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arXiv:2511.21430 · Modern Physics Letters B

Quantum electrodynamic description of ionization of the neutral hydrogen molecule

Hui-hui Miao

quant-phSubmitted Nov 26, 2025• Announced Nov 27, 2025• 0 citations• Revised Jul 17, 2026 (v3)
v1 · Nov 26, 2025v2 · Jul 1, 2026v3 · Jul 17, 2026
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Abstract

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 $\mathrm{H}_2$ formation. Photon dissipation ($γ_Ω$) accelerates stabilization, while electron ($γ_\mathrm{e}$) and phonon ($γ_ω$) dissipation play distinct regulatory roles. Particle influx ($μ_k$) induces complex energy redistribution, populating the atomic state $|\mathrm{H},\mathrm{H}\rangle$. 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 $3/4$. This work provides a unified theoretical foundation for quantum-controlled chemistry and cavity QED experiments.

Journal reference
Modern Physics Letters B 40, No. 20, p. 2650148 (2026)
DOI
10.1142/S0217984926501484
Comments
13 pages, 6 figures; Supplementary Information: 2 animations

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In this paper, we investigate the dynamics of quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to a static external magnetic field and local pure dephasing. The electron–proton spin pair is modeled as a bipartite two-qubit system evolving under the combined effects of hyperfine coupling, Zeeman splitting, and a Lindblad master equation that describes Markovian dissipative processes. Employing exact analytical solutions for the time-dependent density matrix elements (derived in the Markovian open-system framework), we quantify entanglement persistence via concurrence and state stability via Uhlmann fidelity with respect to the initial preparation. For an initial Werner state, numerical results reveal that the external magnetic field substantially modifies the system dynamics: Both concurrence and fidelity exhibit pronounced dependence on the Zeeman parameter, producing field-controlled oscillations, delayed entanglement sudden death, and altered decoherence rates. This behavior originates from Zeeman-induced lifting of hyperfine degeneracies, symmetry breaking of the isotropic Werner state, and redistribution of populations and coherences. Unlike previous studies that treat hyperfine interactions, Zeeman splitting, or decoherence in isolation, the present work provides a unified analytical treatment that simultaneously incorporates all three mechanisms. The findings underscore the competition between coherent hyperfine coupling and environmental noise and open new pathways for precision spectroscopy and robust quantum information protocols based on atomic spin degrees of freedom.
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