Entanglement and spin squeezing in the two - atom Dicke model

We analyze the relation between the entanglement and spin-squeezing parameter in the two-atom Dicke model and identify the source of the discrepancy recently reported by Banerjee and Zhou et al that one can observe entanglement without spin squeezing. Our calculations demonstrate that there are two criteria for entanglement, one associated with the two-photon coherences that create two-photon entangled states, and the other associated with populations of the collective states. We find that the spin-squeezing parameter correctly predicts entanglement in the two-atom Dicke system only if it is associated with two-photon entangled states, but fails to predict entanglement when it is associated with the entangled symmetric state. This explicitly identifies the source of the discrepancy and explains why the system can be entangled without spin-squeezing. We illustrate these findings in three examples of the interaction of the system with thermal, classical squeezed vacuum and quantum squeezed vacuum fields. Entanglement, the most intriguing property of multiparticle systems (or qubits), is one of the key problems in quantum physics and has been the subject of active research in recent years [1]. It describes a multiparticle system which has the astonishing property that the results of a measurement on one particle cannot be specified independently of the results of measurements on the other particles. Therefore, the generation of entanglement between atoms is fundamental not only to demonstrate quantum nonlocality but also would constitute a valuable resource in the fields of quantum information processing, cryptography and quantum computation [2]. In this context, it is not surprising that a tremendous number of theoretical proposals have been made to produce entanglement between separate particles [3]. Several different criteria have been proposed to identify entanglement in two-particle systems, but no definite measure