Backaction of a driven nonlinear resonator on a superconducting qubit

TL;DR

This paper develops an analytical model to understand how a driven nonlinear resonator affects a superconducting qubit, revealing that measurement-induced dephasing can be minimized at high drive powers, unlike in linear resonators.

Contribution

The paper introduces a new analytical model that extends beyond linear response theory to accurately describe the backaction of a driven nonlinear resonator on a superconducting qubit.

Findings

Measurement-induced dephasing can be small at high drive power.

The model agrees with experimental and numerical data in bifurcation and parametric amplification regimes.

Linear response models are insufficient for describing measurement backaction in nonlinear regimes.

Abstract

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.