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Non-Abelian quantum holonomy of hydrogen-like atoms
School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
2011 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 84, no 3, 032111Article in journal (Refereed) Published
Abstract [en]

We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms, where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy, and find a relation between the phase of the whole system with corresponding marginal phases. Based on the result for the model system we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [Phys. Rev. Lett. 85, 2845 (2000)] are in general inequivalent.

Place, publisher, year, edition, pages
2011. Vol. 84, no 3, 032111
Keyword [en]
Quantum holonomy, spin-orbit coupling, hydrogen-like atoms, quantum entanglement
National Category
Physical Sciences Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
URN: urn:nbn:se:uu:diva-149239DOI: 10.1103/PhysRevA.84.032111ISI: 000295005900001OAI: oai:DiVA.org:uu-149239DiVA: diva2:404107
Funder
Swedish Research Council
Note

Additional address (E. Sjöqvist): Centre for Quantum Technologies, NUS, Singapore

Available from: 2011-03-16 Created: 2011-03-16 Last updated: 2017-12-11Bibliographically approved

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Sjöqvist, Erik

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