Quantum electrodynamic description of the neutral hydrogen molecule ionization

TL;DR

The paper tackles the ionization dynamics of neutral hydrogen under a unified quantum electrodynamics and open-system framework. It introduces a first-principles QED model coupled to a Lindblad master equation, spanning closed, dissipative open, and influx-driven open regimes, with a detailed orbital basis including bonding, antibonding, and a high-energy transitional orbital. Key findings show a strong tendency to form H2, with ionization pathways and stabilization speeds governed by the dissipation channels $γ_Ω$, $γ_e$, $γ_ω$ and influx ratios; the anode model imposes a 0.75 upper bound on $|H_2^+ angle$ due to orbital hybridization, and initial photon composition critically shapes outcomes. These results provide a theoretical foundation for quantum-controlled chemistry in cavity QED and offer guidance for future non-Markovian extensions, larger molecular systems, and experimental realizations in quantum simulators.

Abstract

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 ($γ_Ω$), electrons ($γ_e$), and phonons ($γ_ω$) are identified as critical control parameters, with $γ_Ω$ significantly accelerating system stabilization. Furthermore, the introduction of particle influx ($μ_k$) 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.

Figures (5)

• Figure 1: (online color) Ionization dynamics in a hydrogen molecule: unitary vs. dissipative evolution. Panel (a) depicts the ionization process of a hydrogen molecule. Here, the blue and yellow dots, respectively, stand for electrons and photons. Panel (b) shows the unitary evolution under different initial conditions: (b.1) for initial states $|\Psi_{initial}^0\rangle$, $|\Psi_{initial}^1\rangle$, $|\Psi_{initial}^2\rangle$, $|\Psi_{initial}^3\rangle$, and $|\Psi_{initial}^4\rangle$; (b.2) for $|\Psi_{initial}^5\rangle$; (b.3) for $|\Psi_{initial}^6\rangle$; (b.4) for $|\Psi_{initial}^7\rangle$. Panel (c) shows the effect of different particle dissipation intensities on the ionization model (initial state is $|\Psi_{initial}^6\rangle$): the horizontal and vertical axes of each subpanel represent the $\gamma_{\Omega}$ and $\gamma_e$, respectively; the first through fourth rows correspond to $\gamma_{\omega}$ of $10^7$, $10^{7.5}$, $10^8$, and $10^{8.5}$, respectively; the first through third columns correspond to probabilities of $|\rm{H},\rm{H}\rangle$, $|\rm{H}_2\rangle$, and $|\rm{H}_2^+\rangle$, respectively. Here, the color bar for each heatmap ranges from 0 to 1. Panel (d) compares the time it takes for the system to reach a stable state: the four subpanels correspond to $\gamma_{\omega}$ of $10^7$, $10^{7.5}$, $10^8$, and $10^{8.5}$, respectively. Here, the color bar for each heatmap is scaled from 0 to the maximum value.
• Figure 2: (online color) Comparison of the time it takes for the system to reach a stable state. As shown in Fig. \ref{['fig:Model']} (d), we investigated the impact of $\gamma_{\Omega}$ and $\gamma_e$ on the system's stabilization time for $\gamma_{\omega}=10^7,\ 10^{7.5},\ 10^8,$ and $10^{8.5}$, identifying the maximum and minimum times for each case. We then analyzed how these extreme values evolve as $\gamma_{\omega}$ increases from $10^7$ to $10^{8.5}$ (panel (a)). Additionally, the difference between them is plotted against $\gamma_{\omega}$ in panel (b).
• Figure 3: (online color) Dissipative dynamics for different initial conditions. Panel (a) for $|\Psi_{initial}^0\rangle$, $|\Psi_{initial}^1\rangle$, $|\Psi_{initial}^2\rangle$; panel (b) for $|\Psi_{initial}^3\rangle$, $|\Psi_{initial}^4\rangle$; panel (c) for $|\Psi_{initial}^5\rangle$; panel (d) for $|\Psi_{initial}^6\rangle$; panel (e) for $|\Psi_{initial}^7\rangle$.
• Figure 4: (online color) The influx effect. Picture shows the effect of different particle influx intensities on the ionization model (initial state is $|\Psi_{initial}^6\rangle$): the horizontal and vertical axes of each panel represent the influx--dissipation ratio for photons ($\mu_\Omega$) and for electrons ($\mu_e$), respectively; the first through fourth rows correspond to influx--dissipation ratio for phonons ($\mu_\omega$) of $0$, $0.3$, $0.6$, and $0.9$, respectively; the first through third columns correspond to probabilities of $|\rm{H},\rm{H}\rangle$, $|\rm{H}_2\rangle$, and $|\rm{H}_2^+\rangle$, respectively. Here, the color bar for each heatmap ranges from 0 to 1.
• Figure 5: (online color) The model with an anode. In panel (a), the hydrogen molecule is assumed to be in a perfectly isolated environment, preventing free particles from dissipating to the external system. However, electrons can be absorbed by an embedded anode, which is considered as electron escape. Panel (b) shows the time-dependent probabilities of the $|\rm{H}_2^+\rangle$ under different initial conditions.