Sub-optical-cycle electron dynamics in materials driven by intense laser fields can be investigated by high harmonic generation. We observed frequency shift of high harmonic spectrum near the band gap of monolayer MoS2 experimentally. Through semi-classical quantum trajectory analysis, we demonstrated that the phase of transition dipole moment varies according to the recombination timing and momentum of tunneled electrons. It results in either blue- or red-shift of harmonic frequencies, determined by the modulated energy gap by transition dipole phases (TDPs) and Berry connections. Our finding reveals the effect of TDPs on high harmonic frequency in non-central symmetric materials.

A scheme of combining technology of orthogonal cylindrical lens array (OCLA) and polarization control plate (PCP) is introduced to improve target irradiation uniformity in laser fusion. The feasibility of the scheme is also analyzed by detailed two-dimensional simulation. It shows that a focal pattern with flat-top and sharp-edge profile could be obtained with an OCLA, while interference stripes inside the pattern are smoothed out by the use of the polarization control plate (PCP) technique. Moving the target slightly from the exact focal plane of the principal focusing lens can eliminate middle-scale-length intensity fluctuation further. And a well-irradiated laser spot with small nonuniformity and great energy efficiency can be obtained in this scheme.

Berry phase and topology of the Bloch wavefunction, originating from the interplay of internal quantum attributes of crystal electrons1, holds great significance in classifying novel quantum phases2,3 and endowing emergent functions4. In quantum materials with broken time-reversal or spatial-inversion symmetry, Bloch electrons in motion necessarily carry a geometric phase, and define the topological states2,3,5 and various quantum and nonlinear Hall effects6,7. Recent advances in light-wave-driven optical harmonic emission enable the observation of the rapid evolution of Bloch electrons on a subcycle time scale 8-13 and empower the harnessing of electron dynamics associated with Berry phase effects14,15. However, the correlation between subcycle electron motion and the accumulation of the quantum phase in geometric aspects of the evolving Bloch waves has not been observed. Here, we demonstrate that the Berry phase can be measured and manipulated in topological surface states using two-colour high-harmonic spectroscopy16. This is achieved by introducing a weak second harmonic field with a precisely controlled time delay to perturb the phase evolution of Dirac fermions and thus provide access to the Berry phase. Furthermore, we observe an overwhelming Berry phase effect that deforms quantum pathways of electron-hole pairs. Our observation demonstrates the ability to harness the electron spin using lightwaves in quantum materials with strong spin-orbit interaction, in addition, enhances the application of light-wave-driven spintronics and topological electronics.