Abstract
In this paper, a classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics. Based on the Bohr–Sommerfeld model of a hydrogen-like atom in the adiabatic approximation, the computational formulas of the linear and nonlinear parameters and the damping coefficient of the quantized oscillator are derived and further expressed in terms of microphysical quantities, such as electronic charge and mass, Bohr radius, and effective quantum number. In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field. A new relationship is proposed to determine the transition eigenfrequency according to the peak frequency and full width at half maximum of an absorption spectrum. Our theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of two kinds of organic molecules turn out to be in good agreement with the experimental ones. These results suggest that our advancement in the quantization of the Lorentz oscillator is likely successful to make it available for use in the quantitative description of atomic or molecular 1PA and 2PA processes. Generally, the improved Lorentz oscillator may also be more suitable for approximating both linear and nonlinear properties of many dielectric or optoelectronic materials due to its relative simplicity.
Highlights
In the classical theory of light–matter interaction, the outermost electronic motion of a hydrogen-like atom is usually treated with a Lorentz oscillator
A classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics
In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field
Summary
In the classical theory of light–matter interaction, the outermost electronic motion of a hydrogen-like atom is usually treated with a Lorentz oscillator. By putting Bohr theory into the Lorentz harmonic oscillator model, Zhu et al. had theoretically investigated the hydrogen atom spectrum successfully In their efforts, a capacitor with quantized capacity is suggested to functionally substitute the related hydrogen atom in dealing with the charge transfer in the electron transition process. It is an interesting work to quantize the Lorentz oscillator by taking quantum theory into account This effort will be helpful for one to keep using the famous oscillator model to quantitatively describe the linear and nonlinear interaction between light and matter composed of hydrogen atoms and hydrogen-like atoms. We quantitatively compare the theoretical results of the quantized Lorentz oscillator with the relative experimental ones of both 1PA and 2PA of some kinds of atoms and molecules
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