Figure 10

The superconducting microwave resonator modelled as a single-sided cavityfor use as an input-output formulation. The superconducting microwaveresonator modelled as a single-sided cavity for use as an input-outputformulation. The incoming field mode operator is ${\hat{a}}_i(t)$ and the outgoing field mode operator is${\hat{a}}_o(t)$. Loss from the microwave cavityoccurs at a rate γ. Note here that γ is thecoefficient of the amplitude decay, the coefficient for the photon number lossis 2γ. The Hamiltonian dynamics of the cavity mode$\hat{a}$ are governed by theInteraction picture Hamiltonian ℋ.