Volume 78, Number 6, June 2007
Article Number 60004
Number of page(s) 6
Section General
Published online 29 May 2007
EPL, 78 (2007) 60004
DOI: 10.1209/0295-5075/78/60004

Non-Abelian generalization of off-diagonal geometric phases

D. Kult1, J. Åberg2 and E. Sjöqvist1

1  Department of Quantum Chemistry, Uppsala University - Box 518, Se-751 20 Uppsala, Sweden
2  Centre for Quantum Computation, Department of Applied Mathematics and Theoretical Physics, University of Cambridge - Wilberforce Road, Cambridge CB3 0WA, UK

received 12 March 2007; accepted in final form 2 May 2007; published June 2007
published online 29 May 2007

If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.

03.65.Vf - Phases: geometric; dynamic or topological.

© Europhysics Letters Association 2007