetic costs and maintain high reliability standards for repeated erasures at any speed.

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Adiabatic computing for optimal thermodynamic efficiency of information processing

Salambô Dago, Sergio Ciliberto, Ludovic Bellon, PNAS 120 e2301742120 (2023)

[Article] doi: 10.1073/pnas.2301742120
[Dataset] doi: 10.5281/zenodo.6572643

Handling information in the physical world requires energy: Landauer’s principle makes a Landauer’s principle makes a strong connection between information theory and thermodynamics by stating that erasing a one-bit memory at temperature T0 requires an average energy larger than WLB = kBT0 ln2, with kB Boltzmann’s constant. This tiny limit has been saturated in model experiments using quasistatic processes. For faster operations, an overhead proportional to the processing speed and to the memory damping appears. In this article, we show that underdamped systems are a winning strategy to reduce this extra energetic cost. We prove both experimentally and theoretically that, in the limit of vanishing dissipation mechanisms in the memory, the physical system is thermally insulated from its environment during fast erasures, i.e., fast protocols are adiabatic as no heat is exchanged with the bath. Using a fast optimal erasure protocol, we also show that these adiabatic processes produce a maximum adiabatic temperature Ta = 2T0, and that Landauer’s bound for fast erasures in underdamped systems becomes the adiabatic bound: Wa = kBT0.

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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.