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Probing quantum mechanics using nanoparticle Schr\"odinger cats

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that sodium clusters with a mean mass of 172 kDa—over 7,000 atoms each—show matter-wave interference with visibility up to 0.10, and that the power dependence of the fringes follows quantum predictions while excluding…

desk verdict Genuine experimental milestone in high-mass matter-wave interferometry; the 0.78 contrast scale factor is the main soft spot but not a load-bearing flaw. read the letter →

arxiv 2507.21211 v1 pith:GXF2XZOT submitted 2025-07-28 quant-ph

Sebastian Pedalino , Bruno E. Ramírez-Galindo , Richard Ferstl , Klaus Hornberger , Markus Arndt , Stefan Gerlich This is my paper · ORCID
classification quant-ph
keywords quantumsuperpositionmatter-waveinterferenceTalbot-LauinterferometernanoparticlesodiumclusterSchrödingercatmacroscopicitymacrorealism
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports matter-wave interference of neutral sodium clusters with a mean mass of 172 kDa—more than 7,000 atoms per cluster—inside a three-grating optical Talbot-Lau interferometer. The measured fringe visibility reaches up to $V = 0.10 \pm 0.01$, and its dependence on the power of the central phase grating follows the quantum prediction while remaining clearly separated from the classical-trajectory model. From the full dataset the authors derive a macroscopicity of $\mu = 15.5$, which they state is the most stringent exclusion of generic macrorealistic modifications of the Schrödinger equation to date. If the result holds up, it moves matter-wave interference from molecules to metallic nanoparticles and offers a new handle on where quantum mechanics gives way to classical behavior.

What carries the argument

The load-bearing object is the optical Talbot-Lau interferometer: three standing-wave ultraviolet gratings of period $d = 133$ nm and separation $L = 0.983$ m, in which the first and third gratings ionize and remove clusters at their antinodes (acting as absorptive gratings) while the second acts as a phase grating via the optical dipole force. The signal is computed in phase space using the Wigner-Weyl representation: the detected count rate is a Fourier series in the third-grating position whose coefficients are products of Talbot-Lau coefficients $B_n$, which depend on the coherent phase $\zeta_{\mathrm{coh}} = \varphi_0 \sin(\pi \xi)$ and ionization depletion $\zeta_{\mathrm{ion}} = (n_0/2)\cos(\pi\xi)$; the classical model follows from replacing these by their small-$\xi$ asymptotic forms. For masses around 172 kDa the Talbot length is comparable to the interferometer length, so the quantum and classical curves separate; for masses above roughly 1 MDa they converge. Macroscopicity is assigned by a Bayesian test of macrorealistic modifications, implemented through a factor $R_\ell$ multiplying the Fourier coefficients.

What would settle it

Reproduce the visibility-versus-$G_2$-power scan after determining the UV polarizability of 143–197 kDa sodium clusters by an independent method (for example, electric beam deflection) and after separately quantifying each source of contrast loss instead of absorbing it in the 0.78 factor; if the data then no longer separate from the classical curve, the quantum claim is refuted.

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Extended reading notes

Core claim

The central claim is that a beam of neutral sodium clusters with masses centered at 172 kDa can be prepared in a delocalized center-of-mass state whose extent exceeds the cluster diameter by more than an order of magnitude, and that the interference fringes observed after the third grating are genuinely quantum. The evidence is the visibility-versus-$G_2$-power curve: the measured contrasts track the quantum model obtained from the Wigner-Weyl phase-space description, and they deviate from the classical 'microlens' model, after both curves are scaled by the same global factor 0.78 to account for known imperfections. The same data, 3895 points, enter a Bayesian hypothesis test against minimally invasive macrorealistic modifications of quantum mechanics, yielding $\mu = 15.45$ (stated as 15.5), which surpasses the previous record by an order of magnitude and excludes such modifications at a new level.

