Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect

Understand

We present a theoretical study of a superconducting charge qubit dispersively coupled to a transmission line resonator.

• Starting from a master equation description of this coupled system and using a polaron transformation, we obtain an exact effective master equation for the qubit.
• We then use quantum trajectory theory to investigate the measurement of the qubit by continuous homodyne measurement of the resonator out-field.
• Using the same porlaron transformation, a stochastic master equation for the conditional state of the qubit is obtained.