  Warm dense matter (WDM)---an extreme state with high temperatures and
densities that occurs e.g. in astrophysical objects---constitutes one of the
most active fields in plasma physics and materials science. These conditions
can be realized in the lab by shock compression or laser excitation, and the
most accurate experimental diagnostics is achieved with lasers and free
electron lasers which is theoretically modeled using linear response theory.
Here, we present first \textit{ab initio} path integral Monte Carlo results for
the nonlinear density response of correlated electrons in WDM and show that for
many situations of experimental relevance nonlinear effects cannot be
neglected.
