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Ideal Negative Measurements in Quantum Walks Disprove Theories Based on Classical Trajectories

Carsten Robens, Wolfgang Alt, Dieter Meschede, Clive Emary, and Andrea Alberti
Phys. Rev. X 5, 011003 – Published 20 January 2015
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Abstract

We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.

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  • Received 15 June 2014

DOI:https://doi.org/10.1103/PhysRevX.5.011003

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

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Do Quantum Superpositions Have a Size Limit?

Published 20 January 2015

An atom’s walk in an optical lattice is used to test a key principle of quantum physics.

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Authors & Affiliations

Carsten Robens1, Wolfgang Alt1, Dieter Meschede1, Clive Emary2, and Andrea Alberti1,*

  • 1Institut für Angewandte Physik, Universität Bonn, Wegelerstr. 8, D-53115 Bonn, Germany
  • 2Department of Physics and Mathematics, University of Hull, Kingston-upon-Hull HU6 7RX, United Kingdom

Popular Summary

The motion of quantum particles differs dramatically from that of everyday objects. Whereas our experience tells us that a moving object follows a well-defined trajectory, in quantum mechanics, objects move not just along a single path but through a superposition of all possible paths connecting the starting and ending points.

To provide an objective, rigorous test of the existence of such quantum superpositions, Leggett and Garg derived a mathematical inequality that is obeyed by all objects moving along classical trajectories but that can be violated by quantum superpositions. We study experimentally the motion of a single cesium atom performing a quantum walk in a periodic optical lattice; we are able to realize subnanometer precision control of the cesium atoms. We find that this motion gives rise to a significant violation of the Leggett-Garg inequality. Importantly, the measurements that we make are noninvasive. In case we do not find the atom, these (noninvasive) measurements should have no effect on the classical motion, in striking contrast to quantum transport. This fact is an essential condition for any genuine Leggett-Garg test, and it allows us to conclude that the observed violation rules out any straightforward interpretation of our experiment in terms of classical trajectories.

Our measurements set the scene for further tests of mechanical quantum superposition states involving heavier objects split over increasingly larger distances. In this way, we have taken a step towards shedding new light on the emergence of the definiteness of everyday experience from the uncertainty of the quantum world.

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Vol. 5, Iss. 1 — January - March 2015

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