Signature of non-Markovianity in time-resolved energy transfer

TL;DR

This paper investigates how non-Markovian effects influence time-resolved energy transfer in quantum systems, establishing measurable links between energy flow and non-Markovianity indicators, with implications for understanding energy dynamics in open quantum systems.

Contribution

It introduces a quantitative relationship between energy current and non-Markovianity measures in specific quantum models, revealing conditions for energy backflow related to bath spectral functions.

Findings

Energy backflow correlates with non-Markovianity in the damped Jaynes-Cummings model.

In the spin-boson model, energy backflow depends on the bath spectral function.

No energy backflow occurs in Ohmic and sub-Ohmic baths, even with non-Markovian effects.

Abstract

We explore signatures of the non-Markovianity in the time-resolved energy transfer processes for quantum open systems. Focusing on typical systems such as the exact solvable damped Jaynes-Cummings model and the general spin-boson model, we establish quantitative links between the time-resolved energy current and the symmetric logarithmic derivative quantum Fisher information (SLD-QFI) flow, one of measures quantifying the non-Markovianity, within the framework of non-Markovian master equations in time-local forms. From the relationships, we find in the damped Jaynes-Cummings model that the SLD-QFI backflow from the reservoir to the system always correlates with an energy backflow, thus we can directly witness the non-Markovianity from the dynamics of the energy current. In the spin-boson model, the relation is built on the rotating-wave approximation, calibrated against exact numerical results, and proven reliable in the weak coupling regime. We demonstrate that whether the non-Markovianity guarantees the occurrence of an energy backflow depends on the bath spectral function. For the Ohmic and sub-Ohmic cases, we show that no energy backflow occurs and the energy current always flow out of the system even in the non-Markovian regime. While in the super-Ohmic case, we observe that the non-Markovian dynamics can induce an energy backflow.