Recent studies have demonstrated that in a few-cycle laser pulse, a coherent Rydberg atom—an atom in a superposition of the ground and highly excited states—can generate high-order harmonic generation (HHG) spectra with high conversion efficiency and high cutoff energy, making it a potential procedure for producing attosecond pulses. In this study, we theoretically report two interesting findings that can be realized experimentally: the nontrivial dependence of HHG cutoff on the laser carrier-envelope phase (CEP) and the double-plateau structure in the spectrum when the CEP ranges from 75° to 120°. The second effect has not been reported for a Rydberg atom in the previous studies focusing only on CEP of 0°. Finally, using classical simulation and time-frequency analysis, we explain the influence of the CEP on the cutoff energy and, especially, the origin of the double-plateau structure. Unlike the first plateau generated by the recombination of an electron escaping from the Rydberg state but returning to the ground state, the second one arises from the ionization from the ground state. Consequently, by controlling the laser CEP, the electron dynamics can be embedded in the structure of plateaus in the HHG spectra.
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