Spatial Entanglement Between Electrons Confined to Rings

Abstract

We study systems of two and three electrons confined to circular rings. The electrons are considered spinless, and we assume that one electron occupies a single ring. We use the framework of such a model to calculate the linear entropy and, thus, the spatial entanglement between the confined electrons. The geometry of the problem for the case of two electrons incorporates situations in which the planes of the two rings form an arbitrary angle with each other. The resulting Schrödinger’s equation is solved numerically with very high accuracy by means of the exact diagonalization method. We compute the ground state energy and entanglement for all configurations under consideration. We also study the case of three electrons confined to identical, parallel and concentric rings which are located in three different equidistant planes. The vertically separated system of rings is allowed to gradually merge into a single ring geometry, which would represent the equivalent system of a ring with three electrons. It is observed that the system of three electrons gives rise to a richer structure, as the three rings merge into a single one.