  Photonic crystals provide an extremely powerful toolset for manipulation of
optical dispersion and density of states, and have thus been employed for
applications from photon generation to quantum sensing with NVs and atoms. The
unique control afforded by these media make them a beautiful, if unexplored,
playground for strong coupling quantum electrodynamics, where a single, highly
nonlinear emitter hybridizes with the band structure of the crystal. In this
work we demonstrate that such hybridization can create localized cavity modes
that live within the photonic band-gap, whose localization and spectral
properties we explore in detail. We then demonstrate that the coloured vacuum
of the photonic crystal can be employed for efficient dissipative state
preparation. This work opens exciting prospects for engineering long-range spin
models in the circuit QED architecture, as well as new opportunities for
dissipative quantum state engineering.
