  We report strong instantaneous photoinduced absorption (PA) in the
quasi-one-dimensional Mott insulator ${\rm Sr_2CuO_3}$ in the IR spectral
region. The observed PA is to an even-parity two-photon state that occurs
immediately above the absorption edge. Theoretical calculations based on a
two-band extended Hubbard model explains the experimental features and
indicates that the strong two-photon absorption is due to a very large
dipole-coupling between nearly degenerate one- and two-photon states. Room
temperature picosecond recovery of the optical transparency suggests the strong
potential of ${\rm Sr_2CuO_3}$ for all-optical switching.
