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Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics

Simulation of decoherence in 1D systems, a comparison between distinguishable‐ and indistinguishable‐particle collisions

Fabrizio Buscemi, Paolo Bordone, Andrea Bertoni

Published Oct 12, 2007• 7 citations
Publisher

Abstract

Abstract We give a quantitative evaluation of the entanglement dynamics in scattering events between two electrons interacting via Coulomb potential in 1D systems, We apply a method, specifically designed for indistinguishable particles, based on the calculation of the von Neumann entropy of the system density matrix. From the timedependent numerical solution of the two‐particle wavefunction we evaluate the entanglement evolution for different spin configurations. The procedure allows to understand the mechanisms that govern entanglement creation and its connection with the characteristic physical parameters and initial conditions of the system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssc.200776509

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Abstract We give a quantitative evaluation of the entanglement dynamics in scattering events between two electrons interacting via Coulomb potential in 1D systems, We apply a method, specifically designed for indistinguishable particles, based on the calculation of the von Neumann entropy of the system density matrix. From the timedependent numerical solution of the two‐particle wavefunction we evaluate the entanglement evolution for different spin configurations. The procedure allows to understand the mechanisms that govern entanglement creation and its connection with the characteristic physical parameters and initial conditions of the system. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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.
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the linear entropy used to treat quantum entanglement in systems of nonidentical particles. Such a criterion is here applied to an electron-electron scattering in a two-dimensional system in order to perform a quantitative evaluation of the entanglement dynamics for various spin configurations and to compare the linear entropy with alternative approaches. Our numerical results show the dependence of the entanglement evolution upon the initial state of the system and its spin components. The differences with previous analyses accomplished by using the von Neumann entropy are discussed. The evaluation of the entanglement dynamics in terms of the linear entropy results to be much less demanding from the computational point of view, not requiring the diagonalization of the density matrix.
Abstract A quantitative analysis of the electron decoherence is performed in the case where an electron interacts with an environment consisting of a phonon bath at a given temperature T. In particular we study the decoherence in terms of the entanglement formation between the electron, initially described by a Gaussian wavepacket, and the environment by using the linear entropy written in terms of the Wigner function. In our work we evaluate, in a rigorous fully quantum mechanical approach, the electron‐phonon interaction using the Wigner‐function formalism. The problem is numerically solved for different time steps, up to the lowest order in the Neumann expansion. Our numerical procedure allows to analyze the system in different conditions and to understand the effect of the electron velocity and of the phonon momenta on the entanglement formation. Results are obtained in a one‐dimensional silicon system but they can be considered indicative of a more general behaviour. The Wigner function describing the electron and the phonon bath is evaluated by means of Neumann series, whose terms may be graphically represented by the so‐called Wigner paths. They are orbits in the Wigner phase‐space and are formed by ballistic free flights separated by scattering processes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Recently great attention has been addressed to the study of quantum correlations in systems of identical particles. Various definitions of entanglement for indistinguishable particles are present in the literature. Following Schliemann’s theory, here we perform a quantitative evaluation of the entanglement dynamics for electron-electron scattering in a 2D system in terms of the von Neumann entropy of the reduced one-particle density matrix. Our approach allows us to define the time of entanglement formation and to investigate the role of the space and spin degrees of freedom in the building up of quantum correlations.
Abstract Our understanding of the physical properties of quantum many‐particle systems relies normally on the identification of elementary excitations that can be considered as weakly interacting building blocks of the whole system. In systems characterized by the presence of strong interactions between the elementary components, like high‐temperature superconductors and related materials or like ultra‐cold atoms in optical lattices, well known theoretical techniques like mean‐field or perturbation theories fail. On the contrary, quantum Monte Carlo simulations allow to handle such systems in a “numerically exact” way. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract The calculation of the polarizability provides a method of calculating the collective‐modes excitation energies of an electronic system. However, the polarizability is a correlated quantity, thus demanding a major effort when Monte Carlo methods are used for its evaluation. Nevertheless, Quantum Monte Carlo results represent the benchmark in most many‐body physics. We applied a correlated Variational and Diffusion Monte Carlo scheme to a GaAs–AlGaAs quantum dot. Comparison with Raman scattering experiments and previous calculations is considerable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)