Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

Jiang, Zhu; Zhang, Jing; Li, Yuan; Zhang, Yong; Fang, Zhengji; Zhao, Peide; Li, Er‐Ping

doi:10.1063/1.4935786

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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On the strength of the new quantum impedance Lorentz oscillator (QILO) model, a charge-transfer method in molecular photon-absorption is proposed and imaged via the numerical simulations of 1- and 2-photon-absorption (1PA and 2PA) behaviors of the organic compounds LB3 and M4 in this paper. According to the frequencies at the peaks and the full width at half-maximums (FWHMs) of the linear absorptive spectra of the two compounds, we first calculate the effective quantum numbers before and after the electronic transitions. Thus, we obtain the molecular average dipole moments, i.e., 1.8728 × 10–29 C·m (5.6145 D) for LB3 and 1.9626 × 10–29 C·m (5.8838 D) for M4 in the ground state in the tetrahydrofuran (THF) solvent. Then, the molecular 2PA cross sections corresponding to wavelength are theoretically inferred and figured out by QILO. As a result, the theoretical cross sections turn out to be in good agreement with the experimental ones. Our results reveal such a charge-transfer image in 1PA near wavelength 425 nm, where an atomic electron of LB3 jumps from the ground-state ellipse orbit with the semimajor axis a i = 1.2492 × 10–10 m = 1.2492 Å and semiminor axis b i = 0.4363 Å to the excited-state circle (a j = b j = 2.5399 Å). In addition, during its 2PA process, the same transitional electron in the ground state is excited to the elliptic orbit with a j = 2.5399 Å and b j =1.3808 Å, in which the molecular dipole moment reaches as high as 3.4109 × 10–29 C·m (10.2256 D). In addition, we obtain a level-lifetime formula with the microparticle collision idea of thermal motion, which indicates that the level lifetime is proportional (not inverse) to the damping coefficient or FWHM of an absorptive spectrum. The lifetimes of the two compounds at some excited states are calculated and presented. This formula may be used as an experimental method to verify 1PA and 2PA transition selection rules. The QILO model exhibits the advantage of simplifying the calculation complexity and reducing the high cost associated with the first principle in dealing with quantum properties of optoelectronic materials.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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Quantitative analysis of the 1st and 3rd order dispersion based on the one -dimensional oscillator with quantized impedance damping

Zhang

Jiang

et al. 2017

Optik

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

Zhang

Fang

et al. 2021

AIP Advances

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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.

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Quantized impedance dealing with the damping behavior of the one-dimensional oscillator

Cited by 4 publications

References 14 publications

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

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

Quantitative analysis of the 1st and 3rd order dispersion based on the one -dimensional oscillator with quantized impedance damping

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

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