Probing the electron-phonon interaction in correlated systems with coherent lattice fluctuation spectroscopy

Tailoring the properties of correlated oxides is accomplished by chemical doping, pressure, temperature or magnetic field. Photoexcitation is a valid alternative to reach out-of-equilibrium states otherwise inaccessible. Here, we quantitatively estimate the coupling between a lattice distortion and the charge-transfer excitation in (La$_2$CuO$_{4+\delta}$). We photoinduce a coherent La ion vibration and monitor the response of the optical constants in a broad energy range, providing quantitative information on the electron-phonon matrix element that can be compared to theoretical models. We propose the same methodology to probe electron-electron interactions in other materials.