  Strong field terahertz pulses are increasingly used to excite and control
quantum materials at the ultrafast timescale. They have found widespread
application by enabling direct addressing of the superconducting gap or
Josephson resonances and are essential in Higgs spectroscopy. Large non-linear
optical signals can be induced by the strong coupling of the THz and
superconducting degrees of freedom. However, far less attention has been paid
to the strong bi-directional coupling between field and material this implies.
Here, we use the framework of the time-dependent Ginzburg-Landau equations to
study the full field and material evolution of a superconductor driven by
strong field terahertz pulses. We find that at high field strengths, the
backreaction of the superconductor induces large changes to the driving pulse,
which in turn leads to a runaway melting of the superconducting condensate.
This results in a surprisingly large sensitivity to the initial driving pulse
chirp, enabling these purely dynamical changes to result in order of magnitude
different levels of melting. We also find large-scale spectral shifting of the
driving pulse to occur in just a few hundred nanometers of propagation through
a superconductor. We attribute these effects to an inverse plasma redshift, in
which the driving field breaks Cooper pairs and decreases the free-electron
mobility, analogous to reducing the density of a plasma.
