# Simulating quantum light propagation through atomic ensembles using matrix product states

## TL;DR

This paper introduces a matrix product state-based method to simulate quantum light propagation through atomic ensembles, enabling the study of many-body photon states and complex correlations in 1D systems.

## Contribution

It develops a novel spin model approach combined with matrix product states to analyze large photon number propagation in atomic ensembles.

## Key findings

- Demonstrates vacuum induced transparency with photon number-dependent group velocities.
- Provides a scalable numerical framework for many-body quantum light propagation.
- Enables exploration of exotic photon states in atomic ensemble interfaces.

## Abstract

A powerful method to interface quantum light with matter is to propagate the light through an ensemble of atoms. Recently, a number of such interfaces have emerged, most prominently Rydberg ensembles, that enable strong nonlinear interactions between propagating photons. A largely open problem is whether these systems produce exotic many-body states of light and developing new tools to study propagation in the large photon number limit is highly desirable. Here, we provide a method based on a "spin model" that maps quasi one-dimensional (1D) light propagation to the dynamics of an open 1D interacting spin system, where all photon correlations are obtained from those of the spins. The spin dynamics in turn are numerically solved using the toolbox of matrix product states. We apply this formalism to investigate vacuum induced transparency, wherein the different photon number components of a pulse propagate with number-dependent group velocity and separate at output.