Generation of the ultrabroad bandwidth with keV by three-color low intense mid-infrared inhomogeneous pulse

•We solve the time-dependent Schrödinger equation for harmonic generation.•Three-color mid-infrared inhomogeneous pulse is used for harmonic extension.•Coherent superposition initial state of He+ ion is used for harmonic enhancement.

We numerically investigate the high-order harmonic generation and the isolated attosecond pulse generation from the coherent superposition initial state of He+ ion by using the three-color low intense mid-infrared laser field. It is found that by properly controlling the delay times and the carrier envelope phases of the three-color mid-infrared pulse, the harmonic cutoff has been extended, and the harmonic modulations can be controlled. Further, with the introduction of the inhomogeneous parameter of the three-color field, the harmonic cutoff can be further enhanced. As a result, a supercontinuum with the bandwidth of 1773 eV can be obtained. Moreover, we found the harmonic yield is almost 4–6 orders of magnitude higher than that generated from the single initial state case. Classical and the quantum time–frequency analyses have been shown to explain the harmonic emission process. Finally, by properly superposing the harmonics, a series of wavelength-tunable sub-32as X-ray pulses can be obtained, which are almost 4–6 orders of magnitude improvement in comparison with the single ground initial state case.