10 - Entanglement Between Atom Ensembles

Summary

This chapter introduces the notion of entanglement, methods of detection, and various types of two atomic ensemble entangled states. Bipartite The bipartite system constitutes is the simplest and most straightforward way of understanding entanglement, where there is a well-developed theory of detecting and quantifying it. We discuss how von Neumann entropy and negativity are two simple and powerful quantifiers of entanglement in pure and mixed systems, respectively. In the absence of a way to topographically reconstruct the density matrix, other correlation-based entanglement criteria are important practically, since they only involve the measurement of some key correlations. Various approaches to this are introduced, such as the Duan--Giedke--Cirac--Zoller criterion, Hillery--Zubairy criteria, entanglement witness approaches, and covariance matrices. Finally, two types of squeezed states for two atomic ensembles are introduced, : namely the one-axis two-spin and two-axis two-spin squeezed states are introduced.