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Bulletin of the American Physical Society

Phase-space theory for nonlinear detectors of superconducting qubits

I. Serban, Frank K. Wilhelm

Published Mar 16, 2006• 0 citations
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Publisher's Note: Phase-space theory for dispersive detectors of superconducting qubits [Phys. Rev. B76, 104510 (2007)]

I. Serban, E. Solano, Frank K. Wilhelm

Received 17 September 2007DOI:https://doi.org/10.1103/PhysRevB.76.109902©2007 American Physical Society

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Motivated by recent experiments, we study the dynamics of a qubit quadratically coupled to its detector, a damped harmonic oscillator. We use a complex-environment approach, explicitly describing the dynamics of the qubit and the oscillator by means of their full Floquet state master equations in phase-space. We investigate the backaction of the environment on the measured qubit and explore several measurement protocols, which include a long-term full readout cycle as well as schemes based on short time transfer of information between qubit and oscillator. We also show that the pointer becomes measurable before all information in the qubit has been lost.
We propose a novel approach to detect a low power microwave signal with a frequency of the order of several GHz based on a coherent collective response of quantum states occurring in a superconducting qubits network (SQN). An SQN composes of a large number of superconducting qubits embedded in a low-dissipative superconducting resonator. Our theory predicts that an SQN interacting with the off-resonance microwave radiation, demonstrates the collective alternating current Stark effect that can be measured even in the limit of single photon counting. A design of the layout of three terminals SQN detectors containing 10 flux qubits weakly coupled to a low-dissipative R-resonator and T-transmission line was developed. The samples were fabricated by Al-based technology with Nb resonator. The SQN detector was tested in terms of microwave measurements of scattering parameters and two-tone spectroscopy. A substantial shift of the frequency position of the transmission coefficient drop induced by a second tone pump signal was observed, and this effect clearly manifests a nonlinear multiphoton interaction between the second-tone microwave pump signal and an array of qubits.