Fig. 3: Qi measurement of a resonator chip containing CPW resonators with various numbers of tantalum airbridges.

a Optical micrograph of one resonator chip with varied tantalum airbridges. The number of airbridges increases from N = 0 to N = 90 and the resonance frequencies are uniformly distributed between 6.04 GHz and 6.64 GHz. All the airbridges were designed with a fixed length of 60 μm and width of 16 μm, arranged at equal distances. b A zoom-in SEM image of the arranged tantalum airbridges circled by the red rectangle in (a). c Internal quality factor Q_i versus average photon population \(< {n}_{p} >\) for each resonator. The error bars represent the uncertainty of Q_i in the fitting process of S parameters. The solid lines are the fitting results obtained by the TLS model³⁹. Notice that the overall Q_i values tend to decline as the number of airbridges increases. d Loss tangent (1/Q_i) versus number of airbridges. The fitted slope of line represents the added capacitive loss caused by a single airbridge to the CPW resonator.