Ultrafast Modulations and Detection of a Ferro-Rotational Charge Density Wave Using Time-Resolved Electric Quadrupole Second Harmonic Generation

We show the ferro-rotational nature of the commensurate charge density wave (CCDW) in $1T$-$\mathrm{TaS}_2$ and track its dynamic modulations by temperature-dependent and time-resolved electric quadrupole rotation anisotropy-second harmonic generation (EQ RA-SHG), respectively. The ultrafast modulations manifest as the breathing and the rotation of the EQ RA-SHG patterns at three frequencies around the reported single CCDW amplitude mode frequency. A sudden shift of the triplet frequencies and a dramatic increase in the breathing and rotation magnitude further reveal a photo-induced transient CDW phase across a critical pump fluence of ~ 0.5 mJ/cm$^2$.