Nonlinear behavior of geometric phases induced by photon pairs

TL;DR

This paper investigates the nonlinear behavior of two-photon geometric phases in polarization states, revealing enhanced sensitivity for precision polarization measurements through interference fringe shifts.

Contribution

It demonstrates the nonlinear dependence of two-photon geometric phases on polarization, enabling more sensitive polarization change detection compared to single-photon phases.

Findings

Geometric phase shifts manifest as interference fringe shifts.

Two-photon geometric phase exhibits nonlinear variation with polarization.

Enhanced sensitivity to polarization changes is achieved.

Abstract

In this study, we observe the nonlinear behavior of the two-photon geometric phase for polarization states using time-correlated photons pairs. This phase manifests as a shift of two-photon interference fringes. Under certain arrangements, the geometric phase can vary nonlinearly and become very sensitive to a change in the polarization state. Moreover, it is known that the geometric phase for $N$ identically polarized photons is $N$ times larger than that for one photon. Thus, the geometric phase for two photons can become two times more sensitive to a state change. This high sensitivity to a change in the polarization can be exploited for precision measurement of small polarization variation. We evaluate the signal-to-noise ratio of the measurement scheme using the nonlinear behavior of the geometric phase under technical noise and highlight the practical advantages of this scheme.