Phase jump in resonance harmonic emission driven by strong laser fields*

We present a theoretical investigation of the multiphoton resonance dynamics in the high-order-harmonic generation (HHG) process driven by a strong driving continuous wave (CW) field along with a weak control harmonic field. The Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and the combined laser field. Multiple multiphoton-transition paths for the harmonic emission are coherently summed. The phase information about paths can be extracted via the Fourier transform analysis of the harmonic signals which oscillate as a function of the relative phase between driving and control fields. Phase jumps are observed when sweeping across the resonance by varying the frequency or intensity of the driving field. The phase variation as a function of driving frequency at a fixed intensity and as a function of the intensity at a fixed driving frequency allows us to determine the intensity dependence of the transition energy of quantum systems.