Magnetic properties of materials have been under intense scrutiny for decades, motivated on the one hand by the constant need to improve storage applications to meet the requirements of our modern information society and on the other hand by complex and yet not fully understood fundamental phenomena such their connection to high-Tc superconductivity and new phases like altermagnetism with potential long-term applications. Exotic magnetic properties associated to high-order multipole states (quadrupole and beyond) in heavy-fermion metals have also recently attracted interest, not the least due to the connection to unconventional superconductivity [1,2]. Motivated by these questions, the project will investigate quadrupolar and dipolar ordering in a cold atom system of rubidium atoms with light-induced magnetic interactions. Note that in contrast to other quantum simulation schemes, we are operating with real spin in real magnetic fields and not pseudo-spins in synthetic gauge fields. In this well controlled system, spontaneous quadrupolar ordering linked to anti-ferromagnetic dipolar ordering is found similarly to the condensed-matter systems [3-5]. Recently, we observed a spontaneously drifting multipolar spin density wave, an out-of-equilibrium generalization of sliding spin density waves [6], but many aspects of the dynamics are still unclear. The project is aimed at a detailed imaging and understanding of the magnetic atomic structure by optical and microwave means by measurements of the complete Stokes parameters of the transmitted pump and dedicated probe beams. It will analyse the excitation spectrum of the system (magnons) above and below threshold of ordering and look at the mechanisms responsible for the stabilization of the particular phases, in particular the highly interesting time-dependent phase and its relation to dissipative time crystals. We will look at the possibility of skyrmions and magnetic bubbles and their switching dynamics, which are currently discussed for spintronic quantum technologies. In addition, the investigations have an interdisciplinary aspect as the spontaneous emergence of the coupled magnetic light-spin structures has common features with self-organization and nonlinear dynamics in fields like hydrodynamics, biology and chemistry. The experimental results will be compared to a theory based on the density-matrix approach [4]. As the theory developed to describe the complex light matter interaction in arbitrarily oriented magnetic field is fully nonlinear, it is applicable also to understand the behaviour of alkaline-atom based magnetometers at arbitrary light levels. This aspect will be explored in collaboration with the strong activities on high-performance magnetometers within the Experimental Quantum Optics and Photonics group. We have a close collaboration with the Institut de Physique de Nice, Universite Cote d’Azur, France, with the possibility of a placement