Quantum entanglement for two electrons in the excited states of helium-like systems

TL;DR

This study explores quantum entanglement in excited states of helium-like systems using wave functions and entropy measures, revealing how entanglement varies with nuclear charge and approaches theoretical limits at critical points.

Contribution

It introduces a method to calculate entanglement in excited helium-like systems using B-spline wave functions and analyzes entropy behavior across different nuclear charges.

Findings

Entanglement measures increase with nuclear charge Z.

At critical charge Z=1, entropies approach theoretical limits.

Results align with previous calculations for helium atom.

Abstract

The quantum entanglement for the two electrons in the excited states of the helium-like atom/ions is investigated using the two-electron wave functions constructed by the B-spline basis. As a measure of the spatial (electron-electron orbital) entanglement, the von Neumann entropy and linear entropy of the reduced density matrix are calculated for the 1s2s 1,3S excited states for systems with some selected Z values from Z=2 to Z=100. Results for the helium atom are compared with other available calculations. We have also investigated the entropies for these excited states when the nucleus charge is reduced from Z=2 to Z=1. At such a critical charge, all the singly-excited states of this system become unbound, and the linear entropies and the von Neumann entropies for the excited states are approaching 1/2 and 1, respectively, the limits for the entropies when one electron is bound to the nucleus, and the other being free.