Interferometric and Uhlmann phases of mixed polarization states

TL;DR

This paper explores the theoretical and experimental aspects of interferometric and Uhlmann phases in partially polarized light, demonstrating their relationship and dependence on polarization degree through Mach-Zehnder interferometry with different modulation techniques.

Contribution

It introduces the concept of relative Uhlmann phase, links it to the interferometric phase in nonunitary evolution, and experimentally verifies these phases using specific optical modulation setups.

Findings

Interferometric phase equals the relative Uhlmann phase in the rotating QWP setup.

Both phases oscillate with the QWP angle and increase with polarization degree.

Electric field dependencies of phases are evaluated using the orientational Kerr effect theory.

Abstract

In our investigation into the effects of the degree of polarization in modulation of partially polarized light we assume general settings of the interferometry of partially polarized lightwaves and perform theoretical analysis of the Uhlmann and the interferometric phases. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferometer, two different dynamical regimes of light modulation are experimentally studied: (a) modulation of the input light by the rotating quarter-wave plate (QWP); and (b) modulation of the testing beam by a birefringent plate with electrically controlled anisotropy represented by the deformed-helix ferroelectric liquid crystal (DHFLC) cell. In the setup with the rotating QWP, the interferometric phase is found to be equal to the relative Uhlmann phase. Experimental and theoretical results being in excellent agreement both show that this phase is an oscillating function of the QWP angle and increases with the degree of polarization. For modulation by the DHFLC cell, the data derived from our electro-optic measurements are fitted using the theory of the orientational Kerr effect in FLCs. This theory in combination with the results of fitting is used to evaluate electric field dependencies of the interferometric and the Uhlmann phases.