Optical two-dimensional coherent spectroscopy (2DCS) has become a powerful technique to study coupling and dynamics in complex quantum systems such as atoms, semiconductors, 2D materials, perovskites, and photosynthetic proteins. The femtosecond pulses used in 2DCS can probe ultrafast molecular dynamics in the system. The fast temporal dynamics are manifested as broad linewidths in the frequency domain. It is critical to have an effective and reliable method to analyze the lineshape in 2D spectra and extract accurate dynamical information. However, it is usually challenging to fit a 2D spectrum especially when the homogeneous and inhomogeneous linewidths are comparable. An analytical solution based on the projection-slice theorem can fit 1D slices in the diagonal and cross-diagonal directions, but fails to fully utilize the entire 2D spectrum that offers stronger constraint. The whole 2D spectrum can be fit in an improved approach, but fitting might be difficult to converge when there is a noise background.<br/><br/>We propose an alternative approach to analyze 2D spectral lineshape by using a machine learning algorithm. We implemented a deep learning algorithm based on a convolutional neural network (CNN) to extract homogeneous and inhomogeneous linewidths from 2D spectra. We first used a group of simulated 2D spectra with known linewidth values to train the network. The effectiveness and accuracy of the trained network was then tested by analyzing a different set of simulated 2D spectra. Finally, the trained algorithm was used to measure the homogeneous and inhomogeneous linewidths of two experimental 2D spectra. We found the machine learning algorithm is reliable and accurate with a percentage error of 2% or smaller for most cases. It works especially well in the region where the homogeneous and inhomogeneous linewidths are comparable, which is usually challenging for other methods. This approach can potentially be generalized to analyze more sophisticated 2D spectra with multiple 2D peaks and other spectral features. The machine learning algorithm provides a good alternative in the cases that are difficult for conventional fitting.

Extract molecular dynamics from optical two-dimensional coherent spectroscopy by machine learning

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