Load-bearing premise

The load-bearing assumption is that the optical polarizability of the clusters is correctly calibrated from the 0.4–1 MDa fringes and that the remaining contrast loss can be captured by a single global factor of 0.78; if either is wrong, the predicted quantum and classical visibility curves shift and the claimed distinction—and the macroscopicity—could weaken.

Editorial extensions

If this is right

  • Matter-wave interference now extends to a new material class—metallic nanoparticles—with more than 7,000 atoms per particle, complementing previous records set with molecules and atoms.
  • The quantum-versus-classical separation at $m \approx 172$ kDa yields a macroscopicity $\mu = 15.5$, the most stringent exclusion of generic macrorealistic modifications of quantum mechanics reported to date.
  • In the 0.4–1 MDa range the same setup shows even higher fringe visibility (up to $V = 0.66 \pm 0.09$), but quantum and classical predictions coincide there; slowing clusters to about 25 m/s would restore the distinction and allow unambiguous quantum tests beyond 1 MDa.
  • Because the interferometer can accept various metals and dielectrics, it also enables measurement of electric or magnetic susceptibilities of clusters while they propagate as delocalized waves, and a vertical version could raise attainable macroscopicity by up to six orders of magnitude.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A cross-check the paper does not perform: measuring the mass-selected UV polarizability of the 143–197 kDa clusters by an independent, non-interferometric method would remove the main assumption behind the predicted visibility curves and the macroscopicity value.
  • The single 0.78 scale factor lumps together all contrast-reducing effects; replacing it with individually quantified loss terms would not only sharpen the quantum-classical separation but also reduce the uncertainty in $\mu$.
  • If the same techniques were applied to dielectric or biological nanoparticles, the mass frontier could advance without new interferometer hardware, providing a direct test of whether the quantum-classical distinction depends on material composition.
  • A natural near-term milestone follows from the paper's own projection: reaching about 25 m/s for 1 MDa clusters would separate quantum from classical predictions in a regime where current high-mass fringes cannot.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This manuscript reports matter-wave interference of sodium nanoclusters with a mean mass of 172 kDa (more than 7,000 atoms) in an optical Talbot-Lau interferometer, with fringe visibility up to V = 0.10. The authors compare the measured visibility as a function of the second-grating power against quantum and classical models, applying a global scale factor of 0.78 to both curves. They also report a macroscopicity of μ = 15.5 derived from a Bayesian test of minimal macrorealistic modifications, which they claim surpasses previous experiments by an order of magnitude. The paper includes a Wigner-Weyl phase-space description of the interferometer, a photophysics calibration of polarizability and ionization cross section, and a discussion of future improvements.

Significance. If the central claims hold, this is a substantial advance in matter-wave interferometry: it extends quantum superposition to nanoparticles containing thousands of atoms, with a macroscopicity value that would be the highest reported to date. The manuscript's strengths include a clear theoretical framework, an independent cross-check of the photophysics parameters via the transmission signal without additional scaling, and a principled Bayesian macroscopicity assessment. However, the headline claims rest critically on the global visibility scale factor 0.78 and on the calibration of the UV polarizability; these points need to be substantiated and made unambiguous before the result can be fully assessed.

