Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Quantum superposition of molecules beyond 25 kDa


Matter-wave interference experiments provide a direct confirmation of the quantum superposition principle, a hallmark of quantum theory, and thereby constrain possible modifications to quantum mechanics1. By increasing the mass of the interfering particles and the macroscopicity of the superposition2, more stringent bounds can be placed on modified quantum theories such as objective collapse models3. Here, we report interference of a molecular library of functionalized oligoporphyrins4 with masses beyond 25,000 Da and consisting of up to 2,000 atoms, by far the heaviest objects shown to exhibit matter-wave interference to date. We demonstrate quantum superposition of these massive particles by measuring interference fringes in a new 2-m-long Talbot–Lau interferometer that permits access to a wide range of particle masses with a large variety of internal states. The molecules in our study have de Broglie wavelengths down to 53 fm, five orders of magnitude smaller than the diameter of the molecules themselves. Our results show excellent agreement with quantum theory and cannot be explained classically. The interference fringes reach more than 90% of the expected visibility and the resulting macroscopicity value of 14.1 represents an order of magnitude increase over previous experiments2.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Experimental schematic and molecule details.
Fig. 2: Interference data.
Fig. 3: Macroscopicity and CSL bounds.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on request.


  1. 1.

    Arndt, M. & Hornberger, K. Testing the limits of quantum mechanical superpositions. Nat. Phys. 10, 271–277 (2014).

    Article  Google Scholar 

  2. 2.

    Nimmrichter, S. & Hornberger, K. Macroscopicity of mechanical quantum superposition states. Phys. Rev. Lett. 110, 160403 (2013).

    Article  ADS  Google Scholar 

  3. 3.

    Bassi, A., Lochan, K., Satin, S., Singh, T. P. & Ulbricht, H. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471–527 (2013).

    Article  ADS  Google Scholar 

  4. 4.

    Sezer, U., Schmid, P., Felix, L., Mayor, M. & Arndt, M. Stability of high-mass molecular libraries: the role of the oligoporphyrin core. J. Mass Spectrom. 50, 235–239 (2015).

    Article  ADS  Google Scholar 

  5. 5.

    Friedman, J. R., Patel, V., Chen, W., Tolpygo, S. K. & Lukens, J. E. Quantum superposition of distinct macroscopic states. Nature 406, 43–46 (2000).

    Article  ADS  Google Scholar 

  6. 6.

    Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637–641 (1997).

    Article  Google Scholar 

  7. 7.

    Marinković, I. et al. Optomechanical Bell test. Phys. Rev. Lett. 121, 220404 (2018).

    Article  ADS  Google Scholar 

  8. 8.

    Kovachy, T. et al. Quantum superposition at the half-metre scale. Nature 528, 530–533 (2015).

    Article  ADS  Google Scholar 

  9. 9.

    Eibenberger, S., Gerlich, S., Arndt, M., Mayor, M. & Tüxen, J. Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000 amu. Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).

    Article  Google Scholar 

  10. 10.

    Gerlich, S. et al. A Kapitza–Dirac–Talbot–Lau interferometer for highly polarizable molecules. Nat. Phys. 3, 711–715 (2007).

    Article  Google Scholar 

  11. 11.

    Nairz, O., Brezger, B., Arndt, M. & Zeilinger, A. Diffraction of complex molecules by structures made of light. Phys. Rev. Lett. 87, 160401 (2001).

    Article  ADS  Google Scholar 

  12. 12.

    Hornberger, K. et al. Theory and experimental verification of Kapitza–Dirac–Talbot–Lau interferometry. New J. Phys. 11, 043032 (2009).

    Article  ADS  Google Scholar 

  13. 13.

    Koleske, D. D. & Sibener, S. J. Generation of pseudorandom sequences for use in cross‐correlation modulation. Rev. Sci. Instrum. 63, 3852–3855 (1992).

    Article  ADS  Google Scholar 

  14. 14.

    Hackermüller, L. et al. Optical polarizabilities of large molecules measured in near-field interferometry. Appl. Phys. B 89, 469–473 (2007).

    Article  ADS  Google Scholar 

  15. 15.

    Mairhofer, L. et al. Quantum-assisted metrology of neutral vitamins in the gas phase. Angew. Chem. Int. Ed. 56, 10947–10951 (2017).

    Article  Google Scholar 

  16. 16.

    Eibenberger, S., Cheng, X., Cotter, J. P. & Arndt, M. Absolute absorption cross sections from photon recoil in a matter-wave interferometer. Phys. Rev. Lett. 112, 250402 (2014).

    Article  ADS  Google Scholar 

  17. 17.

    Eibenberger, S., Gerlich, S., Arndt, M., Tüxen, J. & Mayor, M. Electric moments in molecule interferometry. New J. Phys. 13, 043033 (2011).

    Article  ADS  Google Scholar 

  18. 18.

    Hornberger, K., Sipe, J. E. & Arndt, M. Theory of decoherence in a matter wave Talbot–Lau interferometer. Phys. Rev. A 70, 053608 (2004).

    Article  ADS  Google Scholar 

  19. 19.

    Fröwis, F., Sekatski, P., Dür, W., Gisin, N. & Sangouard, N. Macroscopic quantum states: measures, fragility, and implementations. Rev. Mod. Phys. 90, 025004 (2018).

    MathSciNet  Article  ADS  Google Scholar 

  20. 20.

