High-harmonic spectroscopy of mobility edges in one-dimensional quasicrystals

Quasicrystals occupy a unique position between periodic and disordered systems, where localization phenomena such as Anderson transitions and mobility edges can emerge even in the absence of disorder. This distinctive behavior motivates the development of robust, all-optical diagnostic tools capable of probing the structural, topological, and dynamical properties of such systems. In this work, focusing on generalized Aubry-André-Harper models and on an incommensurate potential in the continuum limit, we demonstrate that high-harmonic generation phenomenon serves as a powerful probe of localization transitions and mobility edges in quasicrystals. We introduce a new parameter--dipole mobility--which captures the impact of intraband dipole transitions and enables classification of nonlinear optical regimes, where excitation and high-harmonic generation yield can differ by orders of magnitude. We show that the cutoff frequency of harmonics is strongly influenced by the position of the mobility edge, providing a robust and experimentally accessible signature of localization transitions in quasicrystals.