# Creation and detection of photonic molecules in Rydberg gases

## TL;DR

This paper explores how photons in Rydberg gases can form bound states called photonic molecules under electromagnetically induced transparency, analyzing their creation, dynamics, and detection through theoretical and numerical methods.

## Contribution

It introduces a detailed Green's function and numerical wave-function approach to analyze photonic molecule formation and their interplay with scattering states in Rydberg gases.

## Key findings

- Bound states of photons can be formed and detected.
- Scattering states acquire a robust phase useful for separation.
- Analytic solutions clarify conditions for molecule formation.

## Abstract

We consider the propagation of photons in a gas of Rydberg atoms under conditions of electromagnetically induced transparency, where they form strongly interacting massive particles, termed Rydberg polaritons. Depending on the strength of the van der Waals-type interactions of the atoms either bunching or anti-bunching of photons can be observed when driving the atoms off-resonantly. The bunching is associated with the formation of bound states. We employ a Green's function approach and numerical wave-function simulations to analyze the conditions for the creation and the dynamics of these photonic molecules and their interplay with the scattering continuum which can also show photon bunching. Analytic solutions of the pair-propagation problem obtained from a pseudopotential approximation and verified numerically provide a detailed understanding of bound and scattering states. We find that the scattering contributions acquire asymptotically a robust relative phase which can be employed to separate bound-state and scattering contributions by a homodyne detection scheme.