Machine Learning Phonon Spectra for Fast and Accurate Optical Lineshapes of Defects

The optical properties of defects in solids produce rich physics, from gemstone coloration to single-photon emission for quantum networks. Essential to describing optical transitions is electron-phonon coupling, which can be predicted from first-principles but requires computationally expensive evaluation of all phonon modes in simulation cells containing hundreds of atoms. We demonstrate that this bottleneck can be overcome using machine learning interatomic potentials with negligible accuracy loss. A key finding is that atomic relaxation data from routine first-principles calculations suffice as a data set for fine-tuning, though additional data can further improve models. The efficiency of this approach enables studies of defect vibrational properties with high-level theory. We fine-tune to hybrid functional calculations to obtain highly accurate spectra, comparing with explicit calculations and experiments for various defects. Notably, we resolve fine details of local vibrational mode coupling in the luminescence spectrum of the T center in Si, a prominent quantum defect.