# Coherence as a measure for non-Markovianity and its applications to color centers in diamond

## TL;DR

This paper introduces an extended coherence-based measure for non-Markovianity applicable to structured phonon baths in color centers in diamond, providing a practical tool for analyzing quantum system-environment interactions at various temperatures.

## Contribution

It proposes a generalized measure of non-Markovianity that overcomes limitations of previous methods and is adaptable to coherent dynamical maps in complex quantum systems.

## Key findings

- The measure is well-behaved at arbitrary temperatures.
- It reveals how non-Markovianity is influenced by bulk and localized phonon modes.
- The method can eliminate false signs of non-Markovianity in coherent dynamical maps.

## Abstract

The degree of non-Markovianity of a continuous bath can be quantified by means of the coherence. This simple measure is experimentally accessible through Ramsey spectroscopy, but it is limited to incoherent dynamical maps. We propose an extension of this measure and discuss its application to color centers in diamond, where the optical coherence between two orbital states is affected by interactions with a structured phonon bath. By taking realistic phonon spectral density functions into account, we show that this measure is well-behaved at arbitrary temperatures and that it provides additional insights about how non-Markoviantiy is affected by the presence of both bulk and quasi-localized phonon modes. Importantly, with only a little overhead the measure can be adapted to eliminate the false signs of non-Markovianity from coherent dynamical maps and is thus applicable for a large class of systems modeled by the spin-boson Hamiltonian.