Phase-space Gaussian quantum ensemble for high-order harmonic generation

We propose a phase-space Gaussian quantum ensemble to depict the high-order harmonic generation process. Our model takes the wave-particle duality and the uncertainty principle into account. It bridges the ab initio calculation with the semiclassical analysis, enabling us to distinguish different channels and reveal the underlying electron dynamics. We investigate the ionization and recombination time of the short, long, and multi-rescattering trajectory harmonics. Our model also provides access to investigate the position-momentum properties. Results demonstrate that the electron has a nonzero initial velocity at the tunnel exit, revealing the nonadiabatic effect. We prove the validity of our analysis by interpreting the observables in the two-color interference experiments. The nonzero transverse harmonic signal for any two-color delay in the orthogonally polarized fields can be explained by the delocalized distribution of the quantum ensemble. Our model can guide the semiclassical analysis and provide a benchmark for high-order harmonic spectroscopy.