Microscopic mechanism for resonant light-enhanced pair correlations in K$_3$C$_{60}$

Recent experiments on K$_3$C$_{60}$ revealed a giant enhancement of the light-induced superconducting-like optical response for pump frequencies near 10 THz, with an efficiency roughly two orders of magnitude larger than for off-resonant excitation. Here we show that a resonant enhancement of pair correlations arises naturally in a driven electronic model of K$_3$C$_{60}$ derived from \emph{ab initio} parameters. Exact diagonalization on small clusters identifies a symmetry-constrained two-photon pathway: the first photon drives the system from the even-parity ground state to an intermediate odd-parity manifold, and the second photon drives it to an even-parity excited state with enhanced pair correlations. Guided by this structure, we develop a DMRG+Krylov approach for larger clusters and find that the resonance energy shifts downwards with system size due to the kinetic-energy gain of the delocalized doublon excitation. A simplified single-orbital model reproduces the same scaling trend and allows us to reach a 14-site fcc cluster, where the resonant peak is pushed to $\sim$ 30 THz. Our results establish a purely electronic mechanism for resonant light-enhanced pair correlations in K$_3$C$_{60}$ and independently support the view that the experimentally observed 10 THz resonance is indeed due to superconducting-like coherent pair formation rather than improved metallicity. More broadly, they suggest that related resonant pathways may arise in other intermediate-coupling Hubbard materials with on-site repulsion $U$ and electronic bandwidth $W$ on comparable scales.