Transverse Entanglement of Biphotons

TL;DR

This paper introduces a new method to measure the full transverse entanglement of biphotons generated by SPDC, overcoming limitations of the Fedorov ratio by evaluating the first-order coherence, which directly relates to the Schmidt number.

Contribution

The authors develop a coherence-based approach that captures both phase and amplitude information, providing a complete measure of biphoton entanglement beyond intensity correlation methods.

Findings

The new method accurately quantifies the full transverse entanglement.

It theoretically corresponds to a direct measurement of the Schmidt number.

The approach works in both near and far field zones.

Abstract

We measure the transverse entanglement of photon pairs on their propagation from the near to the far field of spontaneous parametric downconversion (SPDC). The Fedorov ratio, depending on the widths of conditional and unconditional intensity measurements, is shown to be only able to characterize entanglement in the near and far field zones of the source. Therefore we also follow a different approach. By evaluating the first-order coherence of a subsystem of the state we can quantify its entanglement. Unlike previous measurements, which determine the Fedorov ratio via intensity correlations, our setup is sensitive to both phase and modulus of the biphoton state and thus always grants experimental access to the full transverse entanglement of the SPDC state. It is shown theoretically that this scheme represents a direct measurement of the Schmidt number.