# Project 18: Imaging non-local photon interactions with structured light

## Summary

Nonlinear, non-local photon interactions can be realised by strong light-matter coupling in Rydberg

gases under conditions of electromagnetically induced transparency (EIT). In this project we aim to

develop a comprehensive picture describing the light propagation through an ultracold Rydberg-EIT

gas of Rubidium atoms in the weakly and strongly interacting regime. For this purpose we will

investigate the optical response of the medium, related to the photon-photon interaction potential,

by measuring its nonlinear susceptibility.

In a first step, we will use structured probe beam light (Fig. 1) to image finite-range photon

interactions in the weakly interacting regime. Since we expect the spatial structure of the third-order

susceptibility to be in the order of the Rydberg blockade radius (approx. a few μm), we plan to design

an objective with a resolution smaller than this emergent length scale. On the theory side, we will

develop an inversion algorithm to reconstruct the non-local susceptibility from the measured Fourier

space components of the output intensity distribution.

Second, we will investigate how the character of the non-local interactions evolves in the crossover

from the weakly to the strongly interacting regime by successively increasing the atomic density.

Here, higher orders of the nonlinear interactions eventually become important and will ultimately

promote rich many body physics. In this regime we plan to explore highly correlated sates of matter

as for example the crystalline state of light.

Fig. 1: Schematic experimental setup for creating structured probe beam light using a spatial light

modulator (SLM) in order to image photon interactions in the weakly interacting regime.

## People

Prof. Dr. Thomas Pohl, Aarhus University

Prof. Dr. Matthias Weidemüller, Physikalisches Institut, Universität Heidelberg