Engineering non-Markovianity from defect-phonon interactions

Understanding defect-phonon interactions in solid-state devices is crucial for improving our current knowledge of quantum platforms. In this work, we develop first-principles calculations for a defect composed of two spin-$1\mathrm{/}2$ particles that interact with phonon modes in a one-dimensional lattice. We follow a bottom-up approach that begins with a dipolar magnetic interaction to ultimately derive the spectral density function and time-local master equation that describes the open dynamics of the defect. We provide theoretical and numerical analysis for the non-Markovian features of the defect-phonon dynamics induced by a pure dephasing channel acting on the Bell basis. Finally, we analyze two measures of non-Markovianity based on the canonical rates and Coherence, shedding more light on the role of the spectral density function and temperature; and envisioning experimental realizations.