A general framework for the Quantum Zeno and anti-Zeno effects

A general treatment of the quantum Zeno and anti-Zeno effects is presented which is valid for an arbitrary system-environment model in the weak system-environment coupling regime. It is shown that the effective lifetime of a quantum state that is subjected to repeated projective measurements depends on the overlap of the spectral density of the environment and a generalized `filter function' which in turn depends on the system state that is repeatedly being prepared, the measurement interval, the system parameters, the system-environment coupling, and the environment correlation function. This general framework is then used to study explicitly the Zeno to anti-Zeno crossover behavior for the spin-boson model where a single two-level system is coupled to a bosonic environment. It is shown that our framework reproduces results for the usual population decay case as well as for the pure dephasing model, while at the same time allowing us to study the Zeno to anti-Zeno transition when both decay and dephasing take place. These results are then extended to many two-level systems coupled collectively to the bosonic environment to show that the distinction between the Zeno and anti-Zeno effects becomes more pronounced as the number of two-level systems increases.