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Physics of Plasmas

Quantum entanglement for helium atom in the Debye plasmas

Y.-C. Lin, T. K. Fang, Y. K. Ho

Published Mar 1, 2015• 32 citations
Publisher

Abstract

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.

DOI
10.1063/1.4916064

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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.
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.
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 BBB-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 1sns1S1sn{s}^{1}S1sns1S states, with n=2n=2n=2--10, of the helium atom. The variation of the spatial entanglement with the nuclear charges Z=2Z=2Z=2--15 for the helium-like ions is reported. Results are compared with the existing predictions.
Abstract In this work we have performed state-of-the-art configuration-interaction (CI) calculations to determine the linear and von Neumann entanglement entropies for the helium-like systems with varying nuclear charge Z in the range . The focus of the work resides on determining accurate entanglement values for 2-electron systems with the lowest computational cost through compact CI-wave functions. Our entanglement results for the helium atom fully agree with the results obtained with higher quality wave functions of the Kinoshita type (Dehesa [5]). We find that the correlation energy is linearly related to the entanglement measures associated with the linear and von Neumann entropies of the single-particle reduced density matrizes, which sheds new light on the physical implications of entanglement in helium-like systems. Moreover, we report CI-wave-function-based benchmark results for the entanglement values for all members of the helium isoelectronic series with an accuracy similar to that of Kinoshita-type wave functions. Finally, we give parametric expressions of the linear and von Neumann entanglement measures for two-electron systems as Z varies from 1 to 10.
The thesis aims to study the applicability of techniques of Quantum Information theory to complex systems, like molecules and biomolecules. Recently, concepts of Quantum Information theory have been applied to the study of phenomena involving molecules, for instance the interaction light-biomolecules. In particular, the entanglement has been proposed to quantify the non-classicality of interactions. The computation of molecular structures and interactions, on the other hand, has been studied for decades mainly to understand reactions? kinetic and energetic characteristics. It is not straightforward to apply these methods to the computation of quantum correlations. We have therefore explored the computability of such effects using Quantum Information techniques. We started with the study of the electronic correlations in the Helium atom, that is the simplest non trivial case, in order to evaluate the computational problems and to develop approximate methods suitable to more complex systems. We start recalling the definition and basic properties of entanglement, as it is considered in Quantum Information theory. We illustrate how it can be measured and the difficulties one encounters when identical particles are involved, then we concentrate on the case of Helium in particular. In order to study the entanglement in Helium, we treat separately the singlet and the triplet configurations. The method we use consists in computing the reduced density matrix and then the entropy. The possible choices of coordinates, basis functions and computation strategies are discussed, together with their impact on the algorithms. The reduced, single-electron von Neumann and linear entropy for several low-energy eigenstates of Helium are computed by means of a simple configuration-interaction variational method.
Abstract In the quantized field formalism, using Kramers–Henneberger unitary transformation as the semi-classical counterpart of Block–Nordsieck transformation, the dynamics of entanglement during the low energy scattering processes in bi-partite systems at the presence of a laser beam fields are studied. The stationary-state Schrodinger equation for the quantum scattering process is obtained for such systems. Then, using partial wave analysis, we introduce a new form of entanglement fidelity considering the effect of high-intensity laser beam fields. The effective potential of hot quantum plasma including plasmon and quantum screening effects is used to obtain the entanglement fidelity ratio as a function of the laser amplitude, and plasmon and Debye length parameters for the elastic electron-ion collisions. It is shown that the plasma free electrons oscillations under interaction with laser beam fields improve the correlations between charged particles and consequently lead to the increase in the system entanglement.