Localization transition for light scattering by cold atoms in an external magnetic field

TL;DR

This paper maps the phase diagram of light localization in a 3D cold atom ensemble under a magnetic field, identifying a critical density and spectral conditions for Anderson localization, and estimates the transition's critical exponent.

Contribution

It provides the first detailed localization phase diagram for light in a 3D atomic ensemble with magnetic field, including critical density and spectral conditions for Anderson localization.

Findings

Localized modes appear above a critical density of approximately 0.1 k_0^3.

The localization transition has a critical exponent of about 1.57.

The transition belongs to the 3D orthogonal universality class.

Abstract

We establish a localization phase diagram for light in a random three-dimensional (3D) ensemble of motionless two-level atoms with a three-fold degenerate upper level, in a strong static magnetic field. Localized modes appear in a narrow spectral band when the number density of atoms $\rho$ exceeds a critical value $\rho_c \simeq 0.1 k_0^3$, where $k_0$ is the wave number of light in the free space. A critical exponent of the localization transition taking place upon varying the frequency of light at a constant $\rho > \rho_c$ is estimated to be $\nu = 1.57 \pm 0.07$. This classifies the transition as an Anderson localization transition of 3D orthogonal universality class.