Phys. Rev. Lett. 129, 023602 (2022) - Giant Diffusion of Nanomechanical Rotors in a Tilted Washboard Potential

Giant Diffusion of Nanomechanical Rotors in a Tilted Washboard Potential

L. Bellando, M. Kleine, Y. Amarouchene, M. Perrin, and Y. Louyer

Phys. Rev. Lett. 129, 023602 – Published 6 July 2022

Abstract

We present an experimental realization of a biased optical periodic potential in the low friction limit. The noise-induced bistability between locked (torsional) and running (spinning) states in the rotational motion of a nanodumbbell is driven by an elliptically polarized light beam tilting the angular potential. By varying the gas pressure around the point of maximum intermittency, the rotational effective diffusion coefficient increases by more than 3 orders of magnitude over free-space diffusion. These experimental results are in agreement with a simple two-state model that is derived from the Langevin equation through using timescale separation. Our work provides a new experimental platform to study the weak thermal noise limit for diffusion in this system.

Received 5 April 2022
Accepted 15 June 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.023602

Physics Subject Headings (PhySH)

Nonequilibrium statistical mechanics Optomechanics

Statistical Physics & ThermodynamicsNonlinear DynamicsAtomic, Molecular & Optical

Authors & Affiliations

L. Bellando^*, M. Kleine , Y. Amarouchene ^†, M. Perrin ^‡, and Y. Louyer^§

Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33405 Talence, France

^*louis.bellando.physique@gmail.com
^†yacine.amarouchene@u-bordeaux.fr
^‡mathias.perrin@u-bordeaux.fr
^§yann.louyer@u-bordeaux.fr

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Vol. 129, Iss. 2 — 8 July 2022

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Figure 1
(a) Illustration of the energy landscape for the rotation of the Brownian dimer around the optical axis for three different tilts. When the polarization is linear (blue dotted line), the potential is not tilted and the orientation of the dimer remains in the locked state. Conversely, for a circular polarization (solid blue line) the potential wells disappear. For elliptical polarization (dashed line), the rotational motion can change from a running state (spinning) to a locked state (torsional) and vice versa. (b) Surface plot in log-log scales of the angular vibration and translational power spectral densities as a function of the gas pressure for a beam ellipticity of $ϕ_{λ / 4} = 25 °$ and an optical power of 180 mW. The solid and dashed curves (red) represent the local maxima of the PSD computed by Langevin simulations of Eq. (2). The three grey horizontal curves at 0.41 mbar, 0.51 mbar, and 0.61 mbar outline the two-state coexistence region where the middle line denotes the maximum of intermittency.
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Figure 2
Time traces of the dimer angular velocity $\dot{φ}$ obtained by short-time Fourier transform for the three pressures that are shown as gray horizontal curves in Fig. 1.
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Figure 3
(a) Probability distribution function of the occupation time from the locked to running states $P (τ_{L})$ , red symbols, and the running to locked states $P (τ_{R})$ , blue symbols, for various pressures where the bistability is observed. Exponential behaviors suggest that stochastic transitions between locked and running states are thermally activated, following an Arrhenius-type law. (b) Pressure dependence of the mean occupation times in the locked and running states [symbols: experiment, solid line: Langevin simulations, Eq. (2)].
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Figure 4
(a) Measured power spectral densities of the dimer angular velocity (dots) and double Lorentzian fit [Eq. (3), solid curves] at the boundaries of the bistable region ( $P = 0.653 mbar$ in blue, $P = 0.408 mbar$ in black), and at the pressure around which the maximum of giant diffusion exists ( $P = 0.560 mbar$ in red). The dashed line represents the free-space diffusion coefficient $D_{0}$ at $P = 0.653 mbar$ , the double arrow displays the excess of diffusion $D_{eff} / D_{0}$ , while both the total escape rate $Γ_{T}$ and the rotational damping rate $Γ_{φ}$ are marked by vertical arrows. (b) On the left axis. Pressure dependence of the effective diffusion coefficient $D_{eff}$ in units of $D_{0}$ estimated by two methods: (i) data from Fig. 4 are fitted by using Eq. (3), blue open circles, while (ii) transition rates obtained from Fig. 3 are used to calculate $D_{eff}$ from Eq. (4), green filled circles. The black solid line results from the Langevin simulations [Eq. (2)]. On the right axis. Proportion of the mean occupancy in the locked state (red squares: experiment and black dashed line: Langevin simulations).
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Physical Review Letters

Giant Diffusion of Nanomechanical Rotors in a Tilted Washboard Potential

L. Bellando, M. Kleine, Y. Amarouchene, M. Perrin, and Y. Louyer

Phys. Rev. Lett. 129, 023602 – Published 6 July 2022

Abstract

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