**Figure 4.** (a) Quasienergies and (b) time-averaged transition probabilities as a function of the intensity of the cavity-mode field. The resonance position is at 1.489 **×** 10^{11} W cm^{−2}. (c) The enhancement of 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} = 0.17 au. The CEP shift is fixed at Δ = 0.4385 **×** 2π. The parameters of the frequency-comb field are peak intensity 1 **×** 10^{14} W cm^{−2}, carrier frequency 563.5 THz and repetition frequency 10 THz of 20 fs FWHM Gaussian pulses. The carrier frequency of the cavity-mode field is 10 THz.

**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.