# (a) Quasienergies and (b) time-averaged transition probabilities as a function of the intensity of the cavity-mode field

**Figure 5.** (a) Quasienergies and (b) time-averaged transition probabilities as a function of the intensity of the cavity-mode field. The resonance position is at 4.395 **×** 10^{11} W cm^{−2}. (c) The enhancement of the HHG power spectra by tuning the intensity of the cavity-mode field. For clarity, HHG peaks of the comb structure are connected by a line. The energy separation is fixed at ω_{αβ} = 0.25 au. The CEP shift is fixed at Δ = 0.1684 **×** 2π. Other parameters used are the same as those in figure 4.

**Abstract**

We present a theoretical investigation of the multiphoton resonance dynamics driven by intense frequency-comb and cavity-mode fields inside a femtosecond enhancement cavity (fsEC). The many-mode Floquet theorem is employed to provide a nonperturbative and exact treatment of the interaction between a quantum system and laser fields. The quasienergy structure driven by the frequency-comb laser field is modified by coupling the cavity-mode field and the multiphoton resonance processes between modified quasienergy states, resulting in the generation of even-order harmonics. The high-order harmonic generation (HHG) from a two-level system driven by the laser fields can be coherently controlled by tuning the laser parameters. In particular, the tuning intensity of the cavity-mode field allows one to coherently control the HHG power spectra without changing the absolute positions of comb frequencies.