Probing quantum mechanics with nanoparticle matter-wave interferometry

Nature 649, 866-870 (2026) · DOI: 10.1038/s41586-025-09917-9

License: CC BY 4.0.

Abstract

The quantum superposition principle is a fundamental concept of physics and the basis of numerous quantum technologies. 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. 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. Over the years, this has been explored with a series of objects of increasing mass and complexity 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 of μ = 15.5, surpassing previous experiments by an order of magnitude.

Figures

6 panels with data across 3 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF.

Fig. 2

• panel (a): Interference fringes of sodium clusters of mean mass 172 kDa: counts against the $G_3$ position (nm) for two independent measurement runs, run 1 (green) and run 2 (purple), each drawn as open markers joined by a dashed line, with the sine fit to each run as a solid curve. data.csv
• panel (b): Visibility and transmission against grating laser power $P_2$ (mW): weighted mean visibility per power bin (filled circles, $1\sigma$ error bars), measured transmission (crosses, right axis), and the quantum (red, solid), classical (blue, dotted) and transmission (black, dashed) models, each with its shaded uncertainty. Five lower error bars cut at zero in the print are shown in full. data.csv

Fig. 3

• panel (a): Predicted fringe visibility $V$ of the quantum model against mass (kDa) and grating laser power $P_2$ (mW), at a mean velocity of 160 m s$^{-1}$. The solid line marks the mass where the Talbot length equals the interferometer length, the dashed line where half of it does. The hosted map peaks near 0.9 where the print reaches 1, and some fringes are offset from the print. data.csv
• panel (b): Predicted fringe visibility $V$ of the classical model against mass (kDa) and grating laser power $P_2$ (mW), at a mean velocity of 160 m s$^{-1}$. The solid line marks the mass where the Talbot length equals the interferometer length, the dashed line where half of it does. The hosted map peaks near 0.9 where the print reaches 1, and some fringes are offset from the print. data.csv
• panel (c): Predicted fringe visibility $V$ of the quantum model for particles slowed against mass (kDa) and grating laser power $P_2$ (mW), at a mean velocity of about 25 m s$^{-1}$. The solid line marks the mass where the Talbot length equals the interferometer length, the dashed line where half of it does. The hosted map peaks near 0.9 where the print reaches 1, and some fringes are offset from the print. data.csv

Fig. 4

• panel (a): Macroscopicity $\mu$ of selected quantum experiments against year: atom interferometry (blue circles), molecule interferometry (red diamonds), Bose-Einstein condensates (orange crosses), mechanical resonators (green squares) and the sodium nanoclusters of this work (red star). The circle the print draws around the star is not drawn. data.csv

Cite

Sebastian Pedalino, Bruno E. Ramírez-Galindo, Richard Ferstl, Klaus Hornberger, Markus Arndt, Stefan Gerlich. Probing quantum mechanics with nanoparticle matter-wave interferometry. Nature 649, 866-870 (2026). https://doi.org/10.1038/s41586-025-09917-9

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