Classical-to-quantum transfer of geometric phase for non-interferometric phase measurement and manipulation of quantum state

TL;DR

This paper introduces a non-interferometric method to transfer and measure the geometric phase from a classical pump beam to entangled photons, enabling precise quantum state control and manipulation.

Contribution

It demonstrates a novel transfer of classical geometric phase to quantum states using a Sagnac interferometer, facilitating phase control without interferometry.

Findings

Geometric phase controls coincidence counts and entanglement visibility.

Sinusoidal modulation of Bell's parameter and state fidelity observed.

Transitions between orthogonal Bell states achieved through phase tuning.

Abstract

The geometric phase, originating from the cyclic evolution of a state, such as polarization on the Poincar\'e sphere, is typically measured through interferometric approaches that often include unwanted contributions from the dynamic phase. Here, we present a non-interferometric technique based on quantum correlation of pair photons to measure the geometric phase of a classical beam. The transfer of geometric phase of the classical pump beam arising from the cyclic evolution of its polarization state on the Poincar\'e sphere onto the polarization-entangled pair photons generated via spontaneous parametric down-conversion in a Sagnac interferometer enables easy control over the quantum state. Characterization of the generated quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum state tomography, and fidelity in close agreement with theoretical predictions. We observe sinusoidal modulation of the Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell-like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric phase-based quantum gates, and compensating unwanted phase acquired by the quantum state on propagation.