Geometric Phases for Mixed States during Cyclic Evolutions

Abstract

The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the Aharonov and Anandan phase in the pure state case. Our definition is consistent with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85}, 2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the parallel transport condition. A comprehensive geometric interpretation is also given. It shows that the geometric phases for mixed states share the same geometric sense with the pure states.

9 pages, 1 figure

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Cited by in corpus (4)

• Geometric phase distributions for open quantum systems
• Observation of nonadditive mixed state phases with polarized neutrons
• Comment on "Geometric phases for mixed states during cyclic evolutions"
• Reply to "comment on Geometric phases for mixed states during cyclic evolutions"