Harvesting Fermionic Field Entanglement in Schwarzschild Spacetime

Abstract: We explore entanglement harvesting using two Unruh-DeWitt (UDW) detectors linearly coupled to the scalar density of a massless spin-1/2 field in 1+1 Schwarzschild spacetime. We consider different vacua, including the Boulware, Hartle Hawking-Israel (HHI), and Unruh vacua, and investigate various configurations depending on the choice of 2-bein in the interaction Hamiltonian. We find that the transition rate of the static UDW detector exhibits the expected Planckian behavior in the HHI state, while the Unruh state leads to the Helmholtz free energy density of a bosonic or fermionic thermal bath corresponding to the static or conformal 2-bein respectively. Further, we observe that the anti-Hawking effect enhances the entanglement between the two detectors while the gravitational redshift and Hawking radiation decreases it. In particular, due to the presence of the anti-Hawking effect, the mutual information and concurrence near the event horizon can be non-zero even for static detectors with static 2-bein, which is in contrast with the case of scalar field. We also show that the near-horizon entanglement properties for static detectors in the HHI state have similar behaviour with those in Minkowski vacua for uniformly accelerated detectors in Rindler spacetime. Conclusions are discussed.