Circuit quantum electrodynamics with a nonlinear resonator

Abstract

This chapter investigates the coupling of a two-level system to a nonlinear resonator, one of the simplest extensions to the well-known Jaynes–Cummings model. In the experiment, the two-level system is a superconducting transmon qubit, and the resonator is a coplanar resonator with a Kerr nonlinearity induced by a Josephson junction. Effects arising from the resonator nonlinearity (bistability, parametric amplification, squeezing) qualitatively modify the dispersive qubit-resonator coupling. This makes it possible to design a qubit readout which has both a high fidelity and the potential of being QND. Motivated by fundamental and practical issues concerning the quantum limit of such a measurement, the chapter also studies spectroscopically the quantum back action exerted by the intraresonator field onto the qubit. Qualitative agreement is obtained with analytical results and quantitative agreement with numerical simulations.