Spatial Kramers-Kronig relation and controlled unidirectional reflection in cold atoms

TL;DR

This paper introduces a spatial Kramers-Kronig relation in cold atoms enabling tunable unidirectional reflection for probe photons, with potential applications in optical control and non-Hermitian photonics.

Contribution

It demonstrates a novel spatial KK relation in cold atoms that allows control over unidirectional reflection and frequency bands through spatially varied control fields.

Findings

Achieves unidirectional reflectionless frequency bands for probe photons.

Demonstrates tunability of reflection direction and frequency band by adjusting control fields.

Enhances reflectivity contrast using Bragg scattering in the spatial KK framework.

Abstract

We propose a model for realizing frequency-dependent spatial variations of the probe susceptibility in a cold atomic sample. It is found that the usual Kramers-Kronig (KK) relation between real and imaginary parts of the probe susceptibility in the frequency domain can be mapped into the space domain as a far detuned control field of intensity linearly varied in space is used. This non-Hermitian medium exhibits then a unidirectional reflectionless frequency band for probe photons incident from either the left or the right sample end. It is of special interest that we can tune the frequency band as well as choose the direction corresponding to the vanishing reflectivity by changing, respectively, the control field intensity and frequency. The nonzero reflectivity from the other direction is typically small for realistic atomic densities, but can be largely enhanced by incorporating the Bragg scattering into the spatial KK relation so as to achieve a high reflectivity contrast.