Arrays of ultra-cold dipolar gases loaded in optical lattices are emerging as powerful quantum simulators of the many-body physics associated with the rich interplay between long-range dipolar interactions, contact interactions, motion, and quantum statistics. In this work we report on our investigation of the quantum many-body dynamics of a large ensemble of bosonic magnetic chromium atoms with spin S = 3 in a three-dimensional lattice as a function of lattice depth. Using extensive theory and experimental comparisons we study the dynamics of the population of the different Zeeman levels and the total magnetization of the gas across the superfluid to the Mott insulator transition. We are able to identify two distinct regimes: At low lattice depths, where atoms are in the superfluid regime, we observe that the spin dynamics is strongly determined by the competition between particle motion, onsite interactions and external magnetic field gradients. Contact spin dependent interactions help to stabilize the collective spin length, which sets the total magnetization of the gas. On the contrary, at high lattice depths, transport is largely frozen out. In this regime, while the spin populations are mainly driven by long range dipolar interactions, magnetic field gradients also play a major role in the total spin demagnetization. We find that dynamics at low lattice depth is qualitatively reproduced by mean-field calculations based on the Gutzwiller ansatz; on the contrary, only a beyond mean-field theory can account for the dynamics at large lattice depths. While the cross-over between these two regimes does not correspond to sharp features in the observed dynamical evolution of the spin components, our simulations indicate that it would be better revealed by measurements of the collective spin length.

Analytic solutions for steady-state expectation values of atomic quantities and second order correlations are obtained for a fully quantum treatment of two stationary dipole-coupled atoms driven in a standard geometric configuration by a near resonant laser. Explicit expressions for the spatial and coherence properties of the farfield scattered light intensity are derived, valid for the full range of system parameters. A comprehensive survey of the steady-state scattering behaviour is given, with key features precisely characterised, including suppression of scattering, and the regime in which the dipole-dipole coupling has significant effect. A regime is also found where the incoherent scattered light develops spatial interference fringes. We examine in detail a decorrelation approximation that has potential application for larger systems of atoms that are intractable in a full quantum treatment. Finally, we introduce the concept of an effective driving field and show that it can provide a direct and intuitive physical interpretation of key aspects of the system behaviour.arXiv:1905.01812v2 [cond-mat.quant-gas]