Experimental Demonstration of the Unified Framework for the Mixed State Geometric Phase

TL;DR

This paper introduces and experimentally validates a unified framework for mixed state geometric phases, demonstrating the first measurement of Uhlmann's phase and its distinction from Sj"{o}qvist's phase.

Contribution

It presents a novel unified formalism for mixed state geometric phases and experimentally confirms its validity, including the first measurement of Uhlmann's phase.

Findings

Unified framework successfully encompasses both approaches.

Experimental measurement confirms the validity of the unified formalism.

Uhlmann's phase differs from Sj"{o}qvist's phase in experiments.

Abstract

Geometrical phases have been applied in virtually every major branch of physics and they play an important role in topology and knot theory in mathematics and quantum computation. However, most of the early works focus on pure quantum states which are very unrealistic and almost never occur in practice. The two existed definitions -Uhlmann's and Sj\"{o}qvist's- would result in different values for the geometric phase in general. The definition of geometric phase in mixed state scenario is still an open question. Here we present a unified framework for both approaches within one and the same formalism based on simple interferometry. We then present experimental results which confirm both approaches to mixed state geometric phase and clearly demonstrate that their unification is possible. Our experiments are furthermore the first such to measure Uhlmann's mixed state geometric phase and show in addition that it is different to the Sj\"{o}qvist's phase.