Role of inertia on the performance of Brownian gyrators

Abstract

Understanding the role of inertia in nanoscale heat transport is fundamental to the design of efficient nano-thermodynamics systems. In this work, we experimentally address the non-equilibrium dynamics of a Brownian gyrator, a paradigmatic model for nano-heat machines, that converts heat flow between two thermal baths into steady-state rotation. Using an optically levitated nanoparticle in a controlled vacuum environment, we study the transition from overdamped to underdamped dynamics of the gyrator. We demonstrate that, while the spatial signature of the non-equilibrium steady state vanishes as damping decreases, the rotational dynamics and energetics are optimized at a critical damping. Our findings reveal the importance of inertia for maximising the performance of nanoscale machines and provide fundamental insights into the design of efficient nano heat engines and processes.

Figures (4)

• Figure 1: Brownian gyrator setup. A laser focused through an objective traps a glass particle in an asymmetric harmonic potential. A pair of electrodes generates a directional effective temperature $T_{\mathrm{hot}}$ along the $x$ axis (red waves) larger than the temperature along the $y-$axis $T_\text{cold}$. The potential principal axes $\bm{x}_\mathrm{pot}$ and $\bm{y}_\mathrm{pot}$ are tilted by an angle $\phi=\pi/4$ relative to the lab frame $(\bm{x}, \bm{y})$ (inset). The broken system symmetry results in a circular counterclockwise motion represented by the light blue flow and the black arrows.
• Figure 2: Gyrator's PDF. Position's PDF and probability current (white arrows) in the $(x, y)$ plane, highlighting the counterclockwise rotation of the particle, for quality-factor a. $\mathsf Q = 1$ (overdamped, $p_\text{gas}=220 \ \mathrm{mbar}$); b. $\mathsf Q = 5.6$ (critical damping, $p_\text{gas}= 33\ \mathrm{mbar}$) and c. $\mathsf Q = 23.5$ (underdamped regime, $p_\text{gas}=8 \ \mathrm{mbar}$). The PDF is fitted with a 2D Gaussian function; highlighted by the 4$\sigma$ iso-contour (purple ellipse). We extract from the fit the PDF tilt angle $\theta$ and its major and minor axes standard deviations $\sigma_+$ and $\sigma_-$ (inset).
• Figure 3: Properties of the gyrator's PDF. a. Angle ($\theta$) and b. aspect ratio of the standard deviations ($\sigma_+/\sigma_-$) along the principal axes of the PDF for different damping values. Experimental data (blue dots) computed from three realizations of the gyrator, and theoretical predictions (black curves) for the experimental parameter set. The error bars are smaller than the dot size.
• Figure 4: Angular momentum and entropy creation. Experimental data (blue dots), as a function of resonator quality factor, computed from three realizations of the gyrator, and theoretical predictions (black curves) for the experimental parameter set. The error bars are smaller than the dot size. The pink dashed line represents the critical damping $\mathsf Q_c=\dfrac{k}{u}$.