Below-threshold harmonics as the evidence of electron excitation in molecular tunneling ionization

Abstract

Determination of the tunneling electron’s quantum state at the tunnel exit is a fundamental issue in the strong-field ionization. Recent experimental and theoretical investigations on atomic systems have established that the tunneling electron may populate highly excited states in the vicinity of the tunnel exit. Here, we address this tunneling-state problem for molecules by analyzing below-threshold harmonics (BTHs) emitted from the prototypical molecular system {\text{H}}_2^{+} induced by the near-circularly polarized laser fields. The BTHs spectrum exhibits a double-plateau structure analogous to the atomic case. However, the cutoff energy of the first plateau displays a pronounced dependence not only on laser intensity but also on the internuclear distance R. These phenomena can be quantitatively described by a semiclassical strong-field model incorporating an analytical treatment of the near-nucleus Coulomb interaction, and attributing the first cutoff energy to the average energy of the excited bound state during tunneling. We further demonstrate that the R-dependent molecular Coulomb potential near the nucleus differs markedly from its atomic counterpart, yielding a significantly lower average energy for the molecular excited state. Our work provides critical evidence of tunneling-electron excitation before ionization in molecules, and sheds a light on the comprehensive understanding of tunneling phenomenon in strong field physics.

Keywords

Below-threshold harmonics / tunneling ionization / electronic state / cutoff energy / molecular internuclear distance

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Higher Education Press 2026

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