From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling

TL;DR

This paper investigates how spin-orbit coupling affects localization phenomena in cold atomic gases, revealing a transition from Anderson localization to anomalous power-law behavior linked to Dyson singularities.

Contribution

It demonstrates a crossover from Anderson to anomalous localization in a spin-orbit coupled system and connects this to the emergence of Dyson singularities in the density of states.

Findings

Crossover from exponential to power-law localization observed

Power-law behavior linked to Dyson singularity at zero energy

Conditions for experimental observation discussed

Abstract

We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger particle with two internal components moving in a random potential. We show that this model can be implemented by the interaction of cold atoms with external lasers and additional Zeeman and Stark shifts. By direct numerical simulations a crossover from an exponential Anderson-type localization to an anomalous power-law behavior of the intensity correlation is found when the spin-orbit coupling becomes large. The power-law behavior is connected to a Dyson singularity in the density of states emerging at zero energy when the system approaches the quasi-relativistic limit of the random mass Dirac model. We discuss conditions under which the crossover is observable in an experiment with ultracold atoms and construct explicitly the zero-energy state, thus proving its existence under proper conditions.