All-Optical Manipulation of Band Gap Dynamics via Electron-Phonon Coupling

The electron-phonon coupling (EPC) is a ubiquitous interaction in condensed systems and plays a vital role in shaping the electronic properties of materials. Yet, achieving coherent manipulation of electron-phonon coupling has posed a considerable challenge. Here, employing time-resolved high-harmonic generation (tr-HHG) spectroscopy, we demonstrate the coherent manipulation of bandgap dynamics in a BaF2 crystal by precisely controlling the EPC using ultrashort light pulses. The tr-HHG spectrum perturbed by a triply degenerate phonon mode T2g, exhibits simultaneously a remarkable two-dimensional (2D) sensitivity, namely intensity domain in addition to the previously reported energy domain. The dynamic compression and enhancement of the harmonics in the intensity domain showed a {\pi}/2 phase shift compared to the manifestation of shifts of the harmonics in the energy domain, an astounding example of a physical phenomenon being observed simultaneously in two different perspectives. To complement our experimental observations, we employed a quantum model that incorporates the EPC, successfully reproducing the results. In addition, we demonstrated complete control over the EPC strength and initial phase of the coherent phonon oscillations by varying the incident electric field polarization over crystal orientation. Our findings lay a foundation for future investigations aiming to harness and exploit the remarkable potential of EPC in solid-state systems.