Pure dephasing destroys two-photon amplitude, not nonlinear phase
Abstract
A two-level emitter chirally coupled to a waveguide imprints a π conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly π at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors---an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in γϕ, discarding $16−−81\%$ of pairs over γϕ/γ=0.1--$1$.
Related
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BibTeX
@misc{kozma2026pure,
title = {{Pure dephasing destroys two-photon amplitude, not nonlinear phase}},
author = {Matthew Kozma and Stephen Hughes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30098},
eprint = {2610.30098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30098},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pure dephasing destroys two-photon amplitude, not nonlinear phase
AU - Matthew Kozma
AU - Stephen Hughes
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30098
UR - https://arxiv.org/abs/2610.30098
AB - A two-level emitter chirally coupled to a waveguide imprints a π conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly π at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors---an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in γ_ϕ, discarding $16−−81\%$ of pairs over γ_ϕ/γ=0.1--$1$.
ER -