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In this work, we study the out-of-equilibrium dynamics of the paradigmaticquasi-one-dimensional material (TaSe$_4$)$_2$I, that exhibits a transition intoan incommensurate CDW phase when cooled just below room temperature, namely atT$_{\rm{CDW}} $= 263 K. We make use of both optical laser and free-electronlaser (FEL) based time-resolved spectroscopies in order to study the effect ofa selective excitation on the normal-state and on the CDW phases, by probingthe near-infrared/visible optical properties both along and perpendicularly tothe direction of the CDW, where the system is metallic and insulating,respectively. Excitation of the core-levels by ultrashort X-ray FEL pulses at47 eV and 119 eV induces reflectivity transients resembling those recorded whenonly exciting the valence band of the compound - by near-infrared pulses at1.55 eV - in the case of the insulating sub-system. Conversely, the metallicsub-system displays a relaxation dynamics which depends on the energy ofphoto-excitation. Moreover, excitation of the CDW amplitude mode is recordedonly for excitation at low-photon-energy. This fact suggests that the couplingof light to ordered states of matter can predominantly be achieved whendirectly injecting delocalized carriers in the valence band, rather thanlocalized excitations in the core levels. On a complementary side, table-topexperiments allow us to prove the quasi-unidirectional nature of the CDW phasein (TaSe$_4$)$_2$I, whose fingerprints are detected along its $c$-axis only.Our results provide new insights on the symmetry of the ordered phase of(TaSe$_4$)$_2$I perturbed by a selective excitation, and suggest a novelapproach based on complementary table-top and FEL spectroscopies for the studyof complex materials.

Ultrafast dynamics in (TaSe$_4$)$_2$I triggered by valence and core-level excitation