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arXiv:quant-ph/0602127 · Physical Review A

Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems

Fabrizio Buscemi, Paolo Bordone, Andrea Bertoni

Published May 16, 2006• 53 citations
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Abstract

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.

DOI
10.1103/physreva.73.052312

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The dynamics and processes involved in particle-molecule scattering, including nuclear dynamics, are described and analyzed using various quantum information quantities throughout the different stages of the scattering. The main process studied and characterized with the information quantities is the interatomic Coulombic electronic capture, an inelastic process that can lead to dissociation of the target molecule. The analysis focuses on a one-dimensional transversely confined NeHe molecule model used to simulate the scattering between an electron ${e}^{\ensuremath{-}}(\text{particle})$ and a NeHe+{\text{NeHe}}^{+}NeHe+ ion (molecule). The time-independent Schr\"odinger equation is solved using the finite element method with a self-developed Julia package FEMTISE to compute potential energy curves and the parameters of the interactions between particles. The time-dependent Schr\"odinger equation is solved using the multiconfiguration time-dependent Hartree algorithm. The time-dependent electronic and nuclear probability densities are calculated for different electron incoming energies, evidencing elastic and inelastic processes that can be correlated to changes in von Neumann entropy, von Neumann mutual information, and Shannon mutual information. The expectation value of the position of the particles, as well as their standard deviations, are analyzed along the whole dynamics and related to the entanglement during the collision and after the process is over, thus highlighting the dynamics of entanglement generation. It is shown that the correlations generated in the collision are partially retained only when the inelastic process is active.