A Continuously Observed Two-level System Interacting with a Vacuum Field

Details A Continuously Observed Two-level System Interacting with a Vacuum Field A Continuously Observed Two-level System Interacting with a Vacuum Field

2007-03-19

arxiv.org/abs/quant-ph/0703167v1

Physics

Quantum Physics

25 pages, no figures

Scientific paper

A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the classical behavior of unstable systems we consider a two-level system interacting with a Bose field, respectively prepared in the excited state and in the Poincare invariant vacuum state. Using time-dependent perturbation theory, we evaluate for a finite time interval the probability of spontaneous decay of the two-level system. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where N goes to infinity and we obtain that the non-decay probability law is a pure exponential, therefore recovering the classical behavior.

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