In recent years, systems of ultracold atoms in optical lattices have opened new opportunities for exploring time-dependent many-body dynamics. In addition to coherent phenomena, it has become possible to engineer open quantum systems, drawing new connections between many-body physics and concepts from quantum optics. At the same time, understanding coherent and dissipative dynamics is also becoming a key to the development of new tools for realising lower temperatures and engineering sensitive many-body states in these systems.
I will discuss some of our recent theoretical work in this direction. In particular, I will describe schemes for adiabatic state preparation of magnetically ordered states in optical lattices, and how they are affected by dissipation and classical noise. In certain regimes, adiabatic processes can be particularly robust against typical noise sources, and in some cases classical noise can be engineered to enhance adiabaticity. I will also discuss dissipative driving of atoms in optical lattices into entangled spin states, by engineering their coupling to a reservoir gas that is not trapped by the lattice.