Anti-Zeno-effect recovery and Lamb-shift modification in modified vacuum

The influence of the modification of the free vacuum on the quantum Zeno and anti-Zeno effects, as well as the Lamb (energy) shift of a multilevel atom, is studied. A unitary transformation method has been used to include the counter-rotating terms and to obtain the ground state of the whole Hamiltonian. The anti-Zeno effect is recovered if the modified density of states (DOS) has a dip near the transition frequency. The modification of DOS by a dip or a peak will change the Lamb shift compared with that in the free vacuum. Together with our unitary transformation method, there are three different methods to obtain the change in the Lamb shift. Using our method we investigate the change in the Lamb shift and obtain a formula for the change, which is the same as obtained with the method of Louisell but different from the method of Cohen-Tannoudji [Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992), pp. 317 and 417]. The correctness of the Lamb shift formulas obtained by the three methods can be easily testified experimentally.