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

TL;DR

This paper develops a theoretical framework using quantum trajectory theory to analyze measurement-induced dynamics, including quantum jumps and the Zeno effect, in a superconducting qubit coupled to a resonator.

Contribution

It provides an exact effective master equation for the qubit and explores the transition from diffusive to jump-like quantum trajectories under strong measurement.

Findings

Quantum trajectories show a crossover from diffusive to jump-like behavior.

Strong homodyne measurement induces quantum Zeno effect in the qubit.

Effective master equation enables precise analysis of measurement times and dynamics.

Abstract

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. From this result, various definitions of the measurement time are studied. Furthermore, we find that in the limit of strong homodyne measurement, typical quantum trajectories for the qubit exhibit a crossover from diffusive to jump-like behavior. Finally, in the presence of Rabi drive on the qubit, the qubit dynamics is shown to exhibit quantum Zeno behavior.