  Optical box traps for cold atoms offer new possibilities for quantum-gas
experiments. Building on their exquisite spatial and temporal control, we
propose to engineer system-reservoir configurations using box traps, in view of
preparing and manipulating topological atomic states in optical lattices.
First, we consider the injection of particles from the reservoir to the system:
this scenario is shown to be particularly well suited to activate
energy-selective chiral edge currents, but also, to prepare fractional Chern
insulating ground states. Then, we devise a practical evaporative-cooling
scheme to effectively cool down atomic gases into topological ground states.
Our open-system approach to optical-lattice settings provides a new path for
the investigation of ultracold quantum matter, including strongly-correlated
and topological phases.
