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We study the backaction of a driven nonlinear resonator on a multi-level superconducting qubit. Using unitary transformations on the multi-level Jaynes-Cummings Hamiltonian and quantum optics master equation, we derive an analytical model that goes beyond linear response theory. Within the limits of validity of the model, we obtain quantitative agreement with experimental and numerical data, both in the bifurcation and in the parametric amplification regimes of the nonlinear resonator. We show in particular that the measurement-induced dephasing rate of the qubit can be rather small at high drive power. This is in contrast to measurement with a linear resonator where this rate increases with the drive power. Finally, we show that, for typical parameters of circuit quantum electrodynamics, correctly describing measurement-induced dephasing requires a model going beyond linear response theory, such as the one presented here.
We measure the quantum fluctuations of a pumped nonlinear resonator, using a superconducting artificial atom as an in-situ probe. The qubit excitation spectrum gives access to the frequency and temperature of the intracavity field fluctuations. These
We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. We modulate the magnetic flux through a superconducting quantum interference device, attached to a quarter-wavelength reso
We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, $k_B T ll hbaromega$. The resonator is terminated by a tunable inductance that provides a Kerr-type nonlinear
In addition to their central role in quantum information processing, qubits have proven to be useful tools in a range of other applications such as enhanced quantum sensing and as spectrometers of quantum noise. Here we show that a superconducting qu
We propose an experimentally realizable hybrid quantum circuit for achieving a strong coupling between a spin ensemble and a transmission-line resonator via a superconducting flux qubit used as a data bus. The resulting coupling can be used to transf