Zeeman Symmetry Breaking as a Tool for Protecting Quantum Coherence and Purity Against Dephasing in Atomic Hydrogen

The hyperfine structure of the hydrogen atom provides a clean, experimentally relevant two-qubit platform in which the coupled electron and proton spins exhibit rich quantum behavior. We investigate the open-system dynamics of this system under the simultaneous influence of the intrinsic hyperfine coupling, an external static magnetic field (via the Zeeman interaction), and local Markovian dephasing noise. Employing the Lindblad master equation, we derive the exact time evolution of the density matrix for general X-shaped initial states and focus on two complementary measures of quantum coherence—the L1-norm coherence CL(t) and the relative entropy of coherence CR(t)—together with the state purity P(t). Numerical results reveal that all three quantities display characteristic damped oscillatory evolution. For a vanishing magnetic field, the decay is relatively rapid and smooth, whereas increasing the proton magnetic parameter markedly raises the oscillation frequency and slows the overall envelope of both coherence and purity. Even under stronger dephasing rates, a suitably chosen external field can substantially postpone the loss of quantum features, acting effectively as a control knob that reshapes the coherent unitary dynamics to counteract dissipative effects. These findings underscore the delicate competition between intrinsic atomic interactions and environmental noise, while offering a practical route for protecting quantum resources in spin-based systems. Our work bridges fundamental atomic physics with resource-theoretic concepts and highlights promising strategies for coherence preservation in realistic, controllable quantum platforms.