Quantum entanglement in two spatial dimensions of rectangular quantum wires
Abstract
We calculate the quantum entanglement of groundstate electron in two spatial dimensions of rectangular GaAs/Al_{x}Ga_{1x}As quantum wires (QWRs) with varying the wire width and the confinement potential. The energy, von Neumman and linear entropies of groundstate electron show rapid convergences as a function of the standingwave basisset size. The nonzero entropies indicate the existence of quantum entanglement in two spatial dimensions. With increasing the wire width, the von Neumann and linear entropies increase rapidly until they reach a maximum after which, they monotonically decrease. The linear entropy is much smaller than the von Neumann entropy, however they show a totally similar entanglement behavior. The maximum entropies increase gradually with increasing the confining potential. When either of QWR dimensions becomes sufficiently large, the entropies are almost zero. At this case, the electron state can then be separated into a product of twodimensional components of the electron wave function. In addition, the probability density distributions have been investigated for a given set of values of the wire width and the confinement potential. The overlap of the barrier region lead to the electron entanglement in two spatial dimensions, which is proportional to the probability finding the electron in the corner of the barrier region.
 Publication:

Physica E LowDimensional Systems and Nanostructures
 Pub Date:
 April 2020
 DOI:
 10.1016/j.physe.2019.113948
 Bibcode:
 2020PhyE..11813948W
 Keywords:

 Spatial entanglement;
 von Neumann entropy;
 Linear entropy;
 Convergence;
 Quantum wire