  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 show different behaviors and total control of the Zeno times depending
on whether the rotating-wave approximation can be applied in the
Jaynes-Cummings model, or not. We exemplify showing the strong dependence of
our results with the properties of the initial field states and suggest
applications for quantum tomography.
