Decoherence of the Hydrogen Atom via Radial Momentum Coupling in the Quantum Brownian Motion Framework

We investigate the decoherence dynamics of a hydrogen atom interacting with a thermal environment through momentum–momentum coupling within the quantum Brownian motion (QBM) framework. Unlike the conventional position coupling paradigm, we consider a bilinear interaction Hamiltonian in which the radial momentum of the hydrogen atom couples to the momenta of environmental oscillators. Using the Born–Markov approximation, we derive a master equation for the reduced density operator of the hydrogen atom. The radial dynamics are treated algebraically using ladder operators, allowing us to obtain a closed-form expression for the time evolution of the momentum operator in the interaction picture. We compute the environment induced decoherence coefficient in terms of the environmental spectral density and a characteristic hydrogenic frequency. For a Lorentz–Drude spectral density, we analyze how decoherence rate varies with the hydrogen atom principal and angular momentum quantum numbers. Our results show that decoherence is strongest for low-[Formula: see text], low-[Formula: see text] states, while it is significantly reduced for Rydberg and high angular momentum states due to their narrow radial momentum distributions. This reduction reflects a relative robustness of highly excited hydrogenic states against environmental noise, which is relevant for applications relying on long atomic coherence times.