Uhlmann phase of coherent states and the Uhlmann-Berry correspondence

Abstract

We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases and present a conditional proof of the correspondence.

23 pages, no figure

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• Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
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• Mixed-state geometric phases of coherent and squeezed spin states
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems