Dispersion relations for stationary light in one-dimensional atomic ensembles

TL;DR

This paper derives dispersion relations for stationary light in one-dimensional atomic ensembles, comparing different atomic schemes and introducing a transfer matrix approach for enhanced control.

Contribution

It provides a unified derivation of dispersion relations across various atomic level schemes and introduces a multi-mode transfer matrix method for controlling stationary light.

Findings

Dispersion relations vary with atomic level schemes.

Positioning atoms discretely enhances control of stationary light.

Transfer matrix theory effectively models multi-mode light interactions.

Abstract

We investigate the dispersion relations for light coupled to one-dimensional ensembles of atoms with different level schemes. The unifying feature of all the considered setups is that the forward and backward propagating quantum fields are coupled by the applied classical drives such that the group velocity can vanish in an effect known as "stationary light". We derive the dispersion relations for all the considered schemes, highlighting the important differences between them. Furthermore, we show that additional control of stationary light can be obtained by treating atoms as discrete scatterers and placing them at well defined positions. For the latter purpose, a multi-mode transfer matrix theory for light is developed.