Theory of weak continuous measurements in a strongly driven quantum bit

Abstract

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.

28 pages

References in corpus (7)

• Coherent Quantum Dynamics of a Superconducting Flux Qubit
• Continuous Monitoring of Rabi Oscillations in a Josephson Flux Qubit
• Quantum-Limited Measurement and Information in Mesoscopic Detectors
• Low-frequency characterization of quantum tunneling in flux qubits
• Decoherence and Relaxation of a Quantum Bit in the Presence of Rabi Oscillations
• Method for direct observation of coherent quantum oscillations in a superconducting phase qubit
• Decoherence of Flux Qubits Coupled to Electronic Circuits

Cited by in corpus (26)

• Evidence for entangled states of two coupled flux qubits
• Single-qubit lasing and cooling at the Rabi frequency
• Electromagnetically induced transparency and Autler-Townes splitting in superconducting flux quantum circuits
• Silent Phase Qubit Based on d-Wave Josephson Junctions
• Dissipation in circuit quantum electrodynamics: lasing and cooling of a low-frequency oscillator
• Possible implementation of adiabatic quantum algorithm with superconducting flux qubits
• Radio-Frequency Method for Investigation of Quantum Properties of Superconducting Structures
• Quantum effects in energy and charge transfer in an artificial photosynthetic complex
• Multiphoton transitions in Josephson-junction qubits (Review Article)
• Resonant excitations of single and two-qubit systems coupled to a tank circuit
• Low frequency Rabi spectroscopy of dissipative two level systems. The dressed state approach
• Weak and strong measurement of a qubit using a switching-based detector
• Quantum state detection of a superconducting flux qubit using a DC-SQUID in the inductive mode
• Multiphoton excitations and inverse population in two-flux-qubit system
• Impedance measurement technique for quantum systems
• Feedback-controlled adiabatic quantum computation
• Noise-induced quantum coherence and persistent Rabi oscillations in a Josephson flux qubit
• A theoretical investigation into the microwave spectroscopy of a phosphorus-donor charge-qubit in silicon: Coherent control in the Si:P quantum computer architecture
• Quantum superposition of three macroscopic states and superconducting qutrit detector
• Cooling a magnetic resonance force microscope via the dynamical back-action of nuclear spins
• Quantum theory of the low-frequency linear susceptibility of interferometer-type superconducting qubits
• Coherent Rabi response of a charge-phase qubit under microwave irradiation
• The two Josephson junction flux qubit with large tunneling amplitude
• Quantum Nondemolition Charge Measurement of a Josephson Qubit
• Rabi-vibronic resonance with large number of vibrational quanta
• State-dependent impedance of a strongly coupled oscillator-qubit system