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.
The origin of many quantum-material phenomena is intimately related to the presence of flat electronic bands. In quantum simulation, such bands have been realized through line-graph lattices, a class of lattices known to exhibit flat bands. Based on that work, we conduct a high-throughput screening for line-graph lattices among the crystalline structures of the Materials Flatband Database and report on new candidates for line-graph materials and lattice models. In particular, we find materials with line-graph-lattice structures beyond the two most commonly known examples, the kagomé and pyrochlore lattices. We also identify materials which may exhibit flat topological bands. Finally, we examine the various line-graph lattices detected and highlight those with gapped flat bands and those most frequently represented among this set of materials. With the identification of real stoichiometric materials and theoretical lattice geometries, the results of this work may inform future studies of flat-band many-body physics in both condensed matter experiment and theory.
The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: Their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.