  By employing unbiased numerical methods, we show that pulse irradiation can
induce unconventional superconductivity even in the Mott insulator of the
Hubbard model. The superconductivity found here in the photoexcited state is
due to the $\eta$-pairing mechanism, characterized by staggered
pair-density-wave oscillations in the off-diagonal long-range correlation, and
is absent in the ground-state phase diagram; i.e., it is induced neither by a
change of the effective interaction of the Hubbard model nor by simple
photocarrier doping. Because of the selection rule, we show that the nonlinear
optical response is essential to increase the number of $\eta$ pairs and thus
enhance the superconducting correlation in the photoexcited state. Our finding
demonstrates that nonequilibrium many-body dynamics is an alternative pathway
to access a new exotic quantum state that is absent in the ground-state phase
diagram and also provides an alternative mechanism for enhancing
superconductivity.
