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Frontiers in Optics

Inhibiting Phase Drift in Multi-Atom Clocks Using the Quantum Zeno Effect

S. U. Shringarpure, J. D. Franson

Published Jan 1, 2022• 0 citations
Publisher

Abstract

We investigate using the quantum Zeno effect to inhibit phase drifts in multi-atom clocks. Frequent quantum measurements confine the atomic evolution to the desired subspace where the phase drift is suppressed.
DOI
10.1364/ls.2022.lm3f.6

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Inhibiting phase drift in multi-atom clocks using the quantum Zeno effect

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The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of NNN atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of 1/N1/\sqrt{N}1/N​. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require N>>1N>>1N>>1 in order to achieve a good signal-to-noise ratio.
Abstract The accuracy of an atomic clock depends in part on the bandwidth of the relevant atomic transitions. Here we consider an ensemble of atoms whose transition frequencies have been independently perturbed by environmental effects or other factors. We consider the possibility of using the quantum Zeno effect to lock the relative phase of the atoms, which would decrease their effective bandwidth by a factor of 1/N.1/\sqrt N .1/N​. We analyze an example in which the quantum Zeno effect can be used to lock the relative phase of a pair of atoms, after which the elapsed time can be determined. Practical applications may require N>>1N>>1N>>1 in order to achieve a good signal-to-noise ratio.
Quantum simulation of lattice gauge theories is a promising tool for the study of many complicated problems including ones with real-time dynamics. For gauge theories, however, there is a major challenge in maintaining gauge invariance during time evolution. Such theories have a full Hilbert space that is larger than the physical space---the set of states which are gauge invariant or equivalently respect the Gauss law. While an exact implementation of Hamiltonian dynamics starting in the physical Hilbert space will keep the system in the physical space, various types of errors will inevitably produce components outside of it. This work proposes a method of suppressing this gauge drift via the Zeno effect. As in the standard picture of the Zeno effect, our method relies on frequent projection onto the physical subspace. Additionally, a technique is discussed to reduce the speed of the gauge drift, which helps to reduce the required frequency of projections. We demonstrate our method on a Z2{\mathbb{Z}}_{2}Z2​ gauge theory toy model.
We study the possibility of suppressing three-body losses in atomic Bose-Einstein condensates via the quantum Zeno effect, which means the delay of quantum evolution by frequent measurements. It turns out that this requires very fast measurements with the rate being determined by the spatial structure of the three-body form factor, i.e., the point interaction approximation ${\ensuremath{\delta}}^{3}(\mathbf{r}\ensuremath{-}{\mathbf{r}}^{'})$ is not adequate. Since the molecular binding energy Eb{E}_{b}Eb​ provides a natural limit for the measurement rate, this suppression mechanism can only work if the form factor possesses certain special properties.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.