Weak continuous monitoring of a flux qubit using coplanar waveguide resonator

We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime, dispersive readout is possible with weak back action on the qubit. The detailed theoretical analysis and simulations give good agreement with the experimental data and allow us to make the qubit characterization.

Figure 1

(a) A micrograph of the central part of the resonator. The central wire and the ground plane are tapered. (b) Electron micrograph of the qubit and the central line of the resonator.

Figure 2

(Color online) (a) Normalized transmission amplitude of the resonator as a function of the qubit energy bias $\epsilon$ and the driving frequency. The data were measured at a nominal temperature of the mixing chamber below 10 mK, ensured $k_{B}T⪡\hslash {\omega }_q,\hslash {\omega }_r$. The calculated frequencies of the lowest photon transition in the qubit-resonator system are depicted as white solid lines. (b) Theoretical calculations. The number of photons is taken to be less than 1; other parameters are taken from the experiment. $\gamma$ is adjusted for better correspondence of the transmission in vicinity of anticrossings.

Figure 3

(Color online) Transmission phase of the resonator as a function of the qubit excitation frequency $\epsilon /h$. The black line depicts the fitted energy level splitting of the qubit.