# Few photon scattering on Bose-Hubbard lattices

## TL;DR

This paper develops a diagrammatic scattering theory to analyze how few photons interact with Bose-Hubbard lattices, revealing non-linear effects like bunching and anti-bunching across various lattice geometries.

## Contribution

It provides explicit analytical formulas for photon correlation functions and a numerical tool applicable to arbitrary Bose-Hubbard graphs, advancing understanding of photon-lattice interactions.

## Key findings

- Demonstrates non-linear photon effects such as bunching and anti-bunching.
- Derives analytical expressions for photonic correlation functions.
- Provides a versatile numerical implementation for various lattice geometries.

## Abstract

We theoretically investigate the scattering of few photon light on Bose-Hubbard lattices using diagrammatic scattering theory. We explicitly derive general analytical expressions for the lowest order photonic correlation functions, which we apply numerically to several different lattices. We focus specifically on non-linear effects visible in the intensity-intensity correlation function and explain bunching and anti-bunching effects in dimers, chains, rings and planes. The numerical implementation can be applied to arbitrary Bose-Hubbard graphs, and we provide it as an attachment to this publication.