Dynamics of Bell-nonlocality and entanglement in a ring cavity induced by spontaneous emission

By considering the spatial motion of the atoms, we study the time evolution of Bell nonlocality and entanglement of a pair of atoms for two kinds of Werner-type internal states in an ideal single-mode ring cavity. We have proved that both Bell nonlocality and entanglement have the phenomena of sudden death and sudden birth for the initial state W±′, while for the initial state W±, Bell nonlocality has the phenomenon of sudden death, but entanglement decays to zero asymptotically over time. We also notice that the preservation of Bell-inequality violation is much shorter than that of entanglement. In addition, it is shown that the disentanglement time and the Bell-inequality violation time both depend on the purity and the width of the wave packet describing the motion of the atomic center of mass.