Quantum electrodynamic description of the neutral hydrogen molecule ionization

The ionization dynamics of a hydrogen molecule, serving as a fundamental benchmark in quantum chemistry, is investigated within a comprehensive framework combining quantum electrodynamics and the Lindblad master equation. This approach enables a first-principles description of light--matter interactions while accounting for dissipative processes and external particle influx. We systematically explore the system's evolution across three distinct regimes: closed, dissipative open, and influx-driven open quantum systems. Our results reveal a universal tendency towards the formation of the neutral hydrogen molecule ($|\rm{H}_2\rangle$) across all configurations. The dissipation strengths for photons ($\gamma_\Omega$), electrons ($\gamma_e$), and phonons ($\gamma_\omega$) are identified as critical control parameters, with $\gamma_\Omega$ significantly accelerating system stabilization. Furthermore, the introduction of particle influx ($\mu_k$) leads to a complex redistribution of energy, notably populating the atomic state ($|\rm{H},\rm{H}\rangle$). The ionization pathway is exquisitely sensitive to the initial quantum state, dictated by the composition and number of photons, which governs the accessible spin-selective excitation channels. This is conclusively demonstrated in a model with an embedded anode, where the maximum ionization probability is fundamentally constrained to $\frac{3}{4}$ by orbital hybridization. This study provides a unified theoretical foundation for quantum-controlled chemistry, with direct implications for future experiments in cavity QED and quantum information processing.