Experimental demonstration of a unified framework for mixed-state geometric phases

¹ Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China - Hefei, Anhui 230026, PRC
² Department of Physics and Shanghai Key Laboratory for Magnetic Resonance, East China Normal University Shanghai 200062, PRC
³ Fakultät Physik, Technische Universität Dortmund - 44221 Dortmund, Germany, EU
⁴ Department of Physics and Astronomy, University of Leeds - Leeds LS2 9JT, UK, EU
⁵ Department of Physics, National University of Singapore - 2 Science Drive, Singapore

^a shmj@ustc.edu.cn
^b djf@ustc.edu.cn

Received: 30 January 2011
Accepted: 17 March 2011

Abstract

Geometric phases have been found in every major branch of physics and play an important role in mathematics and quantum computation. Here, we unify two proposed definitions of the geometric phase in mixed states —Uhlmann's phase and Sjöqvist's phase— in a new formalism based on interferometry and further provide an experimental demonstration in NMR. This is also the first experimental measurement of Uhlmann's geometric phase.