Birth and death of entanglement between two accelerating Unruh-DeWitt detectors coupled with a scalar field

bstract We study two accelerating Unruh-DeWitt detectors coupled linearly or quadratically with a scalar field, by using an approach different from previous ones. We use Rindler frame, and integrate over the spacetime coordinates before over the momenta. In this way, the divergent problem previously encountered is avoided. We show that entanglement between the detectors can be created by coupling with the field, and is divergent only in the limit that the two detectors coincide in spacetime. For linear coupling, entanglement increases monotonically with the decrease of acceleration, as previously found, while for quadratic coupling, entanglement behaves non-monotonically, as noted for the first time.