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arXiv:2004.03392 · Physical Review Research

Quantum-classical hypothesis tests in macroscopic matter-wave interferometry

Björn Schrinski, Stefan Nimmrichter, Klaus Hornberger

Published Jul 8, 2020• 21 citations
arXivHTMLPDF

Abstract

The authors use interference experiments with delocalized molecules and Bose-Einstein-Condensates to probe the quantum superposition principle. The degree of macroscopicity reached can be quantified by a Bayesian hypothesis test based on the direct measurement data.
DOI
10.1103/physrevresearch.2.033034

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Designing experiments which delocalize ever more complex and more massive particles requires a quantitative assessment of new interferometer configurations.Here, we introduce a figure of merit which quantifies the difference between a genuine quantum interference pattern and a classical shadow and use it to compare a number of near-field interferometer schemes.This allows us to identify the most promising setups for future tests of the quantum superposition principle, and to discuss the perspectives of interferometry with complex molecules and clusters.
Abstract The quantum superposition principle is a fundamental concept of physics 1 and the basis of numerous quantum technologies 2,3 . Yet, it is still often regarded counterintuitive because we do not observe its key features on the macroscopic scales of our daily lives. It is, therefore, interesting to ask how quantum properties persist or change as we increase the size and complexity of objects 4 . A model test for this question can be realized by matter-wave interferometry, in which the motion of individual massive particles becomes delocalized and needs to be described by a wave function that spans regions far larger than the particle itself 5 . Over the years, this has been explored with a series of objects of increasing mass and complexity 6–9 and a growing community aims at pushing this to ever larger limits. Here we present an experimental platform that extends matter-wave interference to large metal clusters, a qualitatively new material class for quantum experiments. We specifically demonstrate quantum interference of sodium nanoparticles, which can each contain more than 7,000 atoms at masses greater than 170,000 Da. They propagate in a Schrödinger cat state with a macroscopicity 10 of μ = 15.5, surpassing previous experiments 5,9,11 by an order of magnitude.
Quantum interference is ubiquitous to many (if not all) quantum processes and phenomena, for it is a direct manifestation of their inherent coherence. Experiments based on matter wave interferometry [1] constitute very nice empirical evidences of this property. Though the first diffraction experiments were carried out with electrons [2], nowadays the (matter) particles utilized range from large atoms and single molecules [3-6] to very complex, large molecules [7] and Bose-Einstein condensates (BECs) [8]. This kind of experiments, apart from confirming the wave nature of matter, has also given rise to important practical applications. For example, sensing, metrology or quantum information processing are potential applications which have motivated in the last few years the remarkable development of BEC interferometry [9-11]. This can be observed in the increasing amount of (theoretical and T&F Cat # K11224, Chapter 13, Page 198, 15-9-2010 experimental) work appearing in the literature [12-18] since the first experimental evidence of interference between two freely expanding BECs [19]. The basic scheme upon which this type of interferometry is based is depicted in Figure 13.1. In the first stage (left), the atomic cloud is cooled down in a magnetic trap until condensation takes place. Then (right), the BEC is split up coherently by means of radio-frequency [16] or microwave fields [17]. Finally, the double-well-like trapping potential [20] is switched off, releasing the two resulting BECs, which will interfere by free expansion (e.g., see Figure 6 of Ref. [18] as an illustration of a real experimental outcome).
We address the challenge of certifying quantum behavior with single macroscopic massive particles, subject to decoherence and finite data. We propose a hypothesis-testing framework that distinguishes between classical and quantum mechanics based on position measurements. While interference pattern visibility in single-particle quantum superposition experiments has been commonly used as a sufficient criterion to falsify classical mechanics, we show that, from a hypothesis-testing perspective, it is neither necessary nor efficient. Focusing on recent proposals to prepare macroscopic superposition states of levitated nanoparticles, we show that the likelihood ratio test—which leverages differences across the entire probability distribution—provides an exponential reduction in measurements needed to reach a given confidence level. These results generalize to a broad class of quantum states, and offer a principled, efficient method to falsify classical mechanics in interference experiments, relaxing the experimental constraints faced by current efforts to test quantum mechanics at the macroscopic scale.