Coincidence landscapes for polarized bosons

TL;DR

This paper demonstrates that including polarization in multiphoton interferometry expands the theoretical framework from SU(m) to SU(2m), simplifying the understanding of coincidence landscapes and elucidating the triad phase as a specific SU(6) interferometry case.

Contribution

It introduces a unified SU(2m) framework for polarization-inclusive multiphoton interferometry, clarifying the role of the triad phase within this context.

Findings

Coincidence landscapes are explained by immanants in SU(2m) interferometry.

The triad phase corresponds to SU(6) interferometry with three photons.

Polarization inclusion simplifies the theoretical description of multiphoton interference.

Abstract

Passive optical interferometry with single photons injected into some input ports and vacuum into others is enriched by admitting polarization, thereby replacing the scalar electromagnetic description by a vector theory, with the recent triad phase being a celebrated example of this richness. On the other hand, incorporating polarization into interferometry is known to be equivalent to scalar theory if the number of channels is doubled. We show that passive multiphoton $m$ channel interferometry described by SU($m$) transformations is replaced by SU($2m$) interferometry if polarization is included and thus that the multiphoton coincidence landscape, whose domain corresponds to various relative delays between photon arrival times, is fully explained by the now-standard approach of using immanants to compute coincidence sampling probabilities. Consequently, we show that the triad phase is manifested simply as SU(6) interferometry with three input photons, with one photon in each of three different input ports. Our analysis incorporates passive polarization multichannel interferometry into the existing scalar-field approach to computing multiphoton coincidence probabilities in interferometry and demystifies the triad phase.