Figure 2. Mode profiles and frequency spectrum in the divided cavity.

(a) The mode profile of the lowest-energy cavity mode, calculated using Eq. (4), with a flux through the SQUIDs of (i) Φ = 0.35Φ₀, (ii) Φ = 0.28Φ₀, and (iii) Φ = 0.14Φ₀. (b) The frequencies of the two lowest modes, calculated from Eq. (6), as functions of the bare left-cavity frequency to give the spectrum in the frequency range around the left-right cavity resonance. The first and second modes, for the flux values considered in (a), are marked with squares and circles, respectively. For the cavity parameters, we take a cavity of length L = 12 mm, and a capacitor positioned at x_c = 0.45 L, with capacitance C_c = 0.5 fF. We introduce n_s SQUIDs, each with a critical current I_c0 = 0.3 μA × n_s, into the left side of the cavity. For the center conductor, c = 130 × 10⁻¹² Fm⁻¹, and we take the inductance per unit length of the right cavity region to be ℓ_R = 3.25 × 10⁻⁷ Hm⁻¹, resulting in a characteristic impedance . For these parameters, the bare right-cavity frequency has a value , and the interaction frequency is .