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.

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• Pairing mechanisms
• Superconducting phase transition
• Superconductor-insulator transition
• Mott insulators
• Exact diagonalization
• Hubbard model
• Methods in superconductivity
• Photoexcitation