  Coherent diffractive imaging has enabled the structural analysis of
individual free nanoparticles in a single shot and offers the tracking of their
light induced dynamics with unprecedented spatial and temporal resolution. The
retrieval of structural information from scattering images in CDI experiments
is so far mostly based on the assumption of classical scattering in linear
response. For strong laser fields and in particular for resonant excitations,
both the linear and the classical description may no longer be valid as
population depletion and stimulated emission become important. Here we develop
a density-matrix-based scattering model in order to include such quantum
effects in the local medium response and explore the transition from linear to
non-linear CDI for the resonant scattering from Helium nanodroplets. We find
substantial departures from the linear response case already for experimentally
reachable pulse parameters and show that non-linear spatio-temporal excitation
dynamics results in rich features in the scattering, leading to the proposal of
quantum coherent diffractive imaging (QCDI) as a promising novel branch in
strong-field XUV and x-ray physics.
