Overcoming residual timing jitter in pump–probe–reference interferometry via weak value amplification and deep learning

We introduce a hybrid methodology that synergistically combines weak value amplification (WVA) and deep learning to suppress the limiting effects of residual timing jitter in pump–probe–reference interferometry, achieved through simulations of pump-induced time delays at a few-attosecond resolution. The WVA protocol, employing real weak values, amplifies the minute delay induced by sample perturbation, thereby translating it into a measurable shift of interference fringes between the probe and the reference. However, this amplification introduces significant fringe distortion. To address this, we deploy deep learning architectures as high-precision parameter estimators: a convolutional neural network regressor (CNN-regressor) for direct delay estimation and a classifier (CNN-classifier) for discrete delay categorization. These are systematically benchmarked against traditional Fourier-transform-based analysis. Two key conclusions are drawn: (i) the WVA technique consistently enhances measurement precision across all estimators by effectively increasing the signal-to-noise ratio (SNR); (ii) both deep learning models surpass the traditional FFT approach: the CNN-regressor achieves a higher SNR at small weak values, while the CNN-classifier enables accurate estimation even under a challenging “ π phase shift” condition where conventional analysis fails.