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 $1sn{s}^{1}S$ 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.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 $1sn{s}^{1}S$ 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.

Physical Review AFeb 13, 201357 citations

Quantum Entanglement in Electron Optics

N. Chandra, R. Ghosh

Springer series on atomic, optical, and plasma physicsMar 15, 201213 citations

Spatial entanglement in two-dimensional artificial atoms

Dung Ngoc Pham, Sathwik Bharadwaj, L. R. Ram‐Mohan

Semiconductor quantum dots (QDs) are one of the leading candidates for realizable qubits, as well as for many other advances in quantum computing and quantum communication. The spatial overlapping of wavefunctions describing each single electron in these nanoscale devices results in tunable spatial entanglement. In this article, we explore the case of two electrons in two-dimensional double quantum dot systems. We compute the two-particle wavefunction through a variational method combined with Hermite finite elements and study the spatial entanglement of electrons. We show that symmetry in the geometry of the double quantum dots plays a role in obtaining optimal entanglement, while a broken symmetry can lead to additional resonances in entanglement that are associated with the crossings of states. We also show that one can finely tune the level of spatial entanglement by altering the geometry of the quantum dots or by applying external fields, which corresponds to an “entanglement spectroscopy.” Finally, we study how impurities in the potential profile of the QDs affect the level of entanglement.Semiconductor quantum dots (QDs) are one of the leading candidates for realizable qubits, as well as for many other advances in quantum computing and quantum communication. The spatial overlapping of wavefunctions describing each single electron in these nanoscale devices results in tunable spatial entanglement. In this article, we explore the case of two electrons in two-dimensional double quantum dot systems. We compute the two-particle wavefunction through a variational method combined with Hermite finite elements and study the spatial entanglement of electrons. We show that symmetry in the geometry of the double quantum dots plays a role in obtaining optimal entanglement, while a broken symmetry can lead to additional resonances in entanglement that are associated with the crossings of states. We also show that one can finely tune the level of spatial entanglement by altering the geometry of the quantum dots or by applying external fields, which corresponds to an “entanglement spectroscopy.” Finally, we study how impurities in the potential profile of the QDs affect the level of entanglement.

Journal of Applied PhysicsFeb 8, 20241 citation

Quantum entanglement in a soluble two-electron model atom

R. J. Yaüez, Angel Ricardo Plastino, J. S. Dehesa

The European Physical Journal DNov 6, 200976 citations

Entanglement and density-functional theory: Testing approximations on Hooke’s atom

J. P. Coe, Anthony Sudbery, Irene D’Amico

We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be exactly calculated. We analyze how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results to the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are also considered.We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be exactly calculated. We analyze how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results to the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are also considered.

arXiv:0712.3819Physical Review BMay 22, 200898 citations

Quantum entanglement in an interacting electron gas

S. Hamieh, Haitham Zaraket

The European Physical Journal DAug 4, 20094 citations

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

1sn{s}^{1}S

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.