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arXiv:1209.3136 · Journal of the Physical Society of Japan

Quantum Zeno Effect in an Unstable System with NMR

Yuichiro Matsuzaki, Hirotaka Tanaka

Published Dec 15, 2015• 1 citation
arXivHTMLPDF

Abstract

We theoretically propose a scheme for verification of quantum Zeno effect (QZE) to suppress a decay process with Nuclear Magnetic Resonance (NMR). Nuclear spins are affected by low frequency noise, and so one can naturally observe non-exponential decay behavior, which is prerequisite in observing QZE. We also describe that a key component for QZE, namely measurements on the nuclear spin, can be realized with NMR in the current technology

DOI
10.7566/jpsj.85.014001

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We theoretically propose a scheme for verification of quantum Zeno effect (QZE) to suppress a decay process with Nuclear Magnetic Resonance (NMR). Nuclear spins are affected by low frequency noise, and so one can naturally observe non-exponential decay behavior, which is prerequisite in observing QZE. We also describe that a key component for QZE, namely measurements on the nuclear spin, can be realized with NMR in the current technology
Projective measurements are an essential element of quantum mechanics. In most cases, they cause an irreversible change of the quantum system on which they act. However, measurements can also be used to stabilize quantum states from decay processes, which is known as the quantum Zeno effect (QZE). Here, we demonstrate this effect for the case of a superposition state of a nuclear spin qubit, using an ancilla to perform the measurement. As a result, the quantum state of the qubit is protected against dephasing without relying on an ensemble nature of NMR experiments. We also propose a scheme to protect an arbitrary state by using QZE.
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.
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.
Detailed schemes are investigated for experimental verification of Quantum Zeno effect with a superconducting qubit. A superconducting qubit is affected by a dephasing noise whose spectrum is 1/f1/f1/f and so the decay process of a superconducting qubit shows a naturally nonexponential behavior due to an infinite correlation time of 1/f1/f1/f noise. Since projective measurements can easily influence the decay dynamics having such nonexponential feature, a superconducting qubit is a promising system to observe quantum Zeno effect. We have studied how a sequence of projective measurements can change the dephasing process and also we have suggested experimental ways to observe quantum Zeno effect with a superconducting qubit. It would be possible to demonstrate our prediction in the current technology.