Title: Phonon state tomography of electron correlation dynamics in optically excited solids

Abstract: We introduce phonon state tomography (PST) as a diagnostic probe of electron dynamics in solids whose phonons are optically excited by a laser pulse at an initial time. Using a projected-purified matrix-product states (PP-MPS) algorithm, PST decomposes the exact correlated electron-phonon wavefunction into contributions from purely electronic states corresponding to statistically typical configurations of the optically accessible phononic response, enabling a 'tomographic' reconstruction of the electronic dynamics generated by the phonons. Thus, PST may be used to diagnose electronic behavior in experiments that access only the phonon response, such as thermal diffuse x-ray and electron scattering. To demonstrate the usefulness of PST, we study the dynamics of a metal whose infrared phonons are excited by an optical pulse at initial time and use it to simulate the sample-averaged momentum-resolved phonon occupancy as would be measured experimentally and accurately reconstruct the electronic double occupancy and staggered magnetization. We also use PST to analyze the influence of different pulse shapes on the light-induced enhancement and suppression of electronic correlations.