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

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.

20 pages, 12 figures

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Cited by in corpus (13)

• Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
• Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit
• Two-Qubit State Tomography using a Joint Dispersive Read-Out
• Holographic quantum computing
• Non-linear dispersive regime of cavity QED: The dressed dephasing model
• Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator
• Dynamics of dispersive single qubit read-out in circuit quantum electrodynamics
• Cooling and squeezing the fluctuations of a nanomechanical beam by indirect quantum feedback control
• Proposal for generating and detecting multi-qubit GHZ states in circuit QED
• QND measurements and state preparation in quantum gases by light detection
• Nuclear spin dynamics and Zeno effect in quantum dots and defect centers
• Model for monitoring of a charge qubit using a radio-frequency quantum point contact including experimental imperfections
• Quantum nondemolition-like, fast measurement scheme for a superconducting qubit