  Photoexcitation by ultrashort laser pulses plays a crucial role in
controlling reaction pathways, creating nonequilibrium material properties, and
offering a microscopic view of complex dynamics at the molecular level. The
photo response following a laser pulse is, in general, non-identical between
multiple exposures due to spatiotemporal fluctuations in a material or the
stochastic nature of dynamical pathways. However, most ultrafast experiments
using a stroboscopic pump-probe scheme struggle to distinguish intrinsic sample
fluctuations from extrinsic apparatus noise, often missing seemingly random
deviations from the averaged shot-to-shot response. Leveraging the stability
and high photon-flux of time-resolved X-ray micro-diffraction at a synchrotron,
we developed a method to quantitatively characterize the shot-to-shot variation
of the photoinduced dynamics in a solid-state electrolyte. By analyzing
temporal evolutions of the lattice parameter of a single grain in a powder
ensemble, we found that the sample responses after different shots contain
random fluctuations that are, however, not independent. Instead, there is a
correlation between the nonequilibrium lattice trajectories following adjacent
laser shots with a characteristic "correlation length" of approximately 1,500
shots, which represents an energy barrier of 0.38~eV for switching the
photoinduced pathway, a value interestingly commensurate with the activation
energy of lithium ion diffusion. Not only does our nonequilibrium noise
correlation spectroscopy provide a new strategy for studying fluctuations that
are central to phase transitions in both condensed matter and molecular
systems, it also paves the way for discovering hidden correlations and novel
metastable states buried in oft-presumed random, uncorrelated fluctuating
dynamics.
