Long-range $\eta$-pairing in photodoped Mott insulators

We show that a metastable $\eta$--pairing superconducting phase can be induced by photodoping doublons and holes into a strongly repulsive fermionic Hubbard model. The doublon-hole condensate extends over a wide range of doublon densities and effective temperatures. Different non-equilibrium protocols to realize this state are proposed and numerically tested. We also study the optical conductivity in the superconducting phase, which exhibits ideal metallic behavior, i.e., a delta function at zero-frequency in the conductivity, in conjunction with negative conductivity at large frequencies. These characteristic optical properties can provide a fingerprint of the $\eta$-pairing phase in pump-probe experiments.