  The giant atom system is a new paradigm in quantum optics, in which the
traditional dipole approximation is not available. In this paper, we construct
an artificial giant atom model by coupling a superconducting circuits to a
transmission line by two coupling points. In the ultrastrong coupling regime,
we show that the Lamb shift of the giant atom, which is induced by the
non-negligible counter-rotating atom-waveguide coupling term, will modify its
dissipation process. Furthermore, we investigate quantum Zeno and anti-Zeno
effect where the size of the giant atom serves as a sensitive controller.
Specifically, by comparing the critical measurement interval and the life time
of the giant atom, we clarify the condition for the occurring of quantum
anti-Zeno effect. We hope our work is useful for the application of giant atom
system in the investigation of fundamental problems of quantum mechanics.
