Extracting phonon coupling parameters from multi color center photoluminescence

Vibronic coupling of color centers plays a crucial role in their effectiveness for quantum technologies. This study presents a novel approach to extract key parameters, including the Huang-Rhys factor and the one-phonon coupling function, from photoluminescence spectra containing the signal from multiple color centers. Monotonic splines are used to represent the one-phonon coupling function, optimized using a variable-length non-dominated sorting genetic algorithm. Our method is applied to the combination of the well-studied negatively charged nitrogen-vacancy center and its less explored neutral counterpart in diamond, observed through photoluminescence at 14 K. Despite the complexity inherent in the theoretical framework governing phonon coupling in photoluminescence, we achieve robust fits, yielding a normalized root-mean-squared error of approximately 6 %. The neutral nitrogen-vacancy center exhibits a Huang-Rhys factor of 3.0, while its negatively charged counterpart showcases a value of 3.95. The quasi-localized vibrations of both charge states are clearly present in the fitted one-phonon spectral function. Furthermore, the consistency of our methodology is bolstered by temperature-dependent photoluminescence, which was calculated up to numerical constants using fit-derived parameters, matching the experimental measurements up to 300 K.