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

Electron decoherence in a semiconductor due to electron‐phonon scattering

Fabrizio Buscemi, E. Cancellieri, Paolo Bordone, Andrea Bertoni, Carlo Jacoboni

Published Oct 12, 2007• 10 citations
Publisher

Abstract

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)

DOI
10.1002/pssc.200776541

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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)
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)
Abstract The new method for solving Wigner–Liouville's type equations and studying dynamics of quantum particles has been developed within the Wigner formulation of quantum statistical mechanics. This approach combines both molecular dynamics and Monte Carlo methods and computes traces and spectra of the relevant dynamical quantities. Considering, as an application, the quantum dynamics of an ensemble of interacting electrons in an array of random scatterers clearly demonstrates that the many‐particle interaction between the electrons can lead to an enhancement of the electrical conductivity. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Wigner trajectories in phase space provide a pictorial representation of the quantum evolution of a system of interest in the Wigner-function formulation of quantum mechanics with many analogies with the description of classical evolutions. The existence of Wigner trajectories has been discussed so far only for ballistic coherent electrons moving in an external potential profile. We prove in this paper the existence of Wigner paths that are defined also in the presence of electron-phonon coupling, and go over some interpretative problems related to Wigner trajectories. Wigner paths can be used to determine the evolution of the Wigner function in time during scattering processes. This general result opens new fields of application of the concept of Wigner function, mainly in connection with the numerical study of quantum transport in mesoscopic systems.
Abstract Localization of electron and ion states in a plasma is considered, applying the picture of a test particle in a dissipative environment. The plasma environment is represented by the dielectric function. For the reduced statistical operator a quantum master equation in Born‐Markov‐approximation can be used to quantify the influence of the dissipative background, which gives rise to decoherence and friction. We compare localization of ions due to collisional decoherence with the electronic part with screened interaction and localization by the thermal radiation field. The usual procedure to treat ions classically and electrons as quantum objects is supported by comparing the width of robust states and the mean distance in plasmas. (© 2007 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.
An analysis of the Wigner function for identical particles is presented. Four situations have been considered. i) A scattering process between two indistinguishable electrons described by a minimum uncertainty wave packets showing the exchange and correlation hole in Wigner phase space. ii) An equilibrium ensemble of N electrons in a one-dimensional box and in a one-dimensional harmonic potential showing that the reduced single particle Wigner function as a function of the energy defined in the Wigner phase-space tends to a Fermi distribution. iii) The reduced one-particle transport-equation for the Wigner function in the case of interacting electrons showing the need for the two-particle reduced Wigner function within the BBGKY hierarchy scheme. iv) The electron-phonon interaction in the two-particle case showing co-participation of two electrons in the interaction with the phonon bath.