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Optical box traps for cold atoms offer new possibilities for quantum-gasexperiments. Building on their exquisite spatial and temporal control, wepropose to engineer system-reservoir configurations using box traps, in view ofpreparing 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 activateenergy-selective chiral edge currents, but also, to prepare fractional Cherninsulating ground states. Then, we devise a practical evaporative-coolingscheme to effectively cool down atomic gases into topological ground states.Our open-system approach to optical-lattice settings provides a new path forthe investigation of ultracold quantum matter, including strongly-correlatedand topological phases.

The cold-atom elevator: From edge-state injection to the preparation of fractional Chern insulators