Fig. 2: Band engineering.

a General CCA schematic displaying the cavities in green, with a unit cell including M cavities. b Transmission spectrum ∣S₂₁∣ for CCAs with N = 25, 50 and 100 cavities with rectangular design with M = 1. The shaded region around 8.05 GHz highlights the presence of microwave chip slot modes. c Top: Same as (b) for M = 1 CCAs with J₁/2π = 58 MHz (rectangular design), J₁/2π = 164 MHz (rectangular design), and J₁/2π = 1200 MHz (hexagonal design). Additional slot modes are visible around 11.1 GHz. Inset: a zoom-in on the two lower coupling CCAs in the main panel. Bottom: Frequency difference, Δf = f_i − f_i+1, between two consecutive modes for the corresponding CCAs. The crosses represent the Δf extracted for the CCAs, each plotted in relative to the averaged modes' frequencies (f_i + f_i+1)/2. The continuous black lines indicate fits of the extracted Δf according to the eigenmodes of the CCAs Hamiltonian (see Methods). Inset table collects the coupling J₁/2π, the stray capacitance ratio \({C}^{{\prime} }/{C}_{\Sigma }\), where \({C}^{{\prime} }={C}_{i,i+2}\), and next nearest-neighbor couplings ratio \({J}^{{\prime} }/{J}_{1}\) for the three CCAs. d Top: Same as c for dimerized CCAs (rectangular design, M = 2) with ΔJ/2π = ∣J₂ − J₁∣/2π ~ 50 MHz (100 MHz) on the left (right). Bottom: Extracted modes (crosses) and their fits to the eigenmodes of the CCAs Hamiltonian (continuous line) (see Methods). e Same as c for (top to bottom) unit cells with M = 3, 4, and 5. All the transmission spectra are normalized by their maximum amplitude.