Displaced photon helicity states: a quantum realization of Arago-Fresnel interference
Abstract
The laws of Arago and Fresnel relate the polarization of light to its capacity for interference. We investigate their quantum counterpart at the level of the fundamental helicity states of a single photon. To this end, we introduce displaced photon helicity states (DPHS), constructed by coherently displacing single-photon helicity eigenstates. The displacement bridges the microscopic spin degree of freedom and macroscopic polarization observables, enabling interference effects that would otherwise be inaccessible to isolated photons. We derive analytical expressions for the Stokes parameters associated with the interference between DPHS and coherent optical fields and show that opposite helicities generate distinct parameter dependences in the resulting fringe structure. The interference constitutes a quantum realization of Arago-Fresnel interference and permits the helicity of an unknown photon to be inferred from the Stokes response of the combined field. Beyond this application, DPHS generalize the framework of displaced nonclassical states from photon-number excitations to the helicity degree of freedom of light.
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BibTeX
@misc{zhang2026displaced,
title = {{Displaced photon helicity states: a quantum realization of Arago-Fresnel interference}},
author = {Yan Zhang and Xiang Liu and Hou Ian},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.28231},
eprint = {2607.28231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28231},
}
RIS
TY - UNPB
TI - Displaced photon helicity states: a quantum realization of Arago-Fresnel interference
AU - Yan Zhang
AU - Xiang Liu
AU - Hou Ian
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2607.28231
UR - https://arxiv.org/abs/2607.28231
AB - The laws of Arago and Fresnel relate the polarization of light to its capacity for interference. We investigate their quantum counterpart at the level of the fundamental helicity states of a single photon. To this end, we introduce displaced photon helicity states (DPHS), constructed by coherently displacing single-photon helicity eigenstates. The displacement bridges the microscopic spin degree of freedom and macroscopic polarization observables, enabling interference effects that would otherwise be inaccessible to isolated photons. We derive analytical expressions for the Stokes parameters associated with the interference between DPHS and coherent optical fields and show that opposite helicities generate distinct parameter dependences in the resulting fringe structure. The interference constitutes a quantum realization of Arago-Fresnel interference and permits the helicity of an unknown photon to be inferred from the Stokes response of the combined field. Beyond this application, DPHS generalize the framework of displaced nonclassical states from photon-number excitations to the helicity degree of freedom of light.
ER -