Photon localization: a comparative study
Abstract
We compare different measures for photon localization in terms of two-dimensional Gaussian wave packets of width Delta k. We find that all measures start to coalesce if the wave packet has evolved for times which are larger than a few (c Delta k)^{-1}. However, the Landau-Peierls wave function yields the largest initial offset -ct > 0 while the Fourier transform of the helicity components of the k-space wave packet yields the smallest offset -ct > 0 and converges towards -ct = 0 fastest. We also discuss local detection of photons through a model detector consisting of ions in ion traps. The position-dependent detection probabilities are inferred from the scattering matrix. We find that the local detection probability for photons can be expressed in terms of three of the proposed localization measures, viz. the Landau-Peierls wave function, the energy wave function, and the Hawton density. Those three proposals also remain close throughout the time evolution of the single-photon wave packet. However, the energy wave function is locally related to electromagnetic fields and is therefore confirmed as the preferred tool for the description of local photon densities. The novelty of our observations concerns three items, viz. the possibility to express local photon absorption matrix elements through three of the proposed localization measures, the coalescence of all the proposed localization measures after sufficiently long evolution of a photon wave packet, and the striking differences of some of the proposed localization measures during early wave packet evolution.
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BibTeX
@misc{ferguson2026photon,
title = {{Photon localization: a comparative study}},
author = {Laura M. Ferguson and Ricardo Rojas Castellano and Kayla Oltman and Joshua G. Fenwick and Rainer Dick},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.04134},
eprint = {2608.04134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.04134},
}
RIS
TY - UNPB
TI - Photon localization: a comparative study
AU - Laura M. Ferguson
AU - Ricardo Rojas Castellano
AU - Kayla Oltman
AU - Joshua G. Fenwick
AU - Rainer Dick
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.04134
UR - https://arxiv.org/abs/2608.04134
AB - We compare different measures for photon localization in terms of two-dimensional Gaussian wave packets of width Delta k. We find that all measures start to coalesce if the wave packet has evolved for times which are larger than a few (c Delta k)^{-1}. However, the Landau-Peierls wave function yields the largest initial offset -ct > 0 while the Fourier transform of the helicity components of the k-space wave packet yields the smallest offset -ct > 0 and converges towards -ct = 0 fastest. We also discuss local detection of photons through a model detector consisting of ions in ion traps. The position-dependent detection probabilities are inferred from the scattering matrix. We find that the local detection probability for photons can be expressed in terms of three of the proposed localization measures, viz. the Landau-Peierls wave function, the energy wave function, and the Hawton density. Those three proposals also remain close throughout the time evolution of the single-photon wave packet. However, the energy wave function is locally related to electromagnetic fields and is therefore confirmed as the preferred tool for the description of local photon densities. The novelty of our observations concerns three items, viz. the possibility to express local photon absorption matrix elements through three of the proposed localization measures, the coalescence of all the proposed localization measures after sufficiently long evolution of a photon wave packet, and the striking differences of some of the proposed localization measures during early wave packet evolution.
ER -