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arXiv:2303.10413 · Lobachevskii Journal of Mathematics

Comparing the Effects of Nuclear and Electron Spins on the Formation of Neutral Hydrogen Molecule

Hui‐hui Miao, Yu. I. Ozhigov

Published Aug 1, 2023• 8 citations
arXivHTMLPDF

Abstract

Abstract We introduce the association-dissociation model of neutral hydrogen molecule, which is a finite-dimensional cavity quantum electrodynamics model of chemistry with two two-level artificial atoms on quantum dots placed in optical cavities, based on the Tavis–Cummings–Hubbard model. The motion of the nuclei can be represented in quantum form. Electron spin transition and spin-spin interaction between electron and nucleus are both considered. Consideration is also given to the effects of nuclear and electron spins on the formation of neutral hydrogen molecule.

DOI
10.1134/s1995080223080401

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Abstract We introduce the association-dissociation model of neutral hydrogen molecule, which is a finite-dimensional cavity quantum electrodynamics model of chemistry with two two-level artificial atoms on quantum dots placed in optical cavities, based on the Tavis–Cummings–Hubbard model. The motion of the nuclei can be represented in quantum form. Electron spin transition and spin-spin interaction between electron and nucleus are both considered. Consideration is also given to the effects of nuclear and electron spins on the formation of neutral hydrogen molecule.
This work presents a comprehensive comparison of quantum-mechanical and classical evolution for nuclear motion within a finite-dimensional quantum chemistry model. We employ a modified Tavis–Cummings–Hubbard model featuring two two-level artificial atoms in optical cavities to simulate the association and dissociation of a neutral hydrogen molecule. The initial conditions leading to the formation and decomposition of the molecule are examined. Dissipation in a Markovian open system is simulated by solving the Lindblad master equation. We compare the quantum and classical descriptions of nuclear motion: quantum mobility is characterized by nuclear tunneling, while classical motion is represented via fluctuations in interaction strengths. The emergence of dark states during dissociation and their significant impact on the evolutionary outcome are also analyzed. Key findings show that classical motion reaches the same final molecular states as quantum tunneling but requires an order-of-magnitude shorter time, with distinct patterns of population evolution. Two singlet dark states are identified that modify the branching ratio between neutral and ionic products.
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We investigate hydrogen molecule ionization within a unified framework combining finite-dimensional quantum electrodynamics with the Lindblad master equation, enabling systematic comparison across closed, dissipative, and influx-driven open systems. Our results reveal a universal tendency toward neutral H2\mathrm{H}_2H2​ formation. Photon dissipation (γΩγ_ΩγΩ​) accelerates stabilization, while electron (γeγ_\mathrm{e}γe​) and phonon (γωγ_ωγω​) dissipation play distinct regulatory roles. Particle influx (μkμ_kμk​) induces complex energy redistribution, populating the atomic state ∣H,H⟩|\mathrm{H},\mathrm{H}\rangle∣H,H⟩. The ionization pathway is highly sensitive to initial photon number and composition, which control spin-selective excitation channels. An embedded anode model confirms that orbital hybridization fundamentally constrains the maximum ionization probability to 3/43/43/4. This work provides a unified theoretical foundation for quantum-controlled chemistry and cavity QED experiments.
Suggestion of modifications of finite-dimensional QED models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.
In a helium–hydrogen mixture at T = 300 K, the polarization degree of hydrogen spins, both electron and nuclear, was determined to be as high as (5 ± 1)%. The role of the main processes giving rise to the formation of spin-polarized H atoms has been discussed. It is shown that an effective transfer of angular momentum from the preliminarily optically oriented He * (2 3 S 1 ) atoms to the H atoms is not due to the direct chemi-dissociation of the H 2 molecules by the He * atoms alone, or due to Penning ionization of these molecules followed by the ion-molecular rearrangement reaction H 2 + + H 2 → H 3 + + H alone, but to their summary action. The relative importance of the two mechanisms depends on the rotational temperature and total gas pressure.