From the Quantum Zeno to the Inverse Quantum Zeno Effect

Abstract

The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric criterion is proposed for a transition to occur between these two regimes.

Non-exponential Decay in Quantum Field Theory and in Quantum Mechanics: The Case of Two (or More) Decay Channels

“…The fact that the so called survival probability, i.e. the probability p(t) that an unstable state S formed at the time t = 0 did not decay at the instant t > 0, does not follow an exponential decay law for short times is now theoretically [1,2,3,4,5,6] and experimentally [7,8,9] established in the framework of quantum mechanics. Moreover, oscillations on top of the exponential function can also occur in the short time regime and could eventually last long enough to be detected [10,11].…”

The case of escape probability as linear in short time

“…However, it is generally agreed that in short time the decay of quantum states is quadratic, e.g. [11] and hence the possibility of exact exponential decay is excluded. This also can be seen from equation (5).…”

Three Different Manifestations of the Quantum Zeno Effect

“…Among these, the reach and practical importance of the experiments on the QZE [37][38][39] and the physical meaning of the mathematical expressions "N → ∞" and "K → ∞" [34,4], that may involve delicate quantum field theoretical issues [40]. We will not elaborate on this here, but warn the reader that the expression "large N " and "large K" should not be taken lightheartedly, as they are directly related to the physically relevant timescales characterizing the evolution.…”

“…The numerical figures we have given are realistic and the Hamiltonian (54) is a good approximation of the decay process at short (for the physical meaning of "short", see [4,34,35]) and intermediate times (it is not valid for very large times, where a power law should appear). Related interesting proposals, making use of kicks or continuous coupling in cavity QED, can be found in [36].…”

“…However, the real problem are the relevant timescales: in order to get an effective "protection" of level |b , one needs K > 1/τ Z . More to this, if the decaying state |b has energy ω b = 0, an inverse Zeno effect [33,34] may take place and the requirement for obtaining the QZE becomes even more stringent [34], yielding K > 1/τ 2 Z γ. Both these conditions can be very demanding for a real system subject to dissipation.…”