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Journal of Physics Conference Series

An analysis of Helium resonant states in terms of entropy, information, complexity and entanglement measures

J. P. Restrepo Cuartas, José Luis Sanz‐Vicario

Published Apr 10, 2014• 2 citations
Publisher

Abstract

Shannon entropies and Fisher information calculated from one-particle density distributions and von Neumann and linear entropies (the latter two as a measure of entanglement) computed from the reduced one-particle density matrix are analyzed for the 1 , 3 s e , 1,3 P 0 and 1,3 D e Rydberg series of He doubly excited states below the second ionization threshold. We find that both Fisher information and entanglement measures are able to discriminate resonances pertaining to different (K,T) A series.

DOI
10.1088/1742-6596/488/15/152004

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Quantum entanglement for two electrons in the excited states of helium-like atom or ions is investigated using two-electron wave functions constructed in the B-spline basis. As a measure of 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 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 continuously 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 approach 1/2 and 1, respectively; the limits for the entropies when one electron is bound to the nucleus, and the other is free.
This work present analytical results for the position- and momentum-space information entropies, of the 1s2-state of helium-like ions, using different interaction potentials. The potentials that we used are the Yukawa potential (YP), and the exponential-cosine-screened Coulomb potential (ECSCP). The investigated studies allow us to relate the position-space information with the momentum-space information of Shannon and Fisher, as well as Shannon entropy power, and the Fisher-Shannon information product, through different famous relations. The calculation is done using one-electron charge density of entangled two-parameter wave function. On one hand, the results that are presented for fifteen members in the helium iso-electronic sequence demonstrate with precision the effect of correlation on bare charge distributions. On the other hand, it leads to some very important results for both the correlated and uncorrelated values of the informatic entropies. Analytical formula for the momentum-space information entropies are given. The effect of the nuclear charge and the screening parameter on the informatic expressions has been studied for both potentials. Detailed computational and numerical values and characteristics of these quantities are reported here for the first time. New inequality has been proposed with Fisher’s total value to measure the correlation of two electrons.
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In this work, we study the quantum entanglement for doubly excited resonance states in two-electron atomic systems such as the H - and Ps - ions and the He atom by using highly correlated Hylleraas type functions The resonance states are determined by calculation of density of resonance states with the stabilization method. The spatial (electron-electron orbital) entanglement entropies (linear and von Neumann) for the low-lying doubly excited states are quantified using the Schmidt-Slater decomposition method.