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.
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.
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.
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 formation. Photon dissipation (γΩ) accelerates stabilization, while electron (γe) and phonon (γω) dissipation play distinct regulatory roles. Particle influx (μk) induces complex energy redistribution, populating the atomic state ∣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 3/4. This work provides a unified theoretical foundation for quantum-controlled chemistry and cavity QED experiments.
In this paper, we try to study the quantum discord dynamics in a complex correlated photon-matter model, which is modified from the Tavis-Cummings-Hubbard model - a common cavity quantum electrodynamics model. The target model consists of two hydrogen atoms. A neutral hydrogen molecule can be obtained through an association reaction and disintegrated through dissociation reaction. The formation and breaking of covalent bond is accompanied by the creation and annihilation of phonon. Compared with previous efforts, studying the quantum discord dynamics of this complicated system is more challenging than it was for the simple quantum system, which consisted of a single two-level atom. For convenience, we adopt a bipartite split of the multiqubit system and the two-qubit von Neumann projective measurement on the observed subsystem. We attempt to examine the dissipative dynamics in open quantum system in addition to the unitary evolution of closed quantum system. We are dedicated to identifying the regularity of quantum correlation as the basis for future research on more complex quantum systems, specifically including the impacts of nuclei tunneling effect, covalent bond formation strength, and dissipation intensities of photon (phonon) on quantum discord.
In this paper we propose an ab initio method to solve quantum many-body problems of molecular dynamics where both electronic and nuclear degrees are represented by ensembles of trajectories and guiding waves in physical space. Both electrons and nuclei can be treated quantum mechanically where the guiding waves obey a set of coupled Schrodinger equations (quantum-quantum description) or, alternatively, coupled Schrodinger-Newtonian equations are solved for the quantum-classical approximation. The method takes into account local and nonlocal quantum correlation effects in a self-consistent manner. The general formalism is applied to one- and two-dimensional hydrogen molecules subjected to a strong ultrashort optical pulse. Comparison is made with the results from the "exact" Ehrenfest molecular dynamics for the molecular ionization and for the evolution of the internuclear distance as the molecule dissociates.
This paper investigates the dynamics of quantum and classical geometric correlations in the hyperfine structure of the hydrogen atom under pure dephasing noise, focusing on the interplay between entangled initial states and environmental effects. We employ the Lindblad master equation to model dephasing, deriving differential equations for the density matrix elements to capture the evolution of the system. The study explores various entangled initial states, characterized by parameters a1, a2, and a3, and their impact on correlation dynamics under different dephasing rates Γ. A trace distance approach is utilized to quantify classical and quantum geometric correlations, offering comparative insights into their behavior. Numerical analysis reveals a transition point where classical and quantum correlations equalize, followed by distinct decay and stabilization phases, influenced by initial coherence along the z-axis. Our results reveal a universal sudden transition from classical to quantum decoherence, consistent with observations in other open quantum systems. They highlight how initial state preparation and dephasing strength critically influence the stability of quantum and classical correlations, with direct implications for quantum metrology and the development of noise-resilient quantum technologies. By focusing on the hyperfine structure of hydrogen, this study addresses a timely and relevant problem, bridging fundamental quantum theory with experimentally accessible atomic systems and emerging quantum applications.
Accurately simulating molecular dynamics during chemical reactions remains a central challenge in computational chemistry. These processes are inherently quantum mechanical, involving coupled electronic and nuclear motion and non-adiabatic effects. A fully quantum description is therefore required, yet the associated computational cost grows exponentially with system size. Even with modern supercomputers, storing and evolving a molecular wavefunction rapidly becomes intractable, limiting exact simulations of chemical dynamics. Quantum simulation offers a promising alternative by using controllable quantum systems to directly reproduce molecular dynamics. However, fully digital, qubit-based approaches remain impractical for chemistry due to limited qubit numbers, coherence times, and gate fidelities. This motivates the exploration of more resource-efficient quantum architectures. In this thesis, we demonstrate that mixed-qudit-boson (MQB) quantum simulators provide a practical platform for simulating chemical dynamics in the quantum regime. In MQB devices, multilevel qudits encode electronic states while bosonic modes natively represent vibrational degrees of freedom, avoiding costly qubit encodings of nuclear motion and substantially reducing resource requirements. The thesis makes three main contributions. First, it reports the direct observation of geometric-phase interference in non-adiabatic dynamics using an MQB simulation of the Jahn–Teller model. Second, it extends the MQB framework to open-system chemical dynamics through programmable Lindblad dissipation. Third, it presents a resource analysis showing that MQB simulators can reduce resource costs by several orders of magnitude relative to qubit-only approaches. Together, these results establish MQB quantum simulators as a promising route for studying chemical dynamics beyond the reach of classical computation.