Realization of a micrometre-sized stochastic heat engine

The conversion of energy into mechanical work is essential for almost any industrial process. The original description of classical heat engines by Sadi Carnot in 1824 has largely shaped our understanding of work and heat exchange during macroscopic thermodynamic processes1. Equipped with our present-day ability to design and control mechanical devices at microand nanometre length scales, we are now in a position to explore the limitations of classical thermodynamics, arising on scales for which thermal fluctuations are important2–5. Here we demonstrate the experimental realization of a microscopic heat engine, comprising a single colloidal particle subject to a time-dependent optical laser trap. The work associated with the system is a fluctuating quantity, and depends strongly on the cycle duration time, τ, which in turn determines the efficiency of our heat engine. Our experiments offer a rare insight into the conversion of thermal to mechanical energy on a microscopic level, and pave the way for the design of future micromechanical machines. Macroscopic heat engines operating periodically between two heat baths are described well by the laws of thermodynamics, owing to the large number of internal degrees of freedom, which render fluctuations negligible. In contrast, fluctuations become visible when the typical energy scales of engines are reduced by more than twenty orders of magnitude, down to values around kBT . This regime can be achieved when the typical system dimensions are scaled down from metres to micrometres2. Such conditions are typically met for biomolecules6,7 and other microelectromechanical systems (MEMS; refs 8–10) that can perform translational or rotational motion as a result of chemical reactions and electrical fields. Also, several types of Brownian motor have been discussed that are able to extract useful work by rectification of thermal noise11–13. Despite its conceptual simplicity, no attempt has been made to realize a microscopic heat engine that extracts energy by cyclically working between two heat baths in a regime where fluctuations dominate. Here we present an experimental realization of a Stirling engine, where a single Brownian particle is subjected to a time-dependent optical trap and periodically coupled to different heat baths14. The particle and the trapping potential replace the working gas and the piston of its macroscopic counterpart. As for conventional heat engines where the periodic coupling of the working gas to a cold and a hot heat bath changes volume and pressure inside a piston, the fluctuations of a colloidal particle subjected to an external optical potential vary on changing the temperature of the solvent. As a Brownian particle we used a single melamine bead of diameter 2.94 μm suspended in water and confined in a vitreous sample cell 4 μm in height. Using a highly focused infrared laser beam we exerted a parabolic trapping potential U (R,k) = (1/2)k(t )R2 on the particle, where R is its radial distance from the