Phonon state tomography probes of optically excited phonon-induced electron dynamics

Optical driving of quantum materials has opened a door for new modalities for engineering and controlling novel states of matter enabled by access to the excitation spectrum far away from equilibrium. One important class of experiments involves the optical excitation of specific vibrational modes (phonons) which, because of the dipole selection rules, can only couple nonlinearly to the electron density. A theory of these systems requires understanding the combined electron and phonon subsystems. In this poster, we propose a method, dubbed phonon state tomography (PST), in order to statistically unravel the electronic dynamics in terms of contributions from different phonon configurations. To demonstrate the effectiveness of this approach, we consider a model of a photo-pumped metal whose phonons are excited at an initial time by an optical pulse and show that i) spin and charge exhibit opposite trends as a function of the average phonon number, and ii) charge correlations increase with raising the width of the pump pulse. Thus, this technique may serve as a diagnostic tool for the phonon-induced electron dynamics in pump-probe experiments.