Quantum impedance Lorentz oscillator and its 1- and 2-photon-absorption applications

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.

Charge Transfer and Level Lifetime in Molecular Photon-Absorption upon the Quantum Impedance Lorentz Oscillator

“…In QILO, all of its parameters including the linear parameter, the nonlinear parameter, the damping coefficient, and the oscillator strength have been expressed in terms of the typical quantum physical quantity, such as effective quantum number, Bohr radius, and the ground-state energy of the hydrogen atom. Based on the QILO model, the theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of many organic molecules turn out to be in good agreement with the experimental ones …”

“…the third-order nonlinear parameter where j φ = j, j − 1, j − 2, •••. 37 A possible orbit of the outermost electron of a hydrogenlike atom at an excited state with the effective quantum numbers j and j φ is schematically shown in Figure 2 shown in Figure 2. Thus, the atomic electric dipole moment can be estimated by using the following expression ec e a b j j j j j…”

“…named the i → j transition atom number density in the equilibrium situation between atomic emission and absorption under a light field. 37 In eq 25, g(i) is the degeneracy at state i. Equation 23 shows that the damping coefficient Γ ij just represents the full width at half-maximum (FWHM) of the 1PA spectrum.…”

“…Based on the QILO model, the theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of many organic molecules turn out to be in good agreement with the experimental ones. 37 By means of the QILO model in this paper, we try to figure out a charge-transfer image in molecular photonabsorption via numerical simulations of 1PA and 2PA behaviors of the two organic compounds of LB3 and M4.…”

“…Unfortunately, it provides only a classical insight into the light–matter interaction. The quantum impedance Lorentz oscillator (QILO) model was recently established and proposed, , in which the classical Lorentz oscillator had been quantized via the Bohr–Sommerfeld quantum theory and 1- and 2-photon-absorption selection rules of quantum mechanics. In QILO, all of its parameters including the linear parameter, the nonlinear parameter, the damping coefficient, and the oscillator strength have been expressed in terms of the typical quantum physical quantity, such as effective quantum number, Bohr radius, and the ground-state energy of the hydrogen atom.…”