Entanglement dynamics in $κ$-deformed spacetime

Abstract: We treat two identical and mutually independent two-level atoms that are coupled to a quantum field as an open quantum system. The master equation that governs their evolution is derived by tracing over the degree of freedom of the field. With this, we compare the entanglement dynamics of the two atoms moving with different trajectories in $\kappa$-deformed and Minkowski spacetimes. Notably, when the environment-induced interatomic interaction does not exist, the entanglement dynamics of two static atoms in $\kappa$-deformed spacetime are reduced to that in Minkowski spacetime in the case that the spacetime deformation parameter $\kappa$ is sufficiently large as theoretically predicted. However, if the atoms undergo relativistic motion, regardless of whether inertial or non-inertial, their entanglement dynamics in $\kappa$-deformed spacetime behave differently from that in Minkowski spacetime even when $\kappa$ is large. We investigate various types of entanglement behavior, such as decay and generation, and discuss how different relativistic motions, such as uniform motion in a straight line and circular motion, amplify the differences in the entanglement dynamics between the $\kappa$-deformed and Minkowski spacetime cases. In addition, when the environment-induced interatomic interaction is considered, we find that it may also enhance the differences in the entanglement dynamics between these two spacetimes. Thus, in principle, one can tell whether she/he is in $\kappa$-deformed or Minkowski spacetime by checking the entanglement behavior between two atoms in certain circumstances.