Three dimensional theory for light matter interaction

TL;DR

This paper develops a comprehensive three-dimensional quantum mechanical model of light interacting with an atomic ensemble, capturing quantum fluctuations, atomic randomness, and their effects on light-matter quantum interfaces.

Contribution

It introduces a full 3D quantum theory that extends previous models by including quantum fluctuations and atomic positional randomness, and connects to 1D approximations.

Findings

Quantum fluctuations are mapped between atoms and light.

Atomic positional randomness causes decay via spontaneous emission.

The theory reduces to 1D models under certain limits.

Abstract

We present a full quantum mechanical three dimensional theory describing an electromagnetic field interacting with an ensemble of identical atoms. The theory is constructed such that it describes recent experiments on light-matter quantum interfaces, where the quantum fluctuations of light are mapped onto the atoms and back onto light. We show that the interaction of the light with the atoms may be separated into a mean effect of the ensemble and a deviation from the mean. The mean effect of the interaction effectively give rise to an index of refraction of the gas. We formally change to a dressed state picture, where the light modes are solutions to the diffraction problem, and develop a perturbative expansion in the fluctuations. The fluctuations are due to quantum fluctuations as well as the random positions of the atoms. In this perturbative expansion we show how the quantum fluctuations are mapped between atoms and light while the random positioning of the atoms give rise to decay due to spontaneous emission. Furthermore we identify limits, where the full three dimensional theory reduce to the one dimensional theory typically used to describe the interaction.