Berlin 2008 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 17: Poster I
DY 17.11: Poster
Tuesday, February 26, 2008, 16:00–18:00, Poster C
Decoherence in the central spin model (Gaudin model) — Michael Bortz1, •Christian Schneider2, Joachim Stolze2, and Robert Stübner2 — 1Fachbereich Physik, TU Kaiserslautern, Germany — 2Institut für Physik, TU Dortmund, Germany
The Gaudin (or central spin) model consists of a single spin-1/2 coupled to a bath of independent spins-1/2 by exchange interactions. The model may be used to describe the decoherence of an electron spin quantum bit in a quantum dot which is coupled to many nuclear spins by hyperfine interactions. In general the interactions are inhomogeneous, I.e. each bath spin couples to the central spin with a different strength. For isotropic (Heisenberg-like) couplings the energy eigenstates and eigenvalues may be determined by the Bethe Ansatz (BA). A general formula for the time dependence of the central spin polarization can be derived from the BA. In the special case of homogeneous couplings the model may be diagonalized directly (I.e. without the BA) even for uniaxially anisotropic (XXZ-type) couplings. We develop strategies for finding the necessary BA quantum numbers numerically. Then we discuss the behavior of the central spin for homogeneous and inhomogeneous couplings. We also consider different types of initial states, varying in spin polarization and degree of entanglement.