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The third level has great influence on the time evolution of the spontaneous decay from the excited state, when the counter rotating terms are taken into account. The influence in the cascade-type and V-type three-level systems is investigated for two initial states, excited from the ground states of the whole system (atom plus vacuum modes) and from the bare atom. The third level results in the additional virtual photon processes, emitting a photon from one level and reabsorbing the same photon to another level and vice versus. The main influence of the third level is to accelerate the decay, which leads to or enhances the anti-Zeno effect, especially for the initial state excited from the ground state of the whole system. Therefore, the third level could not be neglected, if the counter rotating terms are taken into account. PACS number: 03.65.Xp, 03.65.Yz, 42.50.Ct (I) Introduction The time evolution of an atomic spontaneous decay in a vacuum reservoir has attracted a lot of attention in recent years, where the Zeno and anti-Zeno effects can be realized [1-19]. For the time evolution, the rotating wave approximation (RWA) cannot be applied, because the counter rotating terms (CRTs) have great influence. It was found that the initial time evolution is quite different for different initial states [20]. It was also found that in the very short time period, the effective decay rate of the initial state is much slower than the exponential decay of the long time limit, which is the so-called quantum Zeno effect (QZE) [1-9]. Further study finds that the effective decay can be larger than the exponential decay after the QZE period, which is the so-called quantum anti-Zeno effect (QAZE) [10-16]. The QAZE was first discussed in a two-level system under the RWA. It was found that there is no QAZE if the CRTs are included for the initial state [15-17] excited from the ground state of the whole system (the atom plus vacuum reservoir) [15,20], while there is QAZE in a two-level atom if the initial state is the excited state of the bare atom (atom alone) [21]. These studies tell us that the QZE and QAZE heavily depend on the initial states and the CRTs. It is well known that the two-level atom is not a good model for the

Effect of the third level on time evolution of the spontaneous upper level decay due to counter-rotating terms