  Femtosecond time-resolved X-ray diffraction is used to study a photo-induced
phase transition between two charge density wave (CDW) states in 1T-TaS$_2$,
namely the nearly commensurate (NC) and the incommensurate (I) CDW states.
Structural modulations associated with the NC-CDW order are found to disappear
within 400 fs. The photo-induced I-CDW phase then develops through a
nucleation/growth process which ends 100 ps after laser excitation. We
demonstrate that the newly formed I-CDW phase is fragmented into several
nanometric domains that are growing through a coarsening process. The
coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth
law, which describes the ordering kinetics in systems exhibiting a
non-conservative order parameter.
