Regensburg 2002 – scientific programme

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TT: Tiefe Temperaturen

TT 8: Mesoskopische Systeme I

TT 8.9: Talk

Tuesday, March 12, 2002, 11:45–12:00, H20

Non-Abelian geometric phases in Josephson junction networks — •Jens Siewert¹, Lara Faoro², and Rosario Fazio³ — ¹Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany — ²Institute for Scientific Interchange (ISI) Foundation, Villa Gualino, I-10133 Torino, Italy — ³NEST INFM and Scuola Normale Superiore, I-56126 Pisa, Italy

It is well known that the state of a quantum system whose parameters undergo a cyclic adiabatic evolution acquires a (scalar) Berry phase. An even more interesting phenomenon occurs if the state is part of a degenerate subspace: cyclic parameter evolution corresponds in general to applying a unitary operation within the degenerate subspace to the state or, in other words, to matrices of phases [1]. It is a particular challenge to detect such non-Abelian holonomies in a macroscopic system. Here we discuss the possibility to obtain and detect them in circuits of small-capacitance Josephson junctions. Further we study possible applications such as charge transfer between superconducting islands and, in particular, holonomic quantum computation [2].
[1] F. Wilczek and A. Zee, Phys. Rev. Lett. 52, 2111 (1984).
[2] P. Zanardi and M. Rasetti, Phys. Lett. A 264, 94 (1999).