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arXiv:1804.01320 · Physical Review A

Conditions for anti-Zeno-effect observation in free-space atomic radiative decay

Emmanuel Lassalle, C. Champenois, Brian Stout, Vincent Debierre, Thomas Durt

Published Jun 22, 2018• 7 citations

Abstract

Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article [A. G. Kofman and G. Kurizki, Nature (London) 405, 546 (2000)], Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of analytical results available for hydrogenlike atoms, we find that in free space, only non-electric-dipole transitions should present an observable AZE, revealing that this effect is consequently much less ubiquitous than first predicted. We then propose an experimental scheme for AZE observation, involving the electric quadrupole transition between ${D}_{5/2}$ and ${S}_{1/2}$ in the alkali-earth ions ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$. The proposed protocol is based on the stimulated Raman adiabatic passage technique, which acts like a dephasing quasimeasurement.

DOI: 10.1103/physreva.97.062122

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Frequent measurements can modify the decay of an unstable quantum state with respect to the free dynamics given by Fermi's golden rule. In a landmark article [A. G. Kofman and G. Kurizki, Nature (London) 405, 546 (2000)], Kofman and Kurizki concluded that in quantum decay processes, acceleration of the decay by frequent measurements, called the quantum anti-Zeno effect (AZE), appears to be ubiquitous, while its counterpart, the quantum Zeno effect, is unattainable. However, up to now there have been no experimental observations of the AZE for atomic radiative decay (spontaneous emission) in free space. In this work, making use of analytical results available for hydrogenlike atoms, we find that in free space, only non-electric-dipole transitions should present an observable AZE, revealing that this effect is consequently much less ubiquitous than first predicted. We then propose an experimental scheme for AZE observation, involving the electric quadrupole transition between

{D}_{5/2}

and

{S}_{1/2}

in the alkali-earth ions

{\mathrm{Ca}}^{+}

and

{\mathrm{Sr}}^{+}

. The proposed protocol is based on the stimulated Raman adiabatic passage technique, which acts like a dephasing quasimeasurement.

The quantum Zeno effect (QZE) is the striking prediction that the decay of any unstable quantum state can be inhibited by sufficiently frequent observations (measurements). The consensus opinion has upheld the QZE as a general feature of quantum mechanics, which should lead to the inhibition of any decay. The claim of QZE generality hinges on the assumption that successive observations can in principle be made at time intervals too short for the system to change appreciably. However, this assumption and the generality of the QZE have scarcely been investigated thus far. We have addressed these issues by showing that (i) the QZE is principally unattainable in radiative or radioactive decay, because the required measurement rates would cause the system to disintegrate; (ii) decay acceleration by frequent measurements (the anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE is shown to be observable as the enhancement of tunneling rates (e.g., for atoms trapped in ramped-up potentials or in current-swept Josephson junctions), fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields) and photon depolarization rates (in randomly modulated Pockels cells).

Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.

The acceleration of decay induced by frequency measurements, namely the quantum anti-Zeno effect (AZE), was first predicted by Kofman and Kurizki [Nature 405 (2000) 546]. The effect of the frequency measurements on nuclear β decay rate is analyzed based on the time-dependent perturbation theory. We present a detailed calculation of the decay rates of 3H, 60Co (β − type), 22Na, 106Ag (β + type) and 18F, 57Co and 111Sn (EC type) under frequency measurements. It is found that the effects of frequency measurements on the decay rates of β + and β − cases are different from the case of EC, and the smaller the β decay energy is, the more favorable it is to observe the AZE in experiment. Based on our analysis, it is suggested that possible experimental candidates should have a small decay energy and a reasonable half life (such as 3H) for observing the AZE in β decay.

It was predicted that frequently repeated measurements on an unstable state may alter the decay rate of the state. This is called the quantum Zeno effect (QZE) or the anti-Zeno effect (AZE), depending on whether the decay is suppressed or enhanced. In conventional theories of the QZE and AZE, effects of measurements are simply described by the projection postulate, assuming that each measurement is an instantaneous and ideal one. However, real measurements are not instantaneous and ideal. For the QZE and AZE by such general measurements, interesting and surprising features have recently been revealed, which we review in this article. The results are based on the quantum measurement theory, which is also reviewed briefly. As a typical model, we consider a continuous measurement of the decay of an excited atom by a photodetector that detects a photon emitted from the atom upon decay. This measurement is an indirect negative-result one, for which the curiosity of the QZE and AZE is emphasized. It is shown that the form factor is renormalized as a backaction of the measurement, through which the decay dynamics is modified. In a special case of the flat response, where the detector responds to every photon mode with an identical response time, results of the conventional theories are reproduced qualitatively. However, drastic differences emerge in general cases where the detector responds only to limited photon modes. For example, against predictions of the conventional theories, the QZE or AZE may take place even for states that exactly follow the exponential decay law. We also discuss relation to the cavity quantum electrodynamics.