The relationship between quantum entanglement and energy in two-electrons system

A.P. MAJTEY; A.R. PLASTINO; J.S. DEHESA

Jornada; V Jornadas de Jóvenes Investigadores en Física Atómica y Molecular; 2012

The entanglement properties of two-electron atomic systems have been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, focusing on numerical computations on particular states of systems such as Helium, or on analytical studies of model-systems such as the Moshinsky atom. Some general trends are beginning to emerge from these studies: the amount of entanglement tends to increase with energy and, in the case of excited states, entanglement does not necessarily tend to zero in the limit of vanishing interaction between the two constituting particles [1,2]. A physical explanation of these properties, shared by the different two-electrons models investigated so far, is still lacking. It has recently been suggested that these features could be due to the particular entanglement measure employed [3]. As a first step towards an explanation, we consider here a perturbative approach to the analysis of entanglement in two-electrons models that sheds new light on the physical origin of the aforementioned features and on their universal character. In particular, this approach clarifies the fact that the second property mentioned above is independent of the entanglement measure used. In the case of the Moshinky model, we also give an upper bound for the amount of entanglement in the limit of vanishing interaction in terms of the total energy of the system [4]