  An exciting frontier in quantum information science is the realization and
control of complex quantum many-body systems. Hybrid nanophotonic system with
cold atoms has emerged as the paradigmatic platform for engineering long-range
spin models from the bottom up, exploiting their modal geometry and group
dispersion for tailored interactions. An important challenge is the physical
limitation imposed by the photonic bath, constraining the types of local
Hamiltonians that decompose the available physical models and restricting the
spatial dimensions to that of the dielectric media. However, at the nanoscopic
scale, atom-field interaction inherently accompanies significant
driven-dissipative quantum forces that may be tamed as a new form of a mediator
for controlling the atomic internal states. Here, we formulate a quantum optics
toolbox for constructing a universal quantum matter with individual atoms in
the vicinity of 1D photonic crystal waveguides. The enabling platform
synthesizes analog quantum materials of universal $2$-local Hamiltonian graphs
mediated by phononic superfluids of the trapped atoms. We generalize our
microscopic theory of analog universal quantum simulator to the development of
dynamical gauge fields. In the spirit of gauge theories, we investigate
emergent lattice models for strongly coupled SU$(n)$-constrained excitations
driven by an underlying multi-body interaction. As a minimal model in the
infrared, we explore the realization of an archetypical strong coupling quantum
field theory, SU($n$) Wess-Zumino-Witten model, and discuss a diagnostic tool
to extract the entire conformal data of the field theory by the static and
dynamical correlators of the fluctuating photons in the guided mode.
