Quantum memory and entanglement dynamics induced by interactions of two moving atoms with a coherent cavity

This study explores the dynamics of atomic entanglement of formation and entropic uncertainty relation (EUR) of two moving atoms interacting with an even coherent cavity during a two-photon interaction. We investigate the impact of the initial even coherent amplitude, the atom-photon coupling strengths, and the atomic motion coupling on the dynamics of quantum memory (QM) entropic uncertainty and entanglement. The dynamics of the entropic uncertainty and entanglement of formation are significantly altered by the atom-photon -atom interaction parameters. By increasing the initial mean photon number, the QM entropic uncertainty and the atomic entanglement can be improved. Bob's capacity to limit his uncertainty regarding Alice's measurement results depends on the initial even coherent state, the atom-photon couplings, and the atomic motion parameter. The atomic location couplings produce QM entropic uncertainty and entanglement with regular oscillatory behavior. The system parameters control the sudden death-birth entanglement phenomenon, which is improved by increasing the atomic location coupling.