Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

TL;DR

This paper demonstrates how optimal control can influence non-Markovian dynamics in an open quantum system modeled by hierarchical equations of motion, revealing a strong correlation between control fields and environmental information flow.

Contribution

It introduces a method to analyze the impact of optimal control on non-Markovianity in open quantum systems using HEOM, with a focus on the bath's response and system-bath interactions.

Findings

Optimal control modifies the non-Markovian information back flow.

Control fields indirectly influence bath dynamics through auxiliary matrices.

Strong system-bath coupling enhances non-Markovian bath responses.

Abstract

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.