  We examine coherent phonons in a strongly driven sample of optimally-doped
high temperature superconductor YBa$_2$Cu$_3$O$_{7-\delta}$. We observe a
non-linear lattice response of the 4.5\,THz copper-oxygen vibrational mode at
high excitation densities, evidenced by the observation of the phonon third
harmonic and indicating the mode is strongly anharmonic. In addition, we
observe how high-amplitude phonon vibrations modify the position of the
electronic charge transfer resonance. Both of these results have important
implications for possible phonon-driven non-equilibrium superconductivity.
