Enhancement of Harvesting Vacuum Entanglement in Cosmic String Spacetime

Abstract

We analyze the entanglement generation in a pair of qubits that experience the vacuum fluctuations of a scalar field in the Cosmic String spacetime. The qubits are modeled as Unruh-DeWitt detectors coupled to a massless scalar field. We introduce a Heisenberg $XY$-interaction between the qubits that enhances the generation of quantum correlations. It is supposed that the qubits begin at a general mixed state described by a density operator with no entanglement while the field stays at its vacuum state. In this way, we find the general properties and conditions to create entanglement between the qubits by exploiting the field vacuum fluctuations. We quantify the qubits entanglement using the Negativity measure based on the Peres-Horodecki positive partial transpose criterion. We find that the Cosmic String would increase the entanglement harvesting when both qubits are near the Cosmic String. When the qubits locations are far from the Cosmic String we recover the usual results for Minkowski space. The Heisenberg $XY$-interaction enhance the entanglement harvesting irrespective of the coupling nature (ferromagnetic or anti-ferromagnetic). When the qubits are far apart from each other we find a maximum entanglement harvesting at the resonance points between the Heisenberg coupling constant and the qubits energy gap.