  The quest for new functionalities in quantum materials has recently been
extended to non-equilibrium states, which are interesting both because they
exhibit new physical phenomena and because of their potential for high-speed
device applications. Notable advances have been made in the creation of
metastable phases and in Floquet engineering under external periodic driving.
In the context of non-equilibrium superconductivity, examples have included the
generation of transient superconductivity above the thermodynamic transition
temperature, the excitation of coherent Higgs mode oscillations, and the
optical control of the interlayer phase in cuprates. Here, we propose
theoretically a novel non-equilibrium phenomenon, through which a prompt quench
from a metal to a transient superconducting state could induce large
oscillations of the order parameter amplitude. We argue that this oscillating
mode could act as a source of parametric amplification of the incident
radiation. We report experimental results on optically driven K$_3$C$_{60}$
that are consistent with these predictions. The effect is found to disappear
when the onset of the excitation becomes slower than the Higgs mode period,
consistent with the theory proposed here. These results open new possibilities
for the use of collective modes in many-body systems to induce non-linear
optical effects.
