Regensburg 2007 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 13: Poster 1

HL 13.61: Poster

Monday, March 26, 2007, 15:00–17:30, Poster A

Geometric spin transformation in quantum dot loops — •Burkhard Scharfenberger, Pablo San-Jose, and Gerd Schön — Institut für Theoretische Festkörperphysik, Universität Karlsruhe, 76128 Karlsruhe

Upon adiabatic variation of control parameters, the wave function of a quantum mechanical system, starting initially in an a non-degenerate eigenstate, acquires a Berry-phase purely dependending on the geometry of the choosen path in parameter-space [1]. In the case of k-fold degeneracies this Berry-phase is extended to a general U(k) transformation [2].
The inherent stability of such a geometric effect against dynamic perturbations has lead to proposals to employ it in the encoding and manipulation of quantum information [3]. We investigate the transformation of an electron spin when it is pumped adiabatically around a loop of N quantum dots in a 2 dimensional electron gas with finite spin-orbit interaction. In the absence of magnetic fields, the two (pseudo-)spin states form a degenerate subspace and the resulting rotation of the electron spin within this subspace depend on the ratio of loop-radius/spin orbit length. Thus, if the loop is comparable in size to the spin-orbit-length, arbitrary rotations become possible controlled by shape and size of the loop.

[1] M.V. Berry, Proc. R. Soc. Lond. A 392, 45 (1984)
[2] F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984)
[3] J.J Jones et al., Nature 403, 869 (2000)