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arXiv quant-ph/9905070quant-phhep-phhep-thphysics.atom-ph
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隧道区多光子过程的微扰研究

Perturbative study of multiphoton processes in the tunneling regime

Marco Frasca

摘要:

在Kramers-Henneberger框架下,利用偶极近似对强电磁场中的薛定谔方程进行了微扰研究.在原子半径远小于自由电子运动幅度的条件下,证明了线偏振激光场的谱中只出现奇次谐波。在这种近似下,在Keldysh参数中获得了一系列微扰,从而描述了隧穿机制中的多光子过程。将该理论应用于类氢原子的情况:导出了高次谐波谱和阈上电离率。以这种方式计算的电离率确定谐波的幅度。原子的波函数被证明相对于微扰是刚性的,因此在计算几率振幅时,激光场对库仑势的影响可以被忽略作为一级近似:这种近似随着电子运动的振幅与原子半径之间的比率变得更大而改进。通过微扰求解薛定谔方程,重新推导了目前谐波产生所采用的半经典描述。

英文摘要:

A perturbative study of the Schrödinger equation in a strong electromagnetic field with dipole approximation is accomplished in the Kramers-Henneberger frame. A prove that just odd harmonics appear in the spectrum for a linear polarized laser field is given, assuming that the atomic radius is much lesser than the free-electron quiver motion amplitude. Within this approximation a perturbation series is obtained in the Keldysh parameter giving a description of multiphoton processes in the tunneling regime. The theory is applied to the case of hydrogen-like atoms: The spectrum of higher order harmonics and the above-threshold ionization rate are derived. The ionization rate computed in this way determines the amplitudes of the harmonics. The wave function of the atom proves to be rigid with respect to the perturbation so that the effect of the laser field on the Coulomb potential in the computation of the probability amplitudes can be neglected as a first approximation: This approximation improves as the ratio between the amplitude of the quiver motion of the electron and the atom radius becomes larger. The semiclassical description currently adopted for harmonic generation is so rederived by solving perturbatively the Schrödinger equation.

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