Spatial correlations of photons interacting via transverse Rydberg blockade
Abstract
We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.
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BibTeX
@misc{das2026spatial,
title = {{Spatial correlations of photons interacting via transverse Rydberg blockade}},
author = {Bankim Chandra Das and Daniil Svirskiy and Matthias Metternich and Wolfgang Alt and Sebastian Hofferberth and Ofer Firstenberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00348},
eprint = {2609.00348},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00348},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spatial correlations of photons interacting via transverse Rydberg blockade
AU - Bankim Chandra Das
AU - Daniil Svirskiy
AU - Matthias Metternich
AU - Wolfgang Alt
AU - Sebastian Hofferberth
AU - Ofer Firstenberg
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00348
UR - https://arxiv.org/abs/2609.00348
AB - We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.
ER -