Entanglement indicators for quantum optical fields: three-mode multiport beamsplitters EPR interference experiments

TL;DR

This paper extends entanglement detection methods to three-mode multiport interferometric experiments in quantum optics, demonstrating their effectiveness with bright squeezed vacuum states and highlighting the advantages of rate-based indicators over intensity-based ones.

Contribution

It introduces new entanglement conditions for three-mode multiport beam splitter setups and shows their violation with bright squeezed vacuum states, emphasizing the utility of rate-based measurements.

Findings

Rate-based entanglement indicators outperform intensity-based ones.

Bright squeezed vacuum states violate the proposed entanglement conditions.

Multiport interferometers enable EPR-like correlations in photon numbers.

Abstract

We generalize a new approach to entanglement conditions for light of undefined photons numbers given in [Phys. Rev. A {\bf 95}, 042113 (2017)] for polarization correlations to a broader family of interferometric phenomena. Integrated optics allows one to perform experiments based upon multiport beamsplitters. To observe entanglement effects one can use multi-mode parametric down-conversion emissions. When the structure of the Hamiltonian governing the emissions has (infinitely) many equivalent Schmidt decompositions into modes (beams), one can have perfect EPR-like correlations of numbers of photons emitted into "conjugate modes" which can be monitored at spatially separated detection stations. We provide entanglement conditions for experiments involving three modes on each side, and three-input-three-output multiport beamsplitters, and show their violations by bright squeezed vacuum states. We show that a condition expressed in terms of averages of observed rates is a much better entanglement indicator than a related one for the usual intensity variables. Thus the rates seem to emerge as a powerful concept in quantum optics, especially for fields of undefined intensities.