Quantum Time-evolution in Qubit Readout Process with a Josephson Bifurcation Amplifier

Abstract

We analyzed the Josephson bifurcation amplifier (JBA) readout process of a superconducting qubit quantum mechanically. This was achieved by employing numerical analyses of the dynamics of the density operator of a driven nonlinear oscillator and a qubit coupled system during the measurement process. In purely quantum cases, the wavefunction of the JBA is trapped in a quasienergy-state, and bifurcation is impossible. Introducing decoherence enables us to reproduce the bifurcation with a finite hysteresis. Moreover, we discuss in detail the dynamics involved when a qubit is initially in a superposition state. We have observed the qubit-probe (JBA) entangled state and it is divided into two separable states at the moment of the JBA transition begins. This corresponds to "projection". To readout the measurement result, however, we must wait until the two JBA states are macroscopically well separated. The waiting time is determined by the strength of the decoherence in the JBA.

4 pages, 5 figures

References in corpus (5)

• Quantum non-demolition measurement of a superconducting two-level system
• High-contrast dispersive readout of a superconducting flux qubit using a nonlinear resonator
• Critical exponents in metastable decay via quantum activation
• Nonlinear response of a driven vibrating nanobeam in the quantum regime
• Dynamics of the quantum Duffing oscillator in the driving induced bistable regime

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• Dissipation in a rotating frame: master equation, effective temperature and Lamb-shift
• Measuring photon-photon interactions via photon detection
• Insufficiency of avoided crossings for witnessing large-scale quantum coherence in flux qubits
• Dissipative dynamics of a qubit coupled to a nonlinear oscillator
• The dissipative quantum Duffing oscillator: a comparison of Floquet-based approaches
• Classical and quantum dissipative dynamics in Josephson junctions: an Arnold problem, bifurcation and capture into resonance
• Control of transition frequency of a superconducting flux qubit by longitudinal coupling to the photon number degree of freedom in a resonator
• Transmon-qubit readout using in-situ bifurcation amplification in the mesoscopic regime
• Dynamics of an ultra-strongly-coupled system interacting with a driven nonlinear resonator
• Using a biased qubit to probe complex systems