  Although high field laser-induced ionization is a fundamental process
underlying many applications, there have been no absolute measurements of the
nonlinear polarizability of atoms and molecules in the presence of ionization.
Such information is crucial, for example, for understanding the propagation of
high intensity ultrashort pulses in matter. Here, we present absolute space-
and time-resolved measurements of the ultrafast laser-driven nonlinear
polarizability in argon, krypton, xenon, nitrogen, and oxygen up to an
ionization fraction of a few percent. These measurements enable determination
of the non-perturbative bound electron nonlinearity well beyond the ionization
threshold, where it is found to be approximately linear in intensity.
