In cuprate high-T_{c} superconductors, resonant excitation of certain lattice vibrations has been shown to induce transient terahertz reflectivity features suggestive of nonequilibrium superconductivity above the critical temperature T_{c}. A microscopic mechanism for these observations is still lacking. Here, time-resolved measurements of scattering-angle- and polarization-dependent second-harmonic generation in driven YBa_{2}Cu_{3}O_{6+x} reveal a three-order-of-magnitude amplification of a 2.5-THz electronic mode, which is unique because of its symmetry, momentum, and temperature dependence. A theory for amplification of finite-momentum Josephson plasma polaritons, which are assumed to be well formed below T_{c} but incoherent throughout the pseudogap phase, explains all these observations. A theoretical solution for the Fresnel-Floquet reflection that starts from the coherently oscillating Josephson plasma polaritons provides a possible mechanism for the nonequilibrium superconductorlike terahertz reflectivity reported earlier. Beyond the immediate case of cuprates, this work underscores the role of nonlinear mode mixing to amplify fluctuating modes above the transition temperature in a wide range of materials.
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