Unruh-DeWitt detectors and entanglement: The anti–de Sitter space

We investigate entanglement harvesting in ${\mathrm{AdS}}_4$. Applying the general results of [K. K. Ng, R. B. Mann, and E. Martín-Martínez, Phys. Rev. D 97, 125011 (2018)], we consider two scenarios: one where two particle detectors are geodesic, with equal redshift; and one where both are static, at unequal redshift. As expected, at large AdS length $L$, our results approximate flat space. However at smaller $L$ we observe nontrivial effects for various field boundary conditions. Furthermore, in the static case we observe a novel feature of the entanglement as a function of switching time delay, which we attribute to different (coordinate) frequencies of the detectors. We also find an island of separability in parameter space, analogous to that observed in ${\mathrm{AdS}}_3$, to which we compare and contrast our other results. The variety of features observed in both cases suggest further study in other spacetimes.