Controlling spatial entanglement in interacting two electrons trapped in superlattices

Entanglement properties of two-electron systems have been the subject of considerable interest in recent years. Solutions to the Hamiltonian in few-electron systems require special techniques to evaluate computationally demanding Coulomb integrals. Here we develop a fully variational action integral formalism to obtain the coordinate space wavefunctions for two electrons trapped in semiconductor superlattices. The entanglement in such systems have contributions from not only the spin part but also from the spatial correlations of the confining potential. The latter contribution has been neglected in most considerations. We show that the probability distributions of electrons largely deviate from those of the widely-used slater-determinant representation. We demonstrate that the entanglement in such systems can be controlled by varying physical parameters, and by applying external fields. The entanglement resonances associated with anti-crossings of eigenstates are displayed for the first time, and these can be manipulated through geometric changes and by the applied electric field.