Quantum Zeno and anti-Zeno dynamics in a spin environment

We analyze the quantum Zeno and anti-Zeno effect in a spin-spin model, where a two-level system is embedded in a sea of spins with nonuniform couplings. By employing a generalized polaron transformation as well as a perturbative approach, the analytical expression of the effective decay rate of the spin-spin model is obtained. Compared with the well-known spin-boson model, we show that the two models share the same short-time dynamical behavior if and only if the environmental temperature is zero. We also find that the effective decay rate in the spin environment is larger than that of the harmonic environment for the sub-Ohmic spectrum case. Moreover, it is demonstrated that the crossover between quantum Zeno effect and anti-Zeno effect is highly sensitive to the details of the bath spectral function regardless of the spin environment or the harmonic environment.