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Journal of Physics Conference Series

Quantification of entanglement entropies for doubly excited resonance states in two-electron atomic systems

Y. K. Ho, Chien-Hao Lin

Published Sep 7, 2015• 3 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/635/9/092025

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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.
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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.
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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.
ABSTRACT: In the present work, we have computed the entanglement between the electronic and nuclear motions in two molecular model systems: the one-dimensional hydrogen molecular ion (H2+) and the Shin-Metiu model, considering the molecules as a bipartite systems: electron and nuclear motion. For that purpose, we have computed the Born-Oppenheimer and non-Born-Oppenheimer (Born-Huang) wave function in terms of the Fourier Grid Hamiltonian basis that expands both the electronic and nuclear wave functions. Also, according to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, there is a much shorter but equivalent expansion in terms of the Schmidt bases for the electronic and nuclear sub-spaces. In these models of distinguishable coupled particles we have shown that the entanglements contents do not increase monotonically with the excitation energy. In the hydrogen molecular ion and in the ShinMetiu model, the entanglements contents for each Born-Oppenheimer electro-nuclear state is quantified through the von-Neumann and linear entropies and we have shown that entanglement serves as a witness of distinguishability of nuclear states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes.