Flat Bands

The one-dimensional nature of CPW lattice sites and their inherent deformability leads naturally to the implementation of line graphs with degenerate flat bands. Qubits coupled to these systems will mediate photon-photon interactions within the flat bands. They will also experience novel electromagnetic environments depending on their detuning with respect to the band structure. The resulting photonic bound states have new and controllable forms which give rise to new types of effective spin-spin interactions, including frustrated short-range antiferromagentism in the flat bands.

A. J. Kollár, M. Fitzpatrick, P. Sarnak, A.A. Houck, Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands and Implementations in Circuit QED, arXiv:1902.02794v1 (2019).
N. M. Sundaresan, R. Lundgren, G. Zhu, A. V. Gorshkov, and A. A. Houck, “Interacting Qubit-Photon Bound States with Superconducting Circuits,” Phys. Rev. X 9, 011021 (2019).
J. S. Douglas, H. Habibian, C.-L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang, “Quantum many-body models with cold atoms coupled to photonic crystals,” Nat. Phys. 9, 326 (2012).

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