Employing the density-matrix renormalization group technique in the matrix-product-state representation, we investigate the photoexcited superconducting correlations induced by the $eta$-pairing mechanism in the half-filled Hubbard chain. We estimate the characteristic pair correlation function and verify the accuracy of our numerical results by comparison with exact-diagonalization data for small systems. The optimal parameter set of the pump that most enhances the $eta$-pair correlations, is calculated in the strong-coupling regime. For such a pump, we explore the possibility of quasi-long-range order.
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