Inverse Scattering for Single Photons in Quantum Optics
Abstract
We study inverse problems for a time-harmonic one-photon model describing the interaction of a single photon with a medium of stationary two-level atoms. After time-harmonic reduction, the unknown compactly supported atomic density appears as a frequency-dependent potential in a scattering equation for the half Laplacian. We prove high-frequency uniqueness results for three types of intensity data: source-driven measurements, renormalized far-field intensity measurements, and phaseless far-field measurements obtained from coherent superpositions of incident plane waves. In each case, the corresponding data, given at all sufficiently large frequencies, determine the atomic density uniquely; the source-driven result requires a geometric visibility condition on the source and observation sets.
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BibTeX
@misc{covi2026inverse,
title = {{Inverse Scattering for Single Photons in Quantum Optics}},
author = {Giovanni Covi and Matti Lassas and Medet Nursultanov and Lauri Oksanen and Mikko Salo and John C. Schotland},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03726},
eprint = {2609.03726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03726},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inverse Scattering for Single Photons in Quantum Optics
AU - Giovanni Covi
AU - Matti Lassas
AU - Medet Nursultanov
AU - Lauri Oksanen
AU - Mikko Salo
AU - John C. Schotland
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03726
UR - https://arxiv.org/abs/2609.03726
AB - We study inverse problems for a time-harmonic one-photon model describing the interaction of a single photon with a medium of stationary two-level atoms. After time-harmonic reduction, the unknown compactly supported atomic density appears as a frequency-dependent potential in a scattering equation for the half Laplacian. We prove high-frequency uniqueness results for three types of intensity data: source-driven measurements, renormalized far-field intensity measurements, and phaseless far-field measurements obtained from coherent superpositions of incident plane waves. In each case, the corresponding data, given at all sufficiently large frequencies, determine the atomic density uniquely; the source-driven result requires a geometric visibility condition on the source and observation sets.
ER -