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Nature

Probing quantum mechanics with nanoparticle matter-wave interferometry

Sebastian Pedalino, Bruno E. Ramírez-Galindo, Richard Ferstl, Klaus Hornberger, Markus Arndt, Stefan Gerlich

Published Jan 21, 2026• 25 citations
Publisher

Abstract

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.

DOI
10.1038/s41586-025-09917-9

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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.
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Matter-wave interferometry has become a ubiquitous and reliable tool for studying fundamental forces and phenomena and for realizing sensitive measurements. Our recent experiments with metal clusters have allowed us to demonstrate the quantum-wave nature of nanoparticles exceeding 170 kDa. Interestingly, the same experiments also allow for the preparation of moiré fringes of objects in the megadalton range. In this work, we demonstrate such moiré fringes of large sodium nanoparticles and, owing to the platform's stability, resolve nanometer-scale fringe displacements between successive contrast revivals, directly observing the predicted π-phase flip as a half-period shift. We further discuss how this feature turns the interferometer into a device for advanced sensing, even when operating in the regime where the predictions of quantum and classical physics merge.
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Quantum superposition is central to quantum theory but challenges our concepts of reality and spacetime when applied to macroscopic objects like Schrödinger's cat. For that reason, it has been a long-standing question whether quantum physics remains valid unmodified even for truly macroscopic objects. By now, the predictions of quantum theory have been confirmed via matter-wave interferometry for massive objects up to 104 10^4\,104 atomic mass units (amu). The rapid development of new technologies promises to soon allow tests of quantum theory for significantly higher test masses by using novel techniques of quantum optomechanics and high-mass matter-wave interferometry. Such experiments may yield novel insights into the foundations of quantum theory, pose stringent limits on alternative theoretical models or even uncover deviations from quantum physics. However, performing experiments of this type on Earth may soon face principal limitations due to requirements of long times of flight, ultra-low vibrations, and extremely high vacuum. Here, we present a short overview of recent developments towards the implementation of the proposed space-mission MAQRO, which promises to overcome those limitations and to perform matter-wave interferometry in a parameter regime orders of magnitude beyond state-of-the-art.