Single-shot coherent process tomography and mid-infrared polarimetry with undetected photons
Abstract
Measurements with undetected photons infer properties of a probe beam that is never detected, transferring mid-infrared information onto silicon-friendly wavelengths. Tomography in this paradigm has so far relied on switched settings or scanned phases, referenced across a drift-sensitive campaign; no protocol reads all Jones parameters from one frame. We show that a folded nonlinear interferometer with a diagonally pumped crossed-crystal source performs coherent process tomography of the undetected beam in a single spectrometer frame: it reconstructs all seven parameters of the beam's round-trip Jones matrix, the coherent part of the channel. Birefringent group-delay walk-off, normally a calibration nuisance, acts as a frequency multiplexer: each Jones-matrix element is assigned its own carrier, a spectral fringe period paired with a detector port. Because the multiplexing exploits the down-conversion bandwidth rather than merely tolerating it, a single Fourier transform per detector trace returns all four moduli and all three relative phases across that bandwidth, i.e., the full round-trip Jones spectrum up to a global phase, with no scan or setting change (after a one-time reference frame). Simultaneity makes every relative phase immune to common-mode drift, and a dark carrier, a self-interference term that unitarity forces to vanish, provides a built-in null test. For realistic parameters of a periodically poled KTP source the scheme yields wavelength-resolved mid-infrared polarimetry across 3.5-4.2 microns (~80 spectral points per Jones element) on a silicon camera, extending to depth-resolved Jones matrices, i.e., polarization-sensitive optical coherence tomography with undetected photons. A Fisher-information analysis, the first we are aware of in undetected-photon tomography, sets the precision budget and compares delay multiplexing to sequential protocols at equal photon number.
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BibTeX
@misc{zeja2026singleshot,
title = {{Single-shot coherent process tomography and mid-infrared polarimetry with undetected photons}},
author = {Marthe Zeja and Wen-Zhe Yan and Zhibo Hou and Sven Ramelow},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31043},
eprint = {2609.31043},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31043},
}
RIS
TY - UNPB
TI - Single-shot coherent process tomography and mid-infrared polarimetry with undetected photons
AU - Marthe Zeja
AU - Wen-Zhe Yan
AU - Zhibo Hou
AU - Sven Ramelow
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31043
UR - https://arxiv.org/abs/2609.31043
AB - Measurements with undetected photons infer properties of a probe beam that is never detected, transferring mid-infrared information onto silicon-friendly wavelengths. Tomography in this paradigm has so far relied on switched settings or scanned phases, referenced across a drift-sensitive campaign; no protocol reads all Jones parameters from one frame. We show that a folded nonlinear interferometer with a diagonally pumped crossed-crystal source performs coherent process tomography of the undetected beam in a single spectrometer frame: it reconstructs all seven parameters of the beam's round-trip Jones matrix, the coherent part of the channel. Birefringent group-delay walk-off, normally a calibration nuisance, acts as a frequency multiplexer: each Jones-matrix element is assigned its own carrier, a spectral fringe period paired with a detector port. Because the multiplexing exploits the down-conversion bandwidth rather than merely tolerating it, a single Fourier transform per detector trace returns all four moduli and all three relative phases across that bandwidth, i.e., the full round-trip Jones spectrum up to a global phase, with no scan or setting change (after a one-time reference frame). Simultaneity makes every relative phase immune to common-mode drift, and a dark carrier, a self-interference term that unitarity forces to vanish, provides a built-in null test. For realistic parameters of a periodically poled KTP source the scheme yields wavelength-resolved mid-infrared polarimetry across 3.5-4.2 microns (~80 spectral points per Jones element) on a silicon camera, extending to depth-resolved Jones matrices, i.e., polarization-sensitive optical coherence tomography with undetected photons. A Fisher-information analysis, the first we are aware of in undetected-photon tomography, sets the precision budget and compares delay multiplexing to sequential protocols at equal photon number.
ER -