Optimization of a neutron-spin test of the quantum Zeno effect

Abstract

A neutron-spin experimental test of the quantum Zeno effect (QZE) is discussed from a practical point of view, when the nonideal efficiency of the magnetic mirrors, used for filtering the spin state, is taken into account. In the idealized case the number N of (ideal) mirrors can be indefinitely increased, yielding an increasingly better QZE. By contrast, in a practical situation with imperfect mirrors, there is an optimal number of mirrors, Nopt, at which the QZE becomes maximum: more frequent measurements would deteriorate the performance. However, a quantitative analysis shows that a good experimental test of the QZE is still feasible. These conclusions are of general validity: in a realistic experiment, the presence of losses and imperfections leads to an optimal frequency Nopt, which is in general finite. One should not increase N beyond Nopt. A convenient formula for Nopt, valid in a broad framework, is derived as a function of the parameters characterizing the experimental setup.

Continuous and Pulsed Quantum Zeno Effect

“…Our observed quantum Zeno suppressions are substantially larger then both previous pulsed [2] and continuous [4] results, and is also greater then that expected from proposed experiments [11,15,26,28] in neutrons.…”

“…Previous works [2,7,26] express the QZE in terms of the survival probability P (N ) for number of measurements N during a π pulse (t = π/ω R ), a duration where without measurements 100% of the atoms would be transferred into the other state. Fig.…”

“…We have extended previous work in pulsed QZE measurements [2,5,7] by exploiting advantages inherent to BoseEinstein condensates. While in theory the Heisenberg uncertainty principal limits how frequently meaningful measurements can be performed, in practice imperfections in real measurements are the limiting factors [26,28]. In ion experiments optical pumping between states during the measurement pulses changed the observed population transfer [2], requiring significant corrections for the N=32 and N=64 pulse measurements (Table I, [2]) to observe a maximum survival probability P (64) = 0.943 (20) [2] (τ EP = 54(30) · 1/ω R ).…”

Sufficient conditions for the anti-Zeno effect

“…For the first time it was formulated explicitly in this context by Beskow and Nilsson [3] and soon after a mathematical analysis [5,14] revealed sufficient conditions under which it exists; it became truly popular after the authors of [20] coined its present name. Recently the effect attracted a new wave of mathematical [8,9,19,22] and physical [11,10,12,13,16,18] interest; in the mentioned papers one can find a more complete bibliography.Although the opposite situation, in which a frequent measurement can on the contrary speed up the decay, or ideally to lead to an immediate disappearance of the unstable system, was also noticed early [6], it attracted attention only recently -see, e.g., [1,2,17,21] and also [22] and references therein. As in the case of the Zeno effect, the problem can be tackled from two points of view.…”

“…For the first time it was formulated explicitly in this context by Beskow and Nilsson [3] and soon after a mathematical analysis [5,14] revealed sufficient conditions under which it exists; it became truly popular after the authors of [20] coined its present name. Recently the effect attracted a new wave of mathematical [8,9,19,22] and physical [11,10,12,13,16,18] interest; in the mentioned papers one can find a more complete bibliography.…”