In this work, we investigate quantum correlations, including entanglement and quantum discord, within the hyperfine structure of the hydrogen atom using the Lindblad master equation to model its dynamics as an open quantum system interacting with an environment. By incorporating realistic environmental influences, we examine the time evolution of two key measures of quantum correlations: concurrence, which quantifies entanglement, and local quantum uncertainty (LQU), a broader indicator of quantumness. Our analysis spans various initial states, including coherent superpositions of hyperfine states, to capture a wide range of possible configurations and demonstrate how these measures capture distinct aspects of quantum behavior. The results reveal the robustness of LQU in regimes where entanglement may vanish. This resilience of LQU underscores its utility as a robust measure of quantum correlations beyond entanglement alone in the hydrogen atom. By elucidating the dynamics of quantum correlations in the hydrogen atom under realistic conditions, this work not only deepens our fundamental understanding of atomic systems but also highlights their potential relevance to quantum information science and the development of quantum technologies.
In this work, we investigate quantum correlations, including entanglement and quantum discord, within the hyperfine structure of the hydrogen atom using the Lindblad master equation to model its dynamics as an open quantum system interacting with an environment. By incorporating realistic environmental influences, we examine the time evolution of two key measures of quantum correlations: concurrence, which quantifies entanglement, and local quantum uncertainty (LQU), a broader indicator of quantumness. Our analysis spans various initial states, including coherent superpositions of hyperfine states, to capture a wide range of possible configurations and demonstrate how these measures capture distinct aspects of quantum behavior. The results reveal the robustness of LQU in regimes where entanglement may vanish. This resilience of LQU underscores its utility as a robust measure of quantum correlations beyond entanglement alone in the hydrogen atom. By elucidating the dynamics of quantum correlations in the hydrogen atom under realistic conditions, this work not only deepens our fundamental understanding of atomic systems but also highlights their potential relevance to quantum information science and the development of quantum technologies.
We investigate the quantum dynamics of entanglement and fidelity in the hyperfine structure of hydrogen atoms under dephasing noise, modeled via the Lindblad master equation. The effective Hamiltonian captures the spin–spin interaction between the electron and proton, with dephasing incorporated through local Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Entanglement is quantified using the concurrence, while fidelity measures the similarity between the evolving state and the initial state. Numerical results demonstrate that entanglement exhibits oscillatory decay modulated by the dephasing rate, with anti-parallel spin states displaying greater robustness compared to parallel configurations, often leading to entanglement sudden death. Fidelity dynamics reveal similar damped oscillations, underscoring the interplay between coherent hyperfine evolution and environmental dephasing. These insights elucidate strategies for preserving quantum correlations in atomic systems, with implications for quantum information processing and metrology.
We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Quantum coherence is quantified through the l1-norm measures, while purity is evaluated to assess mixedness. Results demonstrate that coherence exhibits oscillatory decay modulated by the dephasing rate, with antiparallel spin states showing greater resilience against noise compared to parallel configurations. These findings highlight the interplay between coherent hyperfine dynamics and environmental dephasing, offering insights into preserving quantum resources in atomic systems for applications in quantum information science.
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.
In this work, we investigate the quantum coherence and purity in hydrogen atoms under dissipative dynamics, with a focus on the hyperfine structure states arising from the electron-proton spin interaction. Using the Lindblad master equation, we model the time evolution of the density matrix of the system, incorporating both the unitary dynamics driven by the hyperfine Hamiltonian and the dissipative effects due to environmental interactions. Quantum coherence is quantified using the L1 norm and relative entropy measures, while purity is assessed via von Neumann entropy, for initial states, including a maximally entangled Bell state and a separable state. Our results reveal distinct dynamics: for the Bell states, both coherence and purity decay exponentially with a rate proportional to the dissipation parameter, whereas for a kind of separable state, coherence exhibits oscillatory behavior modulated via the hyperfine coupling constant, superimposed on an exponential decay, and accompanied by a steady increase in entropy. Higher dissipation rates accelerate the loss of coherence and the growth of von Neumann entropy, underscoring the environment's role in suppressing quantum superposition and driving the system towards mixed states. These findings enhance our understanding of coherence and purity preservation in atomic systems and offer insights for quantum information applications where robustness against dissipation is critical.
In the present work, we investigate the detection and control of quantum correlations in the hyperfine structure of hydrogen atoms under dissipative dynamics. The hydrogen atom serves as a fundamental platform for studying bipartite quantum correlations between the electron and proton spins, where entanglement is quantified by concurrence and EPR steering is witnessed through violation of the entropic steering inequality. By modeling the open-system evolution via the Lindblad master equation, we analyze the time-dependent behavior of concurrence, steering, and fidelity under varying dissipation rates. Numerical illustrations highlight the resilience of entanglement relative to steering in noisy environments, providing insights into the control of non-classical phenomena.
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.