    Schrinski, B., Nimmrichter, S., Stickler, B. A. & Hornberger, K. Macroscopicity of quantum mechanical superposition tests via hypothesis falsification. Preprint at (2019).

  21. 21.

    Adler, S. L. Lower and upper bounds on CSL parameters from latent image formation and IGM heating. J. Phys. A 40, 2935–2957 (2007).

    MathSciNet  Article  ADS  Google Scholar 

  22. 22.

    Carlesso, M., Bassi, A., Falferi, P. & Vinante, A. Experimental bounds on collapse models from gravitational wave detectors. Phys. Rev. D 94, 124036 (2016).

    MathSciNet  Article  ADS  Google Scholar 

  23. 23.

    Toroš, M., Gasbarri, G. & Bassi, A. Colored and dissipative continuous spontaneous localization model and bounds from matter-wave interferometry. Phys. Lett. A 381, 3921–3927 (2017).

    Article  ADS  Google Scholar 

  24. 24.

    Kiałka, F. et al. Concepts for long-baseline high-mass matter-wave interferometry. Phys. Scr. 94, 034001 (2019).

    Article  ADS  Google Scholar 

  25. 25.

    Chalfie, M. GFP: lighting up life. Proc. Natl Acad. Sci. USA 106, 10073–10080 (2009).

    Article  ADS  Google Scholar 

  26. 26.

    Debiossac, M. et al. Tailored photocleavable peptides: fragmentation and neutralization pathways in high vacuum. Phys. Chem. Chem. Phys. 20, 11412–11417 (2018).

    Article  Google Scholar 

  27. 27.

    Haberland, H., Karrais, M. & Mall, M. A new type of cluster and cluster ion source. Z. Phys. D 20, 413–415 (1991).

    Article  ADS  Google Scholar 

  28. 28.

    Hutzler, N. R., Lu, H. I. & Doyle, J. M. The buffer gas beam: an intense, cold, and slow source for atoms and molecules. Chem. Rev. 112, 4803–4827 (2012).

    Article  Google Scholar 

  29. 29.

    Barry, J. F. & DeMille, D. Low-temperature physics: a chilling effect for molecules. Nature 491, 539–540 (2012).

    Article  ADS  Google Scholar 

  30. 30.

    Piliarik, M. & Sandoghdar, V. Direct optical sensing of single unlabelled proteins and super-resolution imaging of their binding sites. Nat. Commun. 5, 4495 (2014).

    Article  ADS  Google Scholar 

  31. 31.

    Nimmrichter, S., Hornberger, K., Haslinger, P. & Arndt, M. Testing spontaneous localization theories with matter-wave interferometry. Phys. Rev. A 83, 043621 (2011).

    Article  ADS  Google Scholar 

  32. 32.

    Frost, J. R. et al. H oxygenation catalyzed by a supramolecular ruthenium complex. Angew. Chem. Int. Ed. 54, 691–695 (2015).

    Google Scholar 

  33. 33.

    Fournier, J.-H., Maris, T., Wuest, J. D., Guo, W. & Galoppini, E. Molecular tectonics. Use of the hydrogen bonding of boronic acids to direct supramolecular construction. J. Am. Chem. Soc. 125, 1002–1006 (2003).

    Article  Google Scholar 

  34. 34.

    Dixon, J. M., Taniguchi, M. & Lindsey, J. S. PhotochemCAD 2. A refined program with accompanying spectral databases for photochemical calculations. Photochem. Photobiol. 81, 212–213 (2005).

    Article  Google Scholar 

  35. 35.

    Juffmann, T., Nimmrichter, S., Arndt, M., Gleiter, H. & Hornberger, K. New prospects for de Broglie interferometry. Found. Phys. 42, 98–110 (2010).

    Article  ADS  Google Scholar 

  36. 36.

    Nimmrichter, S. & Hornberger, K. Theory of Talbot–Lau interference beyond the eikonal approximation. Phys. Rev. A 78, 023612 (2008).

    Article  ADS  Google Scholar 

  37. 37.

    Stibor, A., Hornberger, K., Hackermüller, L., Zeilinger, A. & Arndt, M. Talbot–Lau interferometry with fullerenes: sensitivity to inertial forces and vibrational dephasing. Laser Phys. 15, 10–17 (2005).

    Google Scholar 

Download references


We thank L. Mairhofer and M. Debiossac for early contributions to the experiment, A. Shayeghi for computational and experimental support, and B. Stickler and K. Hornberger for discussions and support on macroscopicity and near-field interference theory. This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation program (grant no. 320694) and the Austrian Science Fund (FWF) within programme W1210-N25 (COQUS) and P-30176 (COLMI). Financial support by the Swiss National Science Foundation (grant number 200020-178808) is acknowledged. M.M. acknowledges support by the 111 project (90002-18011002). We acknowledge support from the Vienna Doctoral School.

Author information




M.A. conceived the experiment. Y.Y.F., S.G. and P.G. designed and constructed the experiment. P.Z. and M.M. synthesized the molecules used in the experiment. Y.Y.F, S.G., S.P. and P.G. carried out the experiments described here. Y.Y.F., F.K. and S.G. analysed the data, and Y.Y.F., S.G. and M.A. prepared the manuscript.

Corresponding author

Correspondence to Markus Arndt.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Stephen Adler and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Information.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Fein, Y.Y., Geyer, P., Zwick, P. et al. Quantum superposition of molecules beyond 25 kDa. Nat. Phys. 15, 1242–1245 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing