Measurement of heralded single-photon geometric phases by robust interferometric methods
Phys. Rev. A 113, 013740 – Published 29 January, 2026
DOI: https://doi.org/10.1103/x9lc-j8jb
Abstract
We present an interferometric method to measure geometric phases produced by the evolution of heralded single-photon polarization states. Our arrangement is based on a polarization interferometer and operates in a fully transmission configuration. This feature allows us to avoid the phase instabilities typical of interferometers operating with reflective components such as a Mach-Zehnder or a Michelson interferometer. In contrast with previous implementations where heralded single-photon geometric phases were measured using a polarimetric method for virtual interferometry, our arrangement uses real interferometry of heralded single-photon states; that is, along the optical setup the heralded single-photon states evolve due to transformations from which we extract the geometric phase. This is achieved by measuring the total phase acquired for a given evolution and compensating the dynamical phase to extract only the geometric contribution to the total phase. The presented method to measure geometric phases is not restricted to great-circle trajectories on the Poincaré sphere but works for any custom trajectory on it. We exhibit the versatility of our arrangement by measuring geometric phases acquired during the evolution of heralded single-photon states along three different trajectories that closely fit the predictions. In addition, we experimentally demonstrate the relationship between the geometric phase and the solid angle enclosed by the state trajectory on the Poincaré sphere. Finally, we test how the phase sign changes due to the change in the sense in which the state trajectory is traveled.
