Zero mode, Zero influence: Spatial-derivative coupling in particle detectors
Abstract
It is common in particle detector models in cavity QED to often omit zero modes or assume their state, compromising causality or introducing ambiguity in their predictions. We show that spatial-derivative coupling eliminates both problems. For free massless scalar fields in static periodic or Neumann cavities of any spatial dimension, cavity-frame spatial derivatives annihilate the zero-mode operator while preserving microcausality. Detector dynamics and entanglement harvesting then depend only on the reduced detector-oscillator state, nonperturbatively and even with initial correlations with the zero mode. Time derivatives and moving-detector rest-frame spatial derivatives can retain zero-mode state dependence not compromising causality. Realized through current coupling in superconducting circuits, spatial-derivative coupling thus makes zero-mode state assumptions unnecessary.
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BibTeX
@misc{martinmartinez2026zero,
title = {{Zero mode, Zero influence: Spatial-derivative coupling in particle detectors}},
author = {Eduardo Martín-Martínez and Ireneo James Membrere and Adam Teixidó-Bonfill},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00309},
eprint = {2611.00309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00309},
}
RIS
TY - UNPB
TI - Zero mode, Zero influence: Spatial-derivative coupling in particle detectors
AU - Eduardo Martín-Martínez
AU - Ireneo James Membrere
AU - Adam Teixidó-Bonfill
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00309
UR - https://arxiv.org/abs/2611.00309
AB - It is common in particle detector models in cavity QED to often omit zero modes or assume their state, compromising causality or introducing ambiguity in their predictions. We show that spatial-derivative coupling eliminates both problems. For free massless scalar fields in static periodic or Neumann cavities of any spatial dimension, cavity-frame spatial derivatives annihilate the zero-mode operator while preserving microcausality. Detector dynamics and entanglement harvesting then depend only on the reduced detector-oscillator state, nonperturbatively and even with initial correlations with the zero mode. Time derivatives and moving-detector rest-frame spatial derivatives can retain zero-mode state dependence not compromising causality. Realized through current coupling in superconducting circuits, spatial-derivative coupling thus makes zero-mode state assumptions unnecessary.
ER -