We study the nonequilibrium phase diagram of long-lived photo-doped states in the one-dimensional $U$-$V$ Hubbard model, where $eta$-pairing, spin density wave and charge density wave (CDW) phases are found. The photo-doped states are studied using an effective model obtained by a Schrieffer-Wolff transformation combined with separate chemical potentials for the approximately conserved pseudoparticle excitations, leading to a generalized Gibbs ensemble type description. These photo-doped states are characterized by gapless ($eta$-paring) and gapped (CDW) features in the nonequilibrium spectra. For small $V$, the $eta$-pairing correlations dominate over a wide doping range even when the SU$_c(2)$ symmetry that protects $eta$-pairing in the pure Hubbard model is absent. With increasing $V$, the CDW correlations take over in a wide doping range and are strong relative to the chemically doped case. We attribute the strong CDW correlations to the competition between intra- and inter-species repulsion and the one-dimensional configuration. Our results show that photo-doped strongly correlated systems exhibit different phases than conventional semiconductors.
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