Cooperative effects in dense cold atomic gases including magnetic dipole interactions

We theoretically investigate cooperative effects in cold atomic gases exhibiting both electric and magnetic dipole-dipole interactions, such as occurs, for example, in clouds of dysprosium atoms. After introducing a general framework capturing both the quantum degenerate and nondenegerate cases, we focus on the emergence of tailorable spin models in the quantum nondegenerate regime. In the low-excitation limit, we provide analytical and numerical results detailing the effect of magnetic interactions on the directionality of scattered light and characterize sub and superradiant effects.