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利用数值模拟含时薛定谔方程的方法，研究了氢原子在强激光场作用下产生的阈下高次谐波辐射。在波长为608 nm激光作用下，氢原子可以吸收5个光子，由基态|1s⟩共振跃迁至激发态|2p⟩态；氢原子也可以吸收更多光子发生电离，某些连续态|c⟩在激光缀饰下其能量可以和|2p⟩态能量相当。随后发生的|2p⟩态到|1s⟩态的复合，或|c⟩态到|1s⟩态的复合，可辐射出能量相同的光子。这两个复合路径相互干涉，在第五次谐波中形成典型的法诺线形。进一步研究发现，该法诺线形依赖于激光强度。本研究表明，即便是在单电子体系中，法诺干涉也可以存在，并可以通过控制激光参数改变法诺线形。We numerically solved the time-dependent Schrödinger equation (TDSE) for a hydrogen atom interacting with intense near-infrared laser fields to investigate the mechanism of below-threshold high-harmonic generation (HHG). The primary focus was on understanding the spectral features, particularly resonant structures, arising in the fifth harmonic region under specific driving conditions. Our simulations utilized a laser wavelength of 608 nm. At this wavelength, hydrogen atoms can resonantly absorb five photons, promoting electrons from the ground state |1s⟩ to the excited state |2p⟩. Concurrently, atoms can absorb additional photons leading to ionization. Crucially, due to the AC Stark shift induced by the intense laser field (laser dressing), certain laser-dressed continuum states |c⟩ become energetically degenerate with the laser-dressed |2p⟩ state. High-harmonic radiation at the fifth harmonic frequency can then be emitted via two distinct quantum paths: (1) Bound-bound recombination: Direct recombination from the laser-dressed |2p⟩ state back to the ground state |1s⟩. (2) Continuum-bound recombination: Recombination from the laser-dressed continuum states |c⟩ (reached via ionization) back to |1s⟩. Both pathways emit photons of identical energy corresponding to the fifth harmonic. Our key finding is the pronounced quantum interference between these two recombination channels. This interference manifests spectrally as a characteristic asymmetric Fano lineshape in the intensity profile of the fifth harmonic. Furthermore, we demonstrate that the shape of this Fano resonance exhibits a strong and controllable dependence on the intensity of the driving laser field. This study provides clear evidence that Fano quantum interference, typically associated with multi-electron correlations or autoionizing states in complex systems, can emerge in the fundamental single-electron hydrogen atom system under intense laser fields. The interference arises directly from the coherent superposition of the bound-bound and continuum-bound recombination pathways enabled by laser-induced degeneracy. Importantly, the spectral profile of the Fano resonance can be actively manipulated by tuning the laser intensity, highlighting a novel avenue for coherent control of harmonic emission in simple atomic systems.
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Keywords:
- Hydrogen atom /
- Intense laser field /
- Below-threshold high-harmonic generation /
- Fano resonance
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