Double-blind decoupling of molecular rotation and high-order harmonic generation with a neural network

High-order harmonic generation (HHG) through laser-molecule interaction provides a powerful means for detecting molecular structure and dynamics with subangstr\"om spatial and attosecond temporal resolution. However, accurately extracting molecular information from experimental harmonic spectra requires deconvolution of the angular average over the molecular rotational distribution, which is a challenging task due to the coherent nature of harmonic radiation. In this study we propose a deep-learning approach to disentangle the internal coupling between molecular alignment and single-molecule high-order harmonic radiation in experiments. With our method, the complex single-molecule dipole moments of high-order harmonics in both parallel and perpendicular directions, as well as the time-dependent molecular rotational distribution, can be simultaneously retrieved from the polarization-resolved angular distributions of HHG. From the retrieved harmonic dipole moments we can obtain comprehensive knowledge of the polarization states of the harmonics, including their ellipticity and helicity, without complicated experimental measurements. We demonstrate our method with two prototype molecules, ${\mathrm{N}}_{2}$ and ${\mathrm{CO}}_{2}$, in the experiment. Our approach provides an efficient way to disentangle single-molecule information from HHG experiments and will facilitate the study of molecular structure and dynamics imaging in complex polyatomic molecules.