Optimizing Brownian escape rates by potential shaping

TL;DR

This paper demonstrates experimentally and theoretically that optimizing potential barriers can significantly enhance Brownian escape rates, surpassing traditional expectations, with potential applications in microfluidics and inertial regimes.

Contribution

It introduces a novel approach to potential shaping that maximizes escape rates, including the design of N-shaped barriers and experimental validation using optical tweezers.

Findings

Higher, fine-tuned barriers can increase escape rates beyond exponential scaling.

Optimal N-shaped barriers provide efficient speed-up in escape processes.

Experimental doubling of escape rates in microfluidic setups.

Abstract

Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.