Ultrafast broadband optical spectroscopy for quantifying subpicometric coherent atomic displacements in $WTe_2$

Here we show how time-resolved broadband optical spectroscopy can be used to quantify, with femtometer resolution, the oscillation amplitudes of coherent phonons through a displacive model without free tuning parameters, except an overall scaling factor determined by comparison between experimental data and density functional theory calculations. $WTe_2$ is used to benchmark this approach. In this semimetal, the response is anisotropic and provides the spectral fingerprints of two $A_1$ optical phonons at $\sim$8 and $\sim$80 $cm^-$$^1$. In principle, this methodology can be extended to any material in which an ultrafast excitation triggers coherent lattice modes modulating the high-energy optical properties.