Ultrafast pump-probe phase-randomized tomography.

Measuring fluctuations in matter's low-energy excitations is the key to unveiling the nature of the non-equilibrium response of materials. A promising outlook in this respect is offered by spectroscopic methods that address matter fluctuations by exploiting the statistical nature of light-matter interactions with weak few-photon probes. Here we report the first implementation of ultrafast phase randomized tomography, combining pump-probe experiments with quantum optical state tomography, to measure the ultrafast non-equilibrium dynamics in complex materials. Our approach utilizes a time-resolved multimode heterodyne detection scheme with phase-randomized coherent ultrashort laser pulses, overcoming the limitations of phase-stable configurations and enabling a robust reconstruction of the statistical distribution of phase-averaged optical observables. This methodology is validated by measuring the coherent phonon response in α-quartz. By tracking the dynamics of the shot-noise limited photon number distribution of few-photon probes with ultrafast resolution, our results set an upper limit to the non-classical features of phononic state in α-quartz and provide a pathway to access non-equilibrium quantum fluctuations in more complex quantum materials.