Driven appearance and disappearance of quantum zeno effect in the dynamicsof a four-level trapped ion

An example of constrained unitary quantum dynamics in them context of trapp ed ions is given. We study a laser driven four-level ion system confined in an isotropic three-dimensional Paul microtrap. Our main result is that whe n two independent controllable continuous measurement processes are simulta neously present, the unitary quantum dynamics of the system can be parametr ically frozen into a one-dimensional Hilbert subspace (Quantum Zeno Effect) or constrained into a. two-dimensional one, at will. Conditions under whic h one of the two processes acts upon the physical system inhibiting the eff ects due to the other one, are explicitly found and discussed (Hierarchical ly Controlled Dynamics).