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arXiv:1906.10024 · Physical review. D/Physical review. D.

Measurement of the neutron lifetime and inverse quantum Zeno effect

Francesco Giacosa, Giuseppe Pagliara

Published Mar 5, 2020• 17 citations
arXivHTMLPDF

Abstract

Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the experimental setup for the observation, one could obtain the so called (direct) quantum Zeno and inverse quantum Zeno effects corresponding to a slowing down or a speeding up of the decay, respectively. We argue that the inverse quantum Zeno effect is in principle detectable at a percent level for the neutron decay in experiments with trapped ultracold neutrons. Conversely, this effect is basically undetectable in experiments in which the neutron lifetime is measured by measuring the decays of beams of neutrons. As a test of our claim, we propose a simple qualitative correlation between the number of neutrons in the trap and the neutron lifetime: the larger the number, the faster the decay. Finally we discuss also the presently available measurements of the neutron lifetime and address the issue of the possible discrepancy that has been reported among the results obtained by the different experimental techniques.

DOI
10.1103/physrevd.101.056003

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•Jan 1, 1996•36 citations
Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the experimental setup for the observation, one could obtain the so called (direct) quantum Zeno and inverse quantum Zeno effects corresponding to a slowing down or a speeding up of the decay, respectively. We argue that the inverse quantum Zeno effect is in principle detectable at a percent level for the neutron decay in experiments with trapped ultracold neutrons. Conversely, this effect is basically undetectable in experiments in which the neutron lifetime is measured by measuring the decays of beams of neutrons. As a test of our claim, we propose a simple qualitative correlation between the number of neutrons in the trap and the neutron lifetime: the larger the number, the faster the decay. Finally we discuss also the presently available measurements of the neutron lifetime and address the issue of the possible discrepancy that has been reported among the results obtained by the different experimental techniques.
The lifetime of the neutron, although being a fundamental quantity in particle physics, is to date still associated with a puzzle: different techniques of measurements find values of the lifetime which are mutually incompatible. While methods based on beams of neutrons find a (average) value τnbeam=888.1±2.0\tau_{n}^{\text{beam}} =888.1\pm2.0τnbeam​=888.1±2.0 s, methods based on traps obtain a shorter lifetime τntrap=879.37±0.58\tau_{n} ^{\text{trap}}=879.37\pm0.58τntrap​=879.37±0.58 s, i.e. a ∼4σ\sim 4\sigma∼4σ mismatch. This is the so-called neutron decay anomaly. We propose here a novel interpretation of this puzzle based solely on quantum mechanics (no need of physics beyond the standard model): if the measurement apparatus and the surrounding environment are able to observe the unstable system at very short (but not too short) times after the preparation of it, the so called inverse quantum Zeno (IZE) effect can take place: the IZE corresponds an increase of the decay rate through the interaction of the system with the environment. We argue that such a quantum phenomenon can be realized in the case of trap experiments but not in the case of beam experiments. There are mainly two reasons behind our interpretation of the neutron decay anomaly: (i) the intrinsic dependence of the 3-body weak decay rate on the Q value of the decay (the Sargent rule); (ii) the very peculiar setup of neutron traps, in which up to ∼108\sim 10^{8}∼108 ultra cold neutrons are confined together. This feature can help to increase the frequency of dephasing of the wave function (equivalent to the `collapse'), necessary to obtain the inverse quantum Zeno effect.
We discuss a simple and analytically solvable measurement model which describes the famous Quantum Zeno Effect (QZE) and Inverse Zeno Effect (IZE), that correspond to the slow down and to the increase of the decay rate caused by measurements (or, more in general, by the interaction of an unstable state with the detector and the environment). Within this model one can understand quite general features of the QZE and IZE: by considering an unstable quantum state, such as an unstable particle, whose decay width as function of energy is Γ(ω)=g2ωα,Γ(ω)=g^{2}ω^α,Γ(ω)=g2ωα, then -- under quite general assumptions -- the QZE occurs for α∈(0,1)α\in(0,1)α∈(0,1), while the IZE for α∈(−∞,0)∪(1,∞).α\in(-\infty,0)\cup(1,\infty).α∈(−∞,0)∪(1,∞). This result is valid also for more realistic measurement models than the one described in this work. We then apply these considerations to the decay of the neutron, for which α=5.α=5.α=5. Hence, the realization of the IZE for the neutron decay (and for the majority of weak decays) is in principle possible. Indeed, trap experiments find a lifetime that is 8.7±2.18.7\pm2.18.7±2.1 s shorter than beam experiments, suggesting that the IZE could have taken place.
When a quantum system undergoes a series of repeated measurements during its time evolution to check whether it remains in the initial state, the resulting state lifetime can decrease (the quantum Zeno effect) or increase (the quantum inverse Zeno effect) as the inter-measurement period increases. Several transitions between these two regimes may occur within the same system. A carefully chosen measurement period τ∗τ_\astτ∗​ (or rate r∗r_\astr∗​ in the case of a stochastic measurement protocol) brings the state lifetime to its global minimum. Here, we describe the upper and lower bounds on the optimized state lifetime, which are expressed in terms of characteristic time scales encoded in the state survival probability P(T)P(T)P(T), which is assumed to decrease monotonically to zero at large TTT. In addition, we analyze the bounds on the optimal measurement periods/rates and formulate sufficient conditions for observing the inverse Zeno effect. The analysis is also extended to states with non-monotonic survival functions. The results are illustrated numerically with an example of a system of optically trapped ultra-cold atoms.
Beam and trap methods find incompatible results for the lifetime of the neutron: the former delivers a value which is about 8.7±2.18.7\pm2.18.7±2.1 s longer than the latter. Very recently (1906.10024) it has been proposed that the inverse Zeno effect (IZE) could be responsible for the shorter lifetime in trap experiments. Here, we compare two different models of measurement, one obtained by bang-bang measurements and by a continuous measurement: the IZE turns out to be in both cases very similar, showing that the results do not depend on the details of the measurement process.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the