Figure 3. Decay rates vs. inductance per unit length of the left cavity.

Decay rates to the ground state, for a system prepared in an initial eigenstate of the cavity-qubit system corresponding, away from resonance, to either a qubit excitation (solid line), the excitation of a photon in the right cavity (dashed line), or in the left-cavity (dotted line), as functions of the average inductance per unit length of the left cavity, ℓ_L. We observe a peak in the decay rate of the right-photon–like state at cavity–cavity resonance, and a peak at the left-cavity–qubit resonance for the decay rate of the qubit-like state. The resistor has an effective temperature T = 10 mK, and a resistance of R = 230 Ω. The angular frequency of the qubit is held fixed at 2π × 15.91 GHz. The cavity length is L = 12 mm, and includes a capacitor positioned at x_c = L/2, with capacitance C_c = 0.5 fF, and cavity interaction energy ℏΔω^res = 2πℏ × 16.73 MHz. For the center conductor, we have c = 130 × 10⁻¹² Fm⁻¹, with a characteristic impedance of the right cavity , resulting in a bare right-cavity frequency .