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.

Research on quantum correlations and Uhlmann phase in two-fermion mixed state system

“…A German mathematician named Uhlmann [4,5], introduced an auxiliary system to purify the mixed state and then calculated parallel transport of the density matrix values to obtain the geometric phase of the mixed state, which is called Uhlamnn phase. To some extent, the Uhlmann phase is an extension of the Berry phase, except that the Uhlmann phase is obtained by parallel transport of the matrix values [6]. However, the physical meaning of parallel transport for matrix values and the specific relationship between Uhlmann phase and Berry phase are not clear.…”