Engineering and harnessing giant atoms in high-dimensional baths: a cold atoms' implementation

Emitters coupled simultaneously to distant positions of a photonic bath, the so-called giant atoms, represent a new paradigm in quantum optics. When coupled to one-dimensional baths, as recently implemented with transmission lines or SAW waveguides, they lead to striking effects such as chiral emission or decoherence-free atomic interactions. Here, we show how to create giant atoms in dynamical state-dependent optical lattices, which offers the possibility of coupling them to structured baths in arbitrary dimensions. This opens up new avenues to a variety of phenomena and opportunities for quantum simulation. In particular, we show how to engineer unconventional radiation patterns, like multi-directional chiral emission, as well as collective interactions that can be used to simulate non-equilibrium many-body dynamics with no analogue in other setups. Besides, the recipes we provide to harness giant atoms in high dimensions can be exported to other platforms where such non-local couplings can be engineered.