Quantum entanglement of nontrivial spacetime topology

We analyze the entanglement behaviors for two accelerating atoms interacting with a massless scalar field in the cosmic string spacetime. We calculate different correlation functions for different spacetime topologies. We find that entanglement behaviors are determined by the vacuum fluctuation, two-atom distance, acceleration and nontrivial spacetime topology. It is shown that great two-atom distance and acceleration have negative effect on quantum entanglement. The existence of string has profound impact on the atom-field interaction system and the entanglement behaviors. When deficit angle parameter ν=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu =1$$\end{document} and atoms are far away from the string, the entanglement behaviors are the same with that of Minkowski spacetime. Our analysis about entanglement behaviors in cosmic string spacetime in principle is beneficial to sense the cosmic string spacetime topology structure and property, and discriminate the cosmic string spacetime and Minkowski spacetime. Besides, we also discuss the Unruh thermal effect in the cosmic string spacetime.