This work proposes a hybrid nanophotonic system in which cold atoms interact with photonic crystal waveguides to create analog quantum matter. Phononic superfluids mediate interactions that realise universal 2-local Hamiltonians, enabling the synthesis of complex quantum materials. The authors also introduce a toolkit for mapping conformal field-theory data to photon correlators, paving the way for exploring dynamical gauge fields and emergent SU(n) lattice models.

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