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arXiv:quant-ph/0104035 · Physical Review Letters

Observation of the Quantum Zeno and Anti-Zeno Effects in an Unstable System

Martin C. Fischer, Braulio Gutiérrez–Medina, M. G. Raizen

Published Jul 10, 2001• 444 citations
arXivHTMLPDF

Abstract

We report the first observation of the quantum Zeno and anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.

DOI
10.1103/physrevlett.87.040402

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arXiv:quant-ph/0105138•Physical Review A•May 8, 2001•19 citations
We report the first observation of the quantum Zeno and anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.
We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects.
~Received 30 October 1996! We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects. @S1050-2947~97!50702-5# PACS number~s!: 03.75.Be, 32.80.Pj, 42.50.Vk Tunneling in the center-of mass motion of atoms should become an important process at the low temperatures that are now achieved with laser cooling. This can appear, for example, as a loss mechanism for atoms confined in an optical lattice constructed from interfering beams of light. While atomic motion in these structures has become an active area of research @1,2#, tunneling has been obscured by spontaneous scattering @3#. An alternative atom optics system where tunneling can be significant has appeared in our efforts to develop a cold atomic beam for interferometry. Our approach has been to launch laser-cooled atoms in the potential created by an accelerating, far-detuned, standing wave of light. This system was previously used to study Wannier-Stark ladders @4# and Bloch oscillations @5#. The results reported in this Rapid Communications provide an observation of tunneling in atom optics, and the high degree of experimental control has enabled a quantitative comparison with theory. We consider atomic motion in an accelerating standing wave of light. For sufficiently large detuning from atomic resonance, the atoms remain in their internal ground state and experience an effective one-dimensional potential given by V0cos@2kL(x2at 2 /2)#, where k L52p/l L is the wave number, and a is the acceleration of the standing wave @6#. The well depth V0 is the amplitude of the optical dipole potential. It is proportional to the laser intensity and inversely proportional to detuning from atomic resonance. We neglect variations of the potential in the two transverse directions, which is justified for beams that are sufficiently
A simple model of indirect pre-measurements on an unstable quantum state is presented in this paper. The model is completely solvable and the solutions are used to compare the time evolution of the unstable state with and without the influence of the pre-measurement. We find that by choosing the details of the process of pre-measurement appropriately, it is possible to observe both suppression and enhancement of the rate of decay of the unstable state. When the pre-measurements are assumed to lead on to actual measurements, we see that the quantum Zeno effect, and in some instances the 'anti-Zeno' effect, can be produced by repeating the measurement many times in succession. The Zeno effect can appear in our model either as a real consequence of repeated measurements or sometimes merely as an artefact of the manner in which the observations on the system are performed. The anti-Zeno effect appears almost exclusively as an artefact of the details of the measurement. Numerical investigations are included to delineate the regimes in which the quantum Zeno effect and possibly the anti-Zeno effect can occur.
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).
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.