AbstractThe coupling between superconductors and oscillation cycles of light pulses, i.e., lightwave engineering, is an emerging control concept for superconducting quantum electronics. Although progress has been made towards terahertz-driven superconductivity and supercurrents, the interactions able to drive non-equilibrium pairing are still poorly understood, partially due to the lack of measurements of high-order correlation functions. In particular, the sensing of exotic collective modes that would uniquely characterize light-driven superconducting coherence, in a way analogous to the Meissner effect, is very challenging but much needed. Here we report the discovery of parametrically driven superconductivity by light-induced order-parameter collective oscillations in iron-based superconductors. The time-periodic relative phase dynamics between the coupled electron and hole bands drives the transition to a distinct parametric superconducting state out-of-equalibrium. This light-induced emergent coherence is characterized by a unique phase–amplitude collective mode with Floquet-like sidebands at twice the Higgs frequency. We measure non-perturbative, high-order correlations of this parametrically driven superconductivity by separating the terahertz-frequency multidimensional coherent spectra into pump–probe, Higgs mode and bi-Higgs frequency sideband peaks. We find that the higher-order bi-Higgs sidebands dominate above the critical field, which indicates the breakdown of susceptibility perturbative expansion in this parametric quantum matter.