Fate of entanglement between two Unruh-DeWitt detectors due to their motion and background temperature

Abstract: We investigate the fate of initial entanglement between two accelerated detectors with respect to an observer attached to one of the detectors. Both $(1+1)$ and $(1+3)$ spacetime dimensions are being considered here, with the detectors interacting with real massless scalar fields through monopole terms. The investigation is being performed for both non-thermal as well as thermal fields. In general, irrespective of the detectors moving in the same Rindler wedge or opposite wedges, increase of the field temperature reduces the initial entanglement. In all situations, degradation of entanglement is high for high acceleration $a_A$ of our observer. Interestingly, the degradation depends on the measure of initial entanglement. For $(1+1)$ dimensions, the degradation saturates for small values of $a_A$, whereas the same fluctuates in $(1+3)$ dimensions with the decrease of $a_A$. For motions in opposite Rindler wedges, a noticeable feature we observe in $(1+1)$ dimensions is that, depending on the strength of initial entanglement, there is a possibility of entanglement harvesting in the system for certain values of the observers' acceleration. However the same is absent in $(1+3)$ dimensions. The whole analysis is operationally different from earlier similar investigations. The thermal equilibrium is satisfied throughout the calculations here, by considering the Wightman functions with respect to the Rindler modes evaluated in the vacuum of Unruh modes, contrary to the use of Minkowski modes.