Electron decoherence in a semiconductor due to electron-phonon scattering



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)