  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.
