Abstract:

The quantum Zeno effect in an atomic system relates to slowing down of the decay process under frequent observation. All the previous studies on this interesting effect have been carried out in the so-called rotating wave approximation (RWA). According to these studies the time interval to experimentally observe the quantum Zeno effect in the decay from an atom, such as hydrogen, needs to be less than a femotosecond. However, for such short time interval, the RWA is no longer valid.
We address the question: What is the effect of the counter-rotating terms on the dynamical evolution of the atom at short time, particularly on quantum Zeno and anti-Zeno effects? It is well-known that the contribution of the counter-rotating terms is insignificant in the calculation of the decay rate for the excited state of an atom in the long time limit.? We find the surprising result that the counter-rotating terms can have great impact on the short time evolution of the population of the excited level, and thus on the quantum Zeno and anti-Zeno effects. We present the analytical study for the multi-level atom coupled to the electromagnetic field in free space, obtain simultaneously the electron self-energy, Lamb shift and the short-time dynamics. For the hydrogen atom, we calculate the effective decay rate and find that, because of the counter-rotating terms, the Zeno time is longer by two orders of magnitude than that obtained with rotating-wave approximation, and there is no anti-Zeno effect. Consequently the experimental measurement of the quantum Zeno effect may be much easier than what was determined with the rotating-wave approximation results.
 
 
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