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.
Highlights
Open quantum systems are ubiquitous in physics and chemistry and have many uses from setting quantum technology in condensed phase to exploring long-lived coherence in biological systems [1,2,3,4,5,6]
For a two-level system, this characteristic time is the Rabi period whereas the bath dynamics can be estimated from the time decay of the two-time correlation function of the system bath coupling related to the Fourier transform of the bath spectral density
The originality relies on a complete implementation of an optimal control scheme, together with a fully converged hierarchical equations of motion (HEOM) treatment of the master equation describing the time evolution of the two-level sub-system density matrix beyond a perturbative regime
Summary
Open quantum systems are ubiquitous in physics and chemistry and have many uses from setting quantum technology in condensed phase to exploring long-lived coherence in biological systems [1,2,3,4,5,6]. They consist in selecting a given partitioning into a central quantum system and a statistical surrounding bath. Non-Markovianity is described by strong quantum memory effects leading to temporary information back flow from the environment to the system. The role of transitory information back flow in externally controlled dynamics remains an open issue and an active research area [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]
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