Optimal Control to Minimize Dissipation and Fluctuations in Open Quantum Systems Beyond Slow and Rapid Regimes

TL;DR

This paper explores optimal control strategies in open quantum systems to minimize dissipation and fluctuations beyond traditional slow or rapid regimes, revealing new protocol structures through numerical optimization.

Contribution

It introduces a numerical approach to identify optimal control protocols at intermediate timescales, uncovering novel structures not captured by existing limits.

Findings

Optimal protocols switch discontinuously between solutions as dissipation and fluctuation weights vary.

Multi-step structures emerge in protocols for quantum dot systems.

Distinct optimal control structures are identified beyond conventional regimes.

Abstract

Optimal control is a central problem in quantum thermodynamics. When minimizing dissipated work and work fluctuations defined via the two-point measurement scheme in open quantum systems, existing approaches largely focus on the rapid- and slow-driving limits, leaving the behavior at intermediate timescales elusive. In this work, by numerically optimizing the driving protocols, we demonstrate that the open quantum systems exhibit distinct optimal structures not captured by the conventional limits. Specifically, in the coherent spin-boson model, we find that the optimal protocol switches discontinuously between distinct locally optimal solutions as the relative weight between dissipation and fluctuations is varied. Furthermore, for a single-level quantum dot coupled to a fermionic reservoir, the optimized protocol develops a characteristic multi-step structure.