Fig. 2: Interference between two adjacent plaquettes in a diamond configuration.
From: Programmable synthetic magnetism and chiral edge states in nano-optomechanical quantum Hall networks
a Four resonators aj form a diamond configuration with two adjacent plaquettes, pierced by opposite fluxes Φ, − Φ (top) or equal fluxes Φ (bottom). The perimeter coupling rate is J/(2π) = 5 kHz, and the central link is coupled at \({J}_{{{{\rm{c}}}}}=J\sqrt{2}\). b Measured thermomechanical spectra around the frequency of the apex resonator a1 (left) and central resonator a3 (right) for varying flux Φ. The spectra for the other apex and central resonators are similar. In the diamond with opposite fluxes (top), eigenmodes with flux-independent localization emerge. One antisymmetric mode, \({\tilde{a}}_{{{{\rm{apex}}}}}\), is localized at the apex and remains unaffected by Φ, while the other modes are delocalized and tune like those of a three-mode plaquette with \({J}_{{{{\rm{c}}}}}=J\sqrt{2}\) (Methods). For equal-handed fluxes (bottom), all eigenmodes tune with flux, both in frequency and localization. The central link couples opposite momentum states, and at Φ = 0 and Φ = π, their superpositions localize entirely on either the apex or central resonators. c Weight of central resonator a3 in each hybridized eigenmode \({\tilde{a}}_{k}\) of the diamond. The weight of apex resonator a1, as shown in Supplementary Fig. 1a, is complementary.
