Representation learning for identifying spin-spin interactions with reconstructive latent embeddings

We present an analysis model with nueral network for examining spin-spin interactions in diamond. With representation learning of dynamical decoupling signals induced from spin-spin interactions, two cases that could not been hitherto dealt with are addressed here; (1) overlapped signals of nuclear spins with similar periods. (2) split signals induced by nuclear-nuclear interaction. We train classification model with contrastive-center loss and regression model with reconstructive embedding learning especially identifying undistinguishable signals that cannot be evaluated by traditional regression approaches. Experimentally, we measure Carr-Purcell-Meiboom-Gill(CPMG) signal with the total evolution time of only less than 5 µs and with various numbers of unit π pulses controlling interacting time. Our method successfully recognizes the existence of nuclear-nuclear interaction and the undistinguishable overlapped signals up to 92% accuracy and estimates hyperfine interaction parameters up to 94% accuracy. We also distribute fully automated python modules for analyzing CPMG signals with various external magnetic field to obtain individual spin-spin interaction strengths.