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The possibility of enhancing desirable functional properties of complexmaterials by optical driving is motivating a series of studies of theirnonlinear terahertz response. In high-Tc cuprates, large amplitude excitationof certain infrared-active lattice vibrations has been shown to inducetransient features in the reflectivity suggestive of non-equilibriumsuperconductivity. Yet, a microscopic mechanism for these observations is stilllacking. Here, we report measurements of time- and scattering-angle-dependentsecond-harmonic generation in YBa$_2$Cu$_3$O$_{6+x}$, taken under the sameexcitation conditions that result in superconductor-like terahertzreflectivity. We discover a three-order-of-magnitude amplification of a2.5-terahertz electronic mode, which is unique because of its symmetry,momentum, and temperature dependence. A theory for parametric three-waveamplification of Josephson plasmons, which are assumed to be well-formed belowT$_c$ but overdamped throughout the pseudogap phase, explains all theseobservations and provides a mechanism for non-equilibrium superconductivity.More broadly, our work underscores the role of parametric mode mixing tostabilize fluctuating orders in quantum materials.

Parametrically amplified phase-incoherent superconductivity in YBa$_2$Cu$_3$O$_{6+x}$