The Dirac Equation in a Linear Potential and Quantized Electromagnetic Field: Spin–Rest Entanglement

We derive the exact eigenfunctions and energy equation for a Dirac particle in a monochromatic quantized electromagnetic plane wave and a confining scalar linear potential. It is shown that the system’s energy spectrum exhibits a forbidden region that vanishes when the particle–field interaction is switched off. We then analyze the effect of particle–field coupling on quantum entanglement between the particle’s spin and the remaining degrees of freedom. Our results show that the profile of the spin–rest entanglement, measured by negativity and Von Neumann entropy, follows the energy profile of the state: it is monotonic when the energy is monotonic, and non-monotonic otherwise. These results may provide insights into quantum correlations in Dirac-like systems describing low-energy excitations of graphene and trapped ions.