Giant atoms in one-dimensional structured environments*

Giant atoms (GAs) constitute a new paradigm in quantum optics in which they break the dipole approximation by coupling to light at multiple discrete points. They have been increasingly attracting attention for their ability to interact via a waveguide without decohering, which is why most previous work has been limited to GAs coupled to a one-dimensional (1D) continuous waveguide. Here, we instead consider GAs coupled to a 1D structured bath, e.g., an array of coupled cavities or a photonic crystal waveguide. This environment gives rise to a band structure, where atomic decay and interaction are highly dependent on the energy band to which the atoms are tuned. In particular, we study non-Markovian decay, time delay effects, formation of bound states and decoherence-free interaction, and we analyze how these phenomena are influenced by the number and distance of the GAs' coupling points to the bath.