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Bargmann invariants and off-diagonal geometric phases for multilevel quantum systems: A unitary-group approach

Mukunda, N and Arvind, * and Chaturvedi, S and Simon, R (2002) Bargmann invariants and off-diagonal geometric phases for multilevel quantum systems: A unitary-group approach. In: Physical Review A (Atomic, Molecular, and Optical Physics), 65 (1). 012102/1-10.

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Abstract

We investigate the geometric phases and the Bargmann invariants associated with multilevel quantum systems. In particular, we show that a full set of ‘‘gauge-invariant’’ objects for an n-level system consists of n geometric phases and 1/2 (n-1)(n-2) algebraically independent four-vertex Bargmann invariants. In the process of establishing this result, we develop a canonical form for U(n) matrices that is useful in its own right. We show that the recently discovered ‘‘off-diagonal’’ geometric phases [N. Manini and F. Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analyzed in terms of the basic building blocks developed in this work. This result liberates the off-diagonal phases from the assumption of adiabaticity used in arriving at them.

Item Type: Journal Article
Additional Information: The DOI is currently only displayed. Copyright for this article belongs to American Physical Society (APS)
Keywords: Bargmann invariants;Gauge-invariant
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Date Deposited: 17 May 2004
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ernet.in/id/eprint/298

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