  Photo-excited strongly correlated systems can exhibit intriguing non-thermal
phases, but the theoretical investigation of them poses significant challenges.
In this work, we introduce a generalized Gibbs ensemble type description for
long-lived photo-doped states in Mott insulators. This framework enables
systematic studies of photo-induced phases based on equilibrium methods, as
demonstrated here for the one-dimensional extended Hubbard model. We determine
the nonequilibrium phase diagram, which features $\eta$-pairing and charge
density wave phases in a wide doping range, and reveal physical properties of
these phases. We show that the peculiar kinematics of photo-doped carriers, and
the interaction between them, play an essential role in the formation of the
non-thermal phases, and we clarify the differences between photo-doped Mott
insulators, chemically-doped Mott insulators and photo-doped semiconductors.
Our results demonstrate a new path for the systematic exploration of
nonequilibrium strongly correlated systems and show that photo-doped Mott
insulators host different phases than conventional semiconductors.
