  Quantum emitters coupled to structured photonic reservoirs experience
unconventional individual and collective dynamics emerging from the interplay
between dimensionality and non-trivial photon energy dispersions. In this work,
we systematically study several paradigmatic three dimensional structured baths
with qualitative differences in their bath spectral density. We discover
non-Markovian individual and collective effects absent in simplified
descriptions, such as perfect subradiant states or long-range anisotropic
interactions. Furthermore, we show how to implement these models using only
cold atoms in state-dependent optical lattices and show how this unconventional
dynamics can be observed with these systems.
