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The ultrafast optical manipulation of ordered phases in strongly correlatedmaterials is a topic of significant theoretical, experimental, andtechnological interest. Inspired by a recent experiment on light-inducedsuperconductivity in fullerenes [Mitrano et al., Nature 530, 2016], we developa comprehensive theory of light-induced superconductivity in drivenelectron-phonon systems with lattice nonlinearities. In analogy with theoperation of parametric amplifiers, we show how the interplay between theexternal drive and lattice nonlinearities lead to significantly enhancedeffective electron-phonon couplings. We provide a detailed and unbiased studyof the nonequilibrium dynamics of the driven system using the real-time Green'sfunction technique. To this end, we develop a Floquet generalization of theMigdal-Eliashberg theory and derive a numerically tractable set of quantumFloquet-Boltzmann kinetic equations for the coupled electron-phonon system. Westudy the role of parametric phonon generation and electronic heating indestroying the transient superconducting state. Finally, we predict thetransient formation of electronic Floquet bands in time- and angle-resolvedphoto-emission spectroscopy experiments as a consequence of the proposedmechanism.

The theory of parametrically amplified electron-phonon superconductivity