ar X iv : q ua nt - p h / 04 07 03 2 v 3 1 7 A pr 2 00 7 epl draft Casimir - Polder potentials as entanglement probe

PACS 03.65.Ud – Entanglement and quantum nonlocality PACS 03.67.Mn – Entanglement production, characterization, and manipulation PACS 42.50.Dv – Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements Abstract.-We have considered the interaction of a pair of spatially separated two-level atoms with the electromagnetic field in its vacuum state and we have analyzed the amount of entangle-ment induced between the two atoms by the non local field fluctuations. This has allowed us to characterize the quantum nature of the non local correlations of the electromagnetic field vacuum state as well as to link the induced quantum entanglement with Casimir-Polder potentials. The zero-point fluctuations of the vacuum state of the electromagnetic field are characterized by strong non local correlations [1–3] which are at the origin of phenomena like Casimir-Polder forces [4, 5]. An interesting open problem is the possibility to characterize the quantum nature of such non local correlations. So far most of the efforts done towards this direction have focused on violations of suitable Bell's inequalities by the vacuum state fluctuations [6]. However a direct experimental detection of such inequalities violation for the vacuum state is awkward. In this letter we shall take a somewhat different approach. It is a well known fact that when two quantum subsystems, e.g. two atoms, interact with a common bath, they become entangled (see for instance [7]). Such a pair of subsystems can therefore be used as a probe of the non local vacuum field fluctuations. In other words the quantum nature of such fluctuations can be characterized by the amount of entanglement induced between the two spatially separated probe atoms. Some interesting contributions in this direction have already appeared in literature [8]. In the following we shall quantify the entanglement induced between the two probe atoms by means of the concurrence [9] as this is amenable to a straightforward physical interpretation [10]. Indeed we will show that the concurrence turns out to be linked to the Casimir-Polder potentials. Casimir-Polder forces are long-range interactions between neutral atoms or molecules arising from their interaction with the common electromagnetic radiation field in its vacuum state. For atoms in the ground state the Casimir-Polder potential behaves as R −6 for interatomic distances smaller than a characteristic distance of the order of an appropriate average of the atomic transition wavelengths-but large enough to neglect any overlap between the electron wavefunctions-and as R −7 …