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.
In the present work, we present an investigation on quantum entanglement of the two-electron helium atom immersed in weakly coupled Debye plasmas, modeled by the Debye-Hückel, or screened Coulomb, potential to mimic the interaction between two charged particles inside the plasma. Quantum entanglement is related to correlation effects in a multi-particle system. In a bipartite system, a measurement made on one of the two entangled particles affects the outcome of the other particle, even if such two particles are far apart. Employing wave functions constructed with configuration interaction B-spline basis, we have quantified von Neumann entropy and linear entropy for a series of He 1,3Se and 1,3Po states in plasma-embedded helium atom.
We perform the quantitative evaluation of the entanglement dynamics in scattering events between two indistinguishable electrons interacting via the Coulomb potential in one- and two-dimensional semiconductor nanostructures. We apply a criterion based on the von Neumann entropy and the Schmidt decomposition of the global state vector suitable for systems of identical particles. From the time-dependent numerical solution of the two-particle wave function of the scattering carriers we compute their entanglement evolution for different spin configurations: two electrons with the same spin, with different spin, and singlet and triplet spin states. The procedure allows us to evaluate the mechanisms that govern entanglement creation and their connection with the characteristic physical parameters and initial conditions of the system. The cases in which the evolution of entanglement is similar to the one obtained for distinguishable particles are discussed.
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.
Based on the correlated ground-state wave function of an exactly solvable interacting one-dimensional two-electron model Hamiltonian we address the switch-off of confining and interparticle interactions to calculate the exact time-evolving wave function from a prescribed correlated initial state. Using this evolving wave function, the time-dependent pair probability function $\mathcal{R}({x}_{1},{x}_{2},t)\ensuremath{\equiv}{n}_{2}({x}_{1},{x}_{2},t)/[n({x}_{1},t)\phantom{\rule{0.16em}{0ex}}n({x}_{2},t)]$ is determined via the pair density
n2(x1,x2,t) and single-particle density
n(x,t). It is found that $\mathcal{R}(0,0,t=\ensuremath{\infty})=\mathcal{R}(0,0,t=0)>1$, and
R(x1,x2,t∗)=1 at a finite
t∗ for $\ensuremath{\Lambda}\ensuremath{\ne}0$ interparticle interaction strength in the initial two-electron model. By expanding
n(x,t) in an infinite sum of closed-shell products of time-dependent normalized single-particle states and time-dependent occupation numbers ${P}_{k}(\ensuremath{\Lambda},t)$, the von Neumann entropy $S(\ensuremath{\Lambda},t)=\ensuremath{-}{\ensuremath{\sum}}_{k=0}^{\ensuremath{\infty}}{P}_{k}(t)\mathrm{ln}{P}_{k}(t)$ is calculated as well. The such-defined information entropy is zero at ${t}^{*}(\ensuremath{\Lambda})$ and its maximum in time is $S(\ensuremath{\Lambda},t=\ensuremath{\infty})=S(\ensuremath{\Lambda},t=0)$.
Recently, there has been considerable interest in investigating quantum entanglement in two-electron systems, such as two-electron model atoms and quantum dots. In this work, the quantum entanglement of the helium atom and helium-like ions are explored using the two-electron wave functions constructed by the
B-spline basis. As a measure of the spatial entanglement, the linear entropy of the reduced density matrix is investigated for the ground state and the singlet excited
1sns1S states, with
n=2--10, of the helium atom. The variation of the spatial entanglement with the nuclear charges
Z=2--15 for the helium-like ions is reported. Results are compared with the existing predictions.