Optical Signatures of Non-Markovian Behaviour in Open Quantum Systems

TL;DR

This paper extends the quantum regression theorem to non-Markovian systems, enabling calculation of correlation functions and spectra, and demonstrates observable signatures of non-Markovian dynamics in a quantum dot system.

Contribution

It introduces an explicit extension of the quantum regression theorem for non-Markovian dynamics using projection operator techniques, with practical applications to quantum dots.

Findings

Non-Markovian signatures appear as phonon sidebands in emission spectra.

Information flows back from the environment to the system, indicating non-Markovian behavior.

The method accurately captures non-Markovian effects in open quantum systems.

Abstract

We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator techniques, with which we obtain explicit equations of motion for the correlation functions, making only a second order expansion in the system--environment coupling strength, and invoking the Born approximation at a fixed initial time. The results are used to investigate a driven semiconductor quantum dot coupled to an acoustic phonon bath, where we find the non-Markovian nature of the dynamics has observable signatures in the form of phonon sidebands in the resonance fluorescence emission spectrum. Furthermore, we use recently developed non-Markovianity measures to demonstrate an associated flow of information from the phonon bath back into the quantum dot exciton system.