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Hyperspectral electromechanical imaging at the nanoscale: Dynamical backaction, dissipation and quantum fluctuations

Clément Chardin, Sébastien Pairis, Stéphane Douillet, Mpïra Hocevar, Julien Claudon, Jean-Philippe Poizat, Ludovic Bellon and Pierre Verlot, submitted to Nature Nanotechnology

We report a new scanning thermomechanical microscopy platform enabling to both heat and acquire the fluctuations of mechanical nanostructures with nanometric resolution. We use this platform to image the nanomechanical noise response of a 40 nm diameter nanowire while scanning a localized heat source across its surface. We develop a thermal backaction model, which we use to demonstrate a close connection between the structure of the nanowire, its thermal response, its dissipation and its fluctuations. We notably identify the presence of a localized thermoelastic defect, which we demonstrate behaves as a single fluctuation hub, whose e-beam excitation yields a far off-equilibrium vibrational state, largely dominated by the quantum fluctuations of the heating source. Our platform is of interest for future development of ultra-low loss nanophononic devices, and appears as a new playground for investigating quantum thermodynamics in the strongly dissipative regime and at room temperature.

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Inertial effects in discrete sampling information engines

Aubin Archambault, Caroline Crauste-Thibierge, Sergio Ciliberto, Ludovic Bellon, submitted to EPL

We describe an experiment on an underdamped mechanical oscillator used as an information engine. The system is equivalent to an inertial Brownian particle confined in a harmonic potential whose center is controlled by a feedback protocol which measures the particle position at a specific sampling frequency 1/𝜏. Several feedback protocols are applied and the power generated by the engine is measured as a function of the oscillator parameters and the sampling frequency. The optimal parameters are then determined. The results are compared to the theoretical predictions and numerical simulations on overdamped systems. We highlight the specific effects of inertia, which can be used to increase the amount of power extracted by the engine. In the regime of large 𝜏, we show that the produced work has a tight bound determined by information theories.

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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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Probabilistic work extraction on a classical oscillator beyond the second law

Nicolas Barros, Sergio Ciliberto, Ludovic Bellon, submitted to Phys. Rev. Lett.

arXiv: 2402.18556

We demonstrate experimentally that, applying optimal protocols which drive the system between two equilibrium states characterized by a free energy difference ΔF, we can maximize the probability of performing the transition between the two states with a work W smaller than ΔF. The second law holds only on average, resulting in the inequality ⟨W⟩≥ΔF. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a suitable choice of parameters the probability of obtaining trajectories with W≤ΔF can be larger than 90 %. Very fast protocols are a key feature to obtain these results which are explained in terms of the Jarzynski equality.

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Multimode characterization of an optical beam deflection setup

Alex Fontana and Ludovic Bellon, accepted for publication in Phys. Rev. App. (2024)

arXiv: 2402.04887
[dataset] doi: 10.5281/zenodo.11110783

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.

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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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