major comments (4)
  1. [II. Results, Fig. 2b] The global scale factor of 0.78 applied to both theory curves in Fig. 2b is load-bearing for the agreement with the quantum model and for the claimed distinction from the classical prediction, but the main text gives no quantitative breakdown or uncertainty for this factor. The shaded theory uncertainty bands are stated to include only velocity, mass distribution, absorption cross section, and polarizability, not the scale factor. Please provide an itemized error budget for misalignment, gravitational and rotational phase averaging, vibrations, and thermal or collisional decoherence, with estimated magnitudes and an uncertainty on 0.78; alternatively, treat 0.78 as a fitted nuisance parameter and report its fitted value and confidence interval, and show that the quantum-versus-classical distinction is robust to its value.
  2. [Methods, Photophysics] The UV polarizability α266 is calibrated from high-contrast fringes at 0.4–1 MDa where the quantum and classical models agree, but the paragraph does not state whether the same global scale factor 0.78 was applied during that calibration. If the calibration did not include the scale factor while the 172 kDa modeling does, the extracted α266 could be biased (a 22% contrast deficit would propagate into the fitted polarizability), and applying 0.78 again at 172 kDa would double-count the same contrast loss. Please specify the calibration procedure in detail, including whether any scale factor is used, and quantify how the fitted α266 and its uncertainty change if the scale factor is included or omitted.
  3. [Methods, Macroscopicity assessment] The statement that 'any experimental imperfection and all decoherence processes are attributed to the macrorealistic modification and will therefore only decrease the macroscopicity' is ambiguous about whether the 0.78 scale factor enters the detection probability S(x3) used in the Bayesian likelihood. If the scale factor is included, then not all imperfections are attributed to the modification; if it is excluded, the likelihood model may be misspecified relative to the data presented in Fig. 2b. Please state the exact likelihood model, including how the scale factor enters, and provide a sensitivity analysis of the reported μ = 15.45 to the scale factor and to the polarizability uncertainty. This is essential for supporting the claim that the macroscopicity value is conservative.
  4. [II. Results, Fig. 2b] The claim that the data are 'well described by the quantum model and clearly distinct from the classical prediction' is not backed by a quantitative model comparison. Please report a goodness-of-fit statistic (e.g., reduced chi-square or a Bayesian evidence ratio) for the quantum and classical models, with the scale factor treated as a nuisance parameter with a prior derived from the error budget. This would substantiate the distinction independently of the absolute vertical scale of the visibility curves.
minor comments (6)
  1. [Velocity Distribution] The text 'Time of flight and velocity spectra form/q=100 kTh clusters' appears to contain a typo; it should likely read 'm/z = 100 kDa clusters' or similar.
  2. [Introduction / Abstract] The phrase 'de Broglie wavelengths between 10−22 fm' uses a minus sign that can be misread as subtraction; please use an en dash, '10–22 fm', to denote the range.
  3. [Methods, Eqs. (3) and (4)] The symbol w_y is used in Eqs. (3) and (4) but is not explicitly defined in the main text; please state that it is the vertical Gaussian waist and clarify whether the same value is used for all three gratings.
  4. [Results, Mass selection and detection] The sentence 'The mass filter was centered at 170 kDa' followed by the statement that doubly charged clusters are selected is confusing; please clarify whether 170 kDa refers to the neutral cluster mass or to the m/z setting, given the factor-of-two charge-state correction.
  5. [Fig. 2b caption] The phrase 'G1,3 powers as above' is unclear; it should read 'G1 and G3 powers as in (a)'.
  6. [Methods, Macroscopicity assessment] The value 'Kullback-Leibler divergence 1.27×10−3' should specify the units (nats) and define the reference distribution used for comparison.

Circularity Check

0 steps flagged · score 2.0 of 10

No load-bearing circularity: the quantum-versus-classical distinction is set by the different functional forms of the Talbot phase, not by the shared calibration parameters or the common 0.78 normalization; residual concerns are uncertainty issues rather than circular derivation.

full rationale

The derivation chain is not self-definitional: the ionization cross section is measured from transmission data, and the UV polarizability is extracted from high-mass fringes (0.4–1 MDa) in a regime where the quantum and classical models deliberately coincide. These parameters, together with the velocity and mass distributions and the global scale factor 0.78, are then inserted into both models. Because both predictions share every fitted parameter and the same normalization, the separation between the quantum and classical curves in Fig. 2b cannot be manufactured by those inputs; it follows from the distinct expressions in Eqs. (6)–(9), namely φ0 sin(πξ) versus φ0πξ and (n0/2)cos(πξ) versus n0/2. The 172 kDa visibility data therefore test the predicted functional dependence on G2 power, not merely a fitted amplitude. The macroscopicity analysis uses a Bayesian hypothesis-testing formalism from refs. [30–32], which includes a co-author of the present paper, but that framework is a published, externally applicable method and is applied here to raw count data with a stated conservative treatment of imperfections, so the reported μ = 15.5 is not forced by the citation itself. The most legitimate concern is that the global factor 0.78 is not given an independent error budget in the main text; this could affect the absolute agreement and the precise value of μ, but it does not make the structural quantum-versus-classical distinction circular. A score of 2 reflects the self-cited macroscopicity framework and the unquantified normalization, while recognizing that the central interference claim has independent content.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several fitted parameters: a global visibility scale factor, a UV polarizability extracted from high-mass fringe contrast, and an ionization cross-section slope. The quantum model also assumes complete ionization per absorbed photon and uses established phase-space and macrorealistic frameworks. No new physical entities are introduced.

free parameters (3)
  • Global visibility scale factor = 0.78
    Applied to both quantum and classical visibility predictions to account for interferometer misalignment, vibrations, and decoherence (Section II, Methods).
  • UV optical polarizability per sodium atom = -4πε0 × (4.5±0.5) Å^3
    Determined from high-contrast fringes of 0.4-1 MDa clusters where quantum and classical models agree on visibility (Methods, Photophysics).
  • Effective photo-ionization cross section = (0.537×m/kDa - 1.5)×10^-20 m^2
    Fitted to mass-selected transmission versus grating power measurements (Methods, Photophysics).
assumptions (4)
  • domain assumption Every absorbed 266 nm grating photon ionizes the cluster.
    Assumed in the Talbot-Lau model to define ionization depletion; invoked in Methods: 'We assume that every absorbed grating photon results in the ionization of the sodium cluster.'
  • domain assumption The macrorealistic modification model (MMM) of Nimmrichter and Hornberger is the correct framework for quantifying macroscopicity.
    The macroscopicity μ is defined within this specific class of modifications, cited as [30,31]; the exclusion limit applies to this class, not all possible modifications.
  • standard math The Wigner-Weyl formalism correctly describes near-field Talbot-Lau interferometry for these clusters.
    This is the established theory of matter-wave interferometry; used in Methods.
  • domain assumption The velocity and mass distributions are Gaussian/trapezoidal as measured by TOF and QMS and do not introduce uncontrolled biases.
    These distributions enter the averaging of the predicted signal; deviations could affect the shape comparison. Described in Methods: Velocity Distribution and Mass selection.

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Pith. "Pith review of Probing quantum mechanics using nanoparticle Schr\"odinger cats." pith.science (2026). https://pith.science/paper/GXF2XZOT

@misc{pith2026250721211,
  author       = {Pith},
  title        = {Pith review of: Probing quantum mechanics using nanoparticle Schr\"odinger cats},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GXF2XZOT}},
  note         = {Machine review of arXiv:2507.21211}
}
abstract

The quantum superposition principle is a cornerstone of physics and at the heart of many 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 intriguing to ask how quantum properties persist or change as we increase the size and complexity of objects. A paradigmatic test for this question can be realized by matter-wave interferometry, where 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. Here we present an experimental platform extending matter-wave interference to a qualitatively new class of materials that can vary widely in mass and size. We specifically demonstrate quantum interference of sodium nanoparticles, which can each contain more than 7'000 atoms at masses greater than 170'000 dalton. They propagate in a Schr\"odinger cat state with a macroscopicity of $\mu$ = 15.5, surpassing all previous experiments by an order of magnitude and providing the most stringent exclusion limit for generic macrorealistic modifications of the Schr\"odinger equation to date.

Figures

Figures reproduced from arXiv: 2507.21211 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
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Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Reference graph

Works this paper leans on

51 extracted references · 47 canonical work pages · cited by 1 Pith paper

  1. [1]

    De Broglie, Waves and quanta, Nature112, 540 (1923)

    L. De Broglie, Waves and quanta, Nature112, 540 (1923)

    work page 1923

  2. [2]

    Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Phys

    E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules, Phys. Rev.28, 1049 (1926)

    work page 1926

  3. [3]

    Kovachy, P

    T. Kovachy, P. Asenbaum, C. Overstreet, C. A. Donnelly, S. M. Dickerson, A. Sugarbaker, J. M. Hogan, and M. A. Kasevich, Quantum superposition at the half-metre scale, Nature528, 530 (2015)

    2015

  4. [4]

    C. D. Panda, M. Tao, J. Egelhoff, M. Ceja, V . Xu, and H. Müller, Coherence limits in lattice atom interferometry at the one- minute scale, Nat. Phys.20, 1234–1239 (2024)

    work page 2024

  5. [5]

    Y . Y . Fein, P. Geyer, P. Zwick, F. Kiałka, S. Pedalino, M. Mayor, S. Gerlich, and M. Arndt, Quantum superposition of molecules beyond 25 kda, Nat. Phys.15, 1242–1245 (2019)

    work page 2019

  6. [6]

    A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Wei- des, J. Wenner, J. M. Martinis, and A. N. Cleland, Quantum ground state and single-phonon control of a mechanical res- onator, Nature464, 697 (2010)

    work page 2010

  7. [7]

    J. Chan, T. P. Mayer Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Groeblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature478, 89 (2011)

    2011

  8. [8]

    Delic, M

    U. Delic, M. Reisenbauer, K. Dare, D. Grass, V . Vuletic, N. Kiesel, and M. Aspelmeyer, Cooling of a levitated nanoparti- cle to the motional quantum ground state, Science367, 892–895 (2020)

    work page 2020

Show all 51 references
  1. [9]

    Magrini, P

    L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature595, 373–377 (2021)

    2021

  2. [10]

    Tebbenjohanns, M

    F. Tebbenjohanns, M. L. Mattana, M. Rossi, M. Frimmer, and L. Novotny, Quantum control of a nanoparticle optically levi- tated in cryogenic free space, Nature595, 378 (2021)

    2021

  3. [11]

    Piotrowski, D

    J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez-Ballestero, A. de los Ríos Sommer, N. Meyer, R. Quidant, O. Romero- Isart, R. Reimann, and L. Novotny, Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle, Nat. Phys.19, 1009–1013 (2023)

    2023

  4. [12]

    M. Bild, M. Fadel, Y . Yang, U. v. Luüpke, P. Martin, A. Bruno, and Y . Chu, Schrödinger cat states of a 16-microgram mechan- ical oscillator, Science380, 274–278 (2023)

    2023

  5. [13]

    H. M. Doeleman, T. Schatteburg, R. Benevides, S. V ollenwei- der, D. Macri, and Y . Chu, Brillouin optomechanics in the quan- tum ground state, Phys. Rev Res.5, 043140 (2023)

    2023

  6. [14]

    Schrödinger, Die gegenwärtige Situation in der Quanten- mechanik., Die Naturwissenschaften48, 807–812 (1935)

    E. Schrödinger, Die gegenwärtige Situation in der Quanten- mechanik., Die Naturwissenschaften48, 807–812 (1935)

    1935

  7. [15]

    Bassi, K

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

    2013

  8. [16]

    Haberland, M

    H. Haberland, M. Karrais, and M. Mall, A new type of cluster and cluster ion source, Z. Phys. D20, 413 (1991)

    1991

  9. [17]

    W. A. De Heer, The physics of simple metal clusters: Exper- imental aspects and simple models, Rev. Mod. Phys.65, 611 (1993)

    1993

  10. [18]

    Pedalino, T

    S. Pedalino, T. de Sousa, Y . Y . Fein, S. Gerlich, and M. Arndt, Exploring metal nanoparticles for matter-wave interferometry, Phys. Rev. A106, 023312 (2022)

    2022

  11. [19]

    Clauser, De broglie-wave interference of small rocks and live viruses, inExperimental Metaphysics, edited by R

    J. Clauser, De broglie-wave interference of small rocks and live viruses, inExperimental Metaphysics, edited by R. S. Cohen, M. Horne, and J. Stachel (Kluwer Academic, New York, 1997) pp. 1–11

    1997

  12. [20]

    J. F. Clauser and S. Li, Talbot - von lau atom interferometry with cold slow potassium, Phys. Rev. A49, R2213 (1994)

    1994

  13. [21]

    S. Fray, C. A. Diez, T. W. Hänsch, and M. Weitz, Atomic inter- ferometer with amplitude gratings of light and its applications to atom based tests of the equivalence principle, Phys. Rev. Lett. 93, 240404 (2004)

    2004

  14. [22]

    Pfeiffer, T

    F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, Phase retrieval and differential phase-contrast imaging with low-brilliance x- ray sources, Nat. Phys.2, 258 (2006)

    2006

  15. [23]

    Ariga, A

    A. Ariga, A. Ereditato, R. Ferragut, M. Giammarchi, M. Leone, C. Pistillo, S. Sala, and P. Scampoli, First observation of anti- matter wave interference, Sci. Adv.5, eaav7610 (2019)

    2019

  16. [24]

    Gerlich, L

    S. Gerlich, L. Hackermüller, K. Hornberger, A. Stibor, H. Ul- bricht, M. Gring, F. Goldfarb, T. Savas, M. Müri, M. Mayor, and M. Arndt, A Kapitza-Dirac-Talbot-Lau interferometer for highly polarizable molecules, Nat. Phys.3, 711 (2007)

    2007

  17. [25]

    Lau, Beugungserscheinungen an Doppelrastern, Ann

    E. Lau, Beugungserscheinungen an Doppelrastern, Ann. Phys. 6, 417 (1948)

    1948

  18. [26]

    Kasevich and S

    M. Kasevich and S. Chu, Atomic interferometry using stimu- lated raman transitions, Phys. Rev. Lett.67, 181–184 (1991)

    1991

  19. [27]

    Riehle, T

    F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Borde, Optical ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer, Phys. Rev. Lett.67, 177–180 (1991)

    1991

  20. [28]

    Nimmrichter and K

    S. Nimmrichter and K. Hornberger, Theory of talbot-lau inter- ference beyond the eikonal approximation, Phys. Rev. A78, 023612 (2008)

    2008

  21. [29]

    Bohr, The quantum postulate and the recent development of atomic theory, Nature121, 580 (1928)

    N. Bohr, The quantum postulate and the recent development of atomic theory, Nature121, 580 (1928)

    1928

  22. [30]

    Nimmrichter and K

    S. Nimmrichter and K. Hornberger, Macroscopicity of mechan- ical quantum superposition states, Phys. Rev. Lett.110, 160403 (2013)

    2013

  23. [31]

    Schrinski, S

    B. Schrinski, S. Nimmrichter, B. A. Stickler, and K. Horn- berger, Macroscopicity of quantum mechanical superposition tests via hypothesis falsification, Phys. Rev. A100, 032111 (2019)

    2019

  24. [32]

    Schrinski, S

    B. Schrinski, S. Nimmrichter, and K. Hornberger, Quantum- classical hypothesis tests in macroscopic matter-wave interfer- ometry, Phys. Rev. Res.2, 033034 (2020)

    2020

  25. [33]

    Schrinski, Y

    B. Schrinski, Y . Yang, U. von Lupke, M. Bild, Y . Chu, K. Horn- berger, S. Nimmrichter, and M. Fadel, Macroscopic quantum test with bulk acoustic wave resonators, Phys. Rev. Lett.130, 133604 (2023)

    2023

  26. [34]

    P. W. Rose, A. Prli ´c, and C. e. a. Bi, The RCSB protein data bank: integrative view of protein, gene and 3D structural infor- mation, Nucl. Ac. Res.43, D345 (2015)

    2015

  27. [35]

    Kiałka, Y

    F. Kiałka, Y . Y . Fein, S. Pedalino, S. Gerlich, and M. Arndt, A roadmap for universal high-mass matter-wave interferometry, A VS Quant. Sci.4, 020502 (2022)

    2022

  28. [36]

    Oppenheim, C

    J. Oppenheim, C. Sparaciari, B. Soda, and Z. Weller-Davies, Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity, Nat. Commun.14, 7910 (2023)

    2023

  29. [37]

    X. S. Xu, S. Y . Yin, R. Moro, and W. A. de Heer, Magnetic moments and adiabatic magnetization of free cobalt clusters, Phys. Rev. Lett.95, 237209 (2005)

    2005

  30. [38]

    D. J. M. a. V . V . Kresin, Electrostatic deflection of a molecu- lar beam of massive neutral particles: Fully field-oriented polar molecules within superfluid nanodroplets, J. Phys. Chem. Lett. 7, 4879 (2016). 9

    2016

  31. [39]

    Rivic, T

    F. Rivic, T. M. Fuchs, and R. Schäfer, Discriminating the in- fluence of thermal excitation and the presence of structural iso- mers on the stark and zeeman effect of AlSn12 clusters by com- bined electric and magnetic beam deflection experiments, Phys. Chem. Chem. Phys. 10.10...

    2021 doi

  32. [40]

    Antoine, I

    R. Antoine, I. Compagnon, D. Rayane, M. Broyer, P. Dugourd, G. Breaux, F. C. Hagemeister, D. Pippen, R. R. Hudgins, and M. F. Jarrold, Electric susceptibility of unsolvated glycine- based peptides, J. Am. Chem. Soc.124, 6737 – 6741 (2002)

    2002

  33. [41]

    Haseloff, N

    J. Haseloff, N. A. Mohamed, and R. H. Symons, Viroid RNAs of cadang-cadang disease of coconuts, Nature299, 316–321 (1982)

    1982

  34. [42]

    J. R. Saucedo Carabez, D. Teliz Ortiz, M. R. Vallejo Perez, and H. Beltran Pena, The avocado sunblotch viroid: An invisible foe of avocado, Viruses11, 491 (2019)

    2019

  35. [43]

    Ekeberg, D

    T. Ekeberg, D. Assalauova, J. Bielecki, R. Boll, B. J. Dau- rer, L. A. Eichacker, L. E. Franken, D. E. Galli, L. Gelisio, L. Gumprecht, L. H. Gunn, J. Hajdu, R. Hartmann, D. Hasse, A. Ignatenko, J. Koliyadu, O. Kulyk, R. Kurta, M. Kuster, W. Lugmayr, J. Lubke, A. P. Mancuso, T...

    2024

  36. [44]

    A. K. Samanta, M. Amin, A. D. Estillore, N. Roth, L. Worbs, D. A. Horke, and J. Küpper, Controlled beams of shock-frozen, isolated, biological and artificial nanoparticles, Struct. Dyn.7, 024304 (2020)

    2020

  37. [45]

    Mucha, D

    E. Mucha, D. Thomas, M. Lettow, G. Meijer, K. Pagel, and G. von Helden, Spectroscopy of small and large biomolecular ions in helium-nanodroplets (Springer Int. Pub., Cham, 2022) p. 241–280

    2022

  38. [46]

    Schätti, M

    J. Schätti, M. Kriegleder, M. Debiossac, M. Kerschbaum, P. Geyer, M. Mayor, M. Arndt, and V . Köhler, Neutralization of insulin by photocleavage under high vacuum, Chem. Com- mun. (Camb)55, 12507–12510 (2019)

    2019

  39. [47]

    Strauß, A

    M. Strauß, A. Shayeghi, M. F. X. Mauser, P. Geyer, T. Koster- sitz, J. Salapa, O. Dobrovolskiy, S. Daly, J. Commandeur, Y . Hua, V . Köhler, M. Mayor, J. Benserhir, C. Bruschini, E. Charbon, M. Castaneda, M. Gevers, R. Gourgues, N. Kalhor, A. Fognini, and M. Arndt, Highly sens...

    2023

  40. [48]

    Nimmrichter, P

    S. Nimmrichter, P. Haslinger, K. Hornberger, and M. Arndt, Concept of an ionizing time-domain matter-wave interferom- eter, New J. Phys.13, 075002 (2011)

    2011

  41. [49]

    Göhlich, T

    H. Göhlich, T. Lange