Coherent control of multiphoton dynamics and high-order-harmonic generation driven by two frequency-comb fields with a relative envelope delay

We present a theoretical investigation of the coherent control of multiphoton dynamics and a high-order-harmonic generation (HHG) process driven by two frequency-comb fields, via the interference of multiphoton transition paths by tuning the relative envelope delay between fields. The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and frequency-comb laser fields. The case of two frequency-comb fields with the same repetition frequency and the carrier frequencies of fundamental and second harmonics, respectively, is considered. Due to the coupling of the second harmonic controlling the frequency-comb laser field, multiphoton transitions involving both fundamental- and second-harmonic photons occur. Different multiphoton transition paths can be superpositioned when the matching condition for carrier-envelope-phase shifts is satisfied, offering the possibility of coherent control of HHG power spectra via the interference of paths by tuning the relative envelope delay between fields. The calculated HHG power spectra present both sub-cycle oscillation and multi-cycle modulation behavior when the relative envelope delay is varied. It is also found that, under the condition of multiphoton resonance, the HHG power spectra can be further enhanced by about 10 times via the interference of multiphoton transition paths by tuning the relative envelope delay.