Zeno physics in ultrastrong-coupling circuit QED

We study the Zeno and anti-Zeno effects in a superconducting qubit interacting strongly and ultrastrongly with a microwave resonator. Using a model of a frequently measured two-level system interacting with a quantized mode, we predict different behaviors and total control of the Zeno times depending on whether the rotating-wave approximation can be applied in the Jaynes-Cummings model. As an example, we show the dependence of our results with the properties of the initial field states.