Photoemission Orbital Tomography Using a Robust Sparse PhaseLift

Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) is a powerful technique that visualizes the shape of the molecular orbitals (MOs) of molecular films. For further utilization of POT, a simple and low-cost method of POT is highly required. Here, we propose a new POT method based on the PhaseLift algorithm (PhaseLift POT). This method utilizes a lifting procedure to convert the PMM, which is a second-order polynomial of MO coefficients, into a first-order polynomial of the lifted MO coefficients and further relaxes the equality constraint for a given PMM. We also established a method to improve the accuracy of phase retrieval from the noisy PMM data by using sparsity for MO coefficients (sparse PhaseLift POT). These methods make it possible to reconstruct the three-dimensional MOs, including phases of the wave function, directly from a single experimental PMM. This method can also precisely determine the adsorption-induced molecular deformations with an accuracy of 0.05 [Å]. Furthermore, the robust sparse PhaseLift POT is robust against unavoidable noise in the experimental PMMs due to the relaxation of the matching condition for a given PMM. Therefore, this will be an innovative tool for POT, especially for analyzing the dynamics of the molecules during the chemical reaction and excitation processes.