# Direct observation of geometric phases using a three-pinhole interferometer

## TL;DR

This paper introduces a novel interferometric method to directly measure the geometric phase of a photon’s polarization states without requiring state evolution, phase calibration, or dynamical phase elimination.

## Contribution

A new three-pinhole interferometer technique for directly observing geometric phases based on triangle areas in interference patterns, bypassing traditional calibration steps.

## Key findings

- Successfully measures geometric phase via interference fringe analysis.
- The method is gauge-invariant and unaffected by local phase shifts.
- Eliminates need for state evolution and dynamical phase removal.

## Abstract

We present a method to measure the geometric phase defined for three internal states of a photon (polarizations) using a three-pinhole interferometer. From the interferogram, we can extract the geometric phase related to the three-vertex Bargmann invariant as the area of a triangle formed by interference fringes. Unlike the conventional methods, our method does not involve the state evolution. Moreover, the phase calibration of the interferometer and the elimination of the dynamical phase are not required. The gauge invariance of the geometric phase corresponds to the fact that the area of the triangle is never changed by the local phase shift in each internal state.