Light-Matter Coupling and Multi-Photon Processes in Superconducting-Circuit Arrays

The field of circuit QED has emerged as a rich platform for both quantum computation and quantum simulation. Lattices of coplanar waveguide (CPW) resonators realize artificial photonic materials in the tight-binding limit [1] capable of realizing non-Euclidean geometries [2] and unconventional unit cells [3]. Combined with strong qubit-photon interactions, these systems can be used to study to study quantum many-body phenomena including dynamical phase transitions, driven-dissipative spin models, and interacting bosonic systems. The first coplanar waveguide lattice device featuring both unconventional linear and flat bands, and 3 flux-tunable qubits was presented in [4]. Here, we leverage this device to demonstrate: (i) a general technique for determining light-matter coupling in highly multimode cavity QED systems that does not rely on single-photon resolution or independent photon-number calibrations and which can identify coupling strengths even for highly localized or under-coupled modes (ii) an exotic wave-mixing process dominated by the interaction of the qubits with localized flat-band modes. We present preliminary results toward a full-scale hyperbolic CPW lattice with qubits.

[1] D. Underwood et al., Phys. Rev. A 86, 023837 (2012)

[2] A. J. Kollár et al., Nature 571, 45 (2019)

[3] A. J. Kollár et al., Comm. Math. Phys. 376,1909 (2019)

[4] O’Brien et al., arXiv:2505.05559 (2025), PRX Quantum (in press, 2026)