Non-equilibrium dynamics of forward scattering superconductors

Recent experiments have observed a surprisingly high critical temperature in a monolayer of FeSe on SrTiO3 an substrate. Among the proposed origins of this effect is enhancement or determination of the superconducting phase by a phonon within the SrTiO3 substrate, whose effect on the FeSe monolayer is to provide a source of forward scattering. It remains an open question whether such a \textit{forward scattering superconductor} is realized in the FeSe/SrTiO3 system. Using a non-equilibrium Keldysh approach, we study the effect of a pump laser field on superconducting phase of a model forward scattering superconductor. We compare the resulting temporal dynamics to those of a more typical BCS-like \textit{isotropic} superconductor, where the phonon scattering is not as limited. We demonstrate how pump-probe experiments can be used to distinguish the two types of superconductors under consideration.