Measuring the quality factor of a microwave cavity using superconducting qubit devices

We propose a method to create superpositions of two macroscopic quantum states of a single-mode microwave cavity field interacting with a superconducting charge qubit. The decoherence of such superpositions can be determined by measuring either the Wigner function of the cavity field or the charge qubit states. Then the quality factor $Q$ of the cavity can be inferred from the decoherence of the superposed states. The proposed method is experimentally realizable within current technology even when the $Q$ value is relatively low and the interaction between the qubit and the cavity field is weak.

Figure 1

(Color online) Wigner functions $W_{+}(x,p)$ of Eq. (14) and $W_{+D}(x,p)$ of Eq. (16) for the cavity field without and with the energy dissipation are shown in (a) and (b), for the input state $\mid \alpha ⟩$ with $\overline{n}=16$. Here the Wigner functions $W_{+}(x,p)$ and $W_{+D}(x,p)$ are normalized to $\pi N_{+}$.

Figure 2

(Color online) The probability $P_g\left(\tau \right)$ to measure the qubit ground state $\mid g⟩$ as a function of the evolution time $\tau$. This $P_g\left(\tau \right)$ is shown for several values of the quality factor $Q$ and for different intensities of the input coherent state $\mid \alpha ⟩$.