High-Harmonic Spectroscopy as a Probe of Fractional Quantum Dynamics

We investigate high-order harmonic generation (HHG) driven by strong laser fields in a reduced-dimensionality time-dependent Schrödinger equation (TDSE) model generalized through a fractional kinetic-energy operator. By fixing the ionization potential, we isolate the effect of the fractional continuum dispersion from trivial changes in the binding energy. A classical three-step analysis is first extended to the fractional case, showing that the maximum return energy remains proportional to a fractional ponderomotive scale, but with a cutoff coefficient that decreases systematically as the fractional exponent is reduced. We then benchmark these predictions with TDSE simulations for different values of the fractional exponent $\alpha$. The computed HHG spectra exhibit a progressive reduction in the accessible cutoff region and pronounced modifications of the plateau interference structure. Time-frequency Gabor analysis of the dipole acceleration further reveals that the fractional kinetic operator reshapes the recollision dynamics, modifying the emission branches and enhancing interference features associated with multiple quantum pathways and returns. Finally, we analyze cutoff scaling laws with respect to laser intensity and wavelength. At fixed wavelength, the shifted cutoff harmonic follows an effective fractional intensity scaling, while at fixed intensity the cutoff energy shift follows a fractional wavelength scaling. Although the cutoff extracted from finite-pulse TDSE spectra should be regarded as an empirical measure, the combined spectral, scaling, and time-frequency analyses demonstrate, within the present model, that non-quadratic continuum dispersion can produce distinctive signatures in strong-field dynamics.