Efficient two-dimensional control of barrier crossing

TL;DR

This paper develops optimized two-dimensional control protocols for barrier crossing that minimize energy dissipation, improving efficiency in optical trapping and molecular dynamics simulations across different driving speeds.

Contribution

It introduces novel two-dimensional control protocols that outperform traditional methods by reducing dissipation and increasing flux during barrier crossing.

Findings

Fast driving protocols jump halfway between control endpoints.

Slow driving protocols tighten the trap for energy savings.

Combined protocols improve performance at all speeds.

Abstract

Driven barrier crossings are pervasive in optical-trapping experiments and steered molecular-dynamics simulations. Despite the high fidelity of control, the freedom in the choice of driving protocol is rarely exploited to improve efficiency. We design protocols that reduce dissipation for rapidly driven barrier crossing under two-dimensional control of a harmonic trapping potential, controlling both trap center and stiffness. For fast driving, the minimum-dissipation protocol jumps halfway between the control-parameter endpoints. For slow driving, the minimum-dissipation protocol generically slows down and tightens the trap as it crosses the barrier, resulting in both significant energy savings and increased flux compared to naive and one-dimensional protocols (that only change trap center). Combining fast and slow results, we design protocols that improve performance at all speeds.