Circuit QED with a Nonlinear Resonator: ac-Stark Shift and Dephasing

Coupling a superconducting qubit to a superconducting resonator enables to investigate the interaction between light and matter with a unique flexibility of design, and allows to reach coupling regimes hardly accessible otherwise [Wallraff Nature 2004]. In this talk, we discuss the ac-Stark shift and the measurement induced dephasing of a qubit embedded in a \emph{nonlinear} resonator, an architecture that has demonstrated high fidelity single-shot qubit state readout [Mallet Nat. Phys. 2009]. In our experiment, a transmon qubit [Koch PRA 2007] is capacitively coupled to a coplanar waveguide resonator incorporating a Josephson junction that provides a Kerr nonlinearity. We have measured the qubit spectrum while pumping the nonlinear resonator with a microwave tone. Measurements of the qubit frequency shift provide a sensitive probe of the intracavity field, yielding a precise characterization of the resonator nonlinearity. The qubit linewidth has a complex dependence on the pump frequency and amplitude, which is correlated with the gain of the nonlinear resonator operated as a small-signal amplifier. The corresponding dephasing rate is found to be close to the quantum limit for most pump parameters.