Atomic “bomb testing”: the Elitzur–Vaidman experiment violates the Leggett–Garg inequality

Appl. Phys. B (2017) 123:12 DOI 10.1007/s00340-016-6581-y Atomic “bomb testing”: the Elitzur–Vaidman experiment violates the Leggett–Garg inequality Carsten Robens1 · Wolfgang Alt1 · Clive Emary2 · Dieter Meschede1 · Andrea Alberti1 Received: 20 September 2016 / Accepted: 4 November 2016 / Published online: 19 December 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract Elitzur and Vaidman have proposed a measurement scheme that, based on the quantum superposition principle, allows one to detect the presence of an object— in a dramatic scenario, a bomb—without interacting with it. It was pointed out by Ghirardi that this interaction-free measurement scheme can be put in direct relation with falsification tests of the macro-realistic worldview. Here we have implemented the “bomb test” with a single atom trapped in a spin-dependent optical lattice to show explicitly a violation of the Leggett–Garg inequality—a quantitative criterion fulfilled by macro-realistic physical theories. To perform interaction-free measurements, we have implemented a novel measurement method that correlates spin and position of the atom. This method, which quantum mechanically entangles spin and position, finds general application for spin measurements, thereby avoiding the shortcomings inherent in the widely used push-out technique. Allowing decoherence to dominate the evolution of our system causes a transition from quantum to classical behavior in fulfillment of the Leggett–Garg inequality. This article is part of the topical collection “Enlightening the World with the Laser” - Honoring T. W. Hänsch guest edited by Tilman Esslinger, Nathalie Picqué, and Thomas Udem. The original version of this article has been revised: In the editorial publishing process, the shaded band in Fig. 3 representing the theoretical model was omitted. Now, the Fig. 3 has been corrected. * Andrea Alberti ‑bonn.de 1 Institut Für Angewandte Physik, Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany 2 Joint Quantum Centre Durham‑Newcastle, Newcastle University, Newcastle upon Tyne NE1 7RU, UK 1 Introduction Measuring physical properties of an object—whether macroscopic or microscopic—is in most cases associated with an interaction. For example, scattering photons off an object allows one to detect its presence in a given region of space. However, this also produces a small perturbation of its state by direct momentum transfer. It is well known from numerous discussions on the physics of the quantum measurement process (see, e.g., Refs. [1, 2]) that a measurement in general modifies the quantum evolution unless the object is already in an eigenstate of the measurement apparatus [3]. This is even the case when the measurement yields a negative outcome, that is, when we did not find the particle on a certain trajectory that had originally a nonvanishing probability amplitude to be occupied. For example, in a double-slit experiment, quantum interference is suppressed as soon as a measurement detects the whichway information, regardless of whether the information is acquired by direct interaction or indirect negative inference. Quantum mechanics formalizes the loss of interference in terms of the quantum measurement process, showing that measurements are generally invasive as they entail a modification of the subsequent quantum evolution. While the quantum measurement process is still intensely debated in the literature [4], we adopt here the pragmatic view that a measurement applied to a superposition state causes a sudden reduction of the wave function to a subspace of the Hilbert space. Ideal negative measurements, that is, measurements without direct interaction, play an important role in a physical scenario known as macro-realism [5–7]. This scenario advocates a classical worldview describing the state of macroscopic objects, according to which macroscopic objects are always in one of several possible 13 Page 2 of 10 13 (a) A BS BS B D1 D2 counts (b) A BS BS B D1 25% macroscopically distinct states. In a macro-realistic worldview, it is plausible to assume that a negative outcome of a measurement cannot affect the evolution of a macroscopic system, meaning that negative measurements are noninvasive [8]. In order to rigorously test the macro-realistic point of view, Leggett and Garg have derived an inequality from the assumptions of macro-realism and noninvasive measurability, which can be violated by quantum-mechanical superposition states [9]. Relying on the implementation of an ideal negative measurement protocol—a prerequisite for any genuine test of the Leggett–Garg inequality—experimental violations of the macro-realistic worldview have been experimentally demonstrated with phosphor impurities in silicon by Knee et al. [10] and with trapped atoms by Robens et al. [11]. The definition of the degree of “macroscopic distinctness” has been a matter of discussion in the literature ever since [12], and is likely to remain as such till an experiment [13] will shed new light, for example, discovering a physical “classicalization” mechanism that causes an objective reduction of wave packets. Recently, Nimmrichter and Hornberger proposed a quantitative criterion based on a minimal macro-realistic extension of quantum mechanics to quantify the macroscopicity of an object [14]. Their objective criterion of macroscopicity allows us to experimentally test the behavior of a single trapped atom—however microscopic it is, according to our intuition—under the hypothesis of macro-realism, as we can put its macroscopicity directly in relation to that of other, ideally more massive physical objects. It was pointed out by Ghirardi [15] that a Leggett–Garg test of macro-realism is naturally related to the notion of interaction-free measurements introduced by Elitzur and Vaidman [16]. In a rather dramatic scenario, Elitzur and Vaidman proposed a quantum device able to single out live “bombs” from a collection containing also duds without triggering them nor interacting with them. While the first realizations of the Elitzur–Vaidman experiment employed “flying” photons [17] and “flying” neutrons [18], we here implement a variation of this experiment with neutral atoms trapped in a one-dimensional optical lattice. A convenient scheme for interaction-free measurements with neutral atoms has been demonstrated by Robens et al. [11] exploiting state-dependent optical potentials. Following the idea of Ghirardi, we tested the hypothesis of macro-realism with our atomic implementation of the Elitzur–Vaidman “bomb testing” Gedankenexperiment. Our experiment shows explicitly that the Leggett–Garg inequality is violated by 21 σ . In addition, trapped atoms can be held for long times. By controlling the duration of a suitably chosen wait interval, it is straightforward to study the influence of decoherence and experimentally observe the gradual transition from quantum to classic (...truncated)