Local Quantum Uncertainty and Entanglement in the Hyperfine Structure of the Hydrogen Atom: A Lindblad Approach

Kamal Berrada () and Smail Bougouffa
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Kamal Berrada: Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia
Smail Bougouffa: Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia

Mathematics, 2025, vol. 13, issue 20, 1-14

Abstract: 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.

Keywords: Lindblad master equation; dephasing effect; hyperfine structure; hydrogen atom; quantum entanglement; local quantum uncertainty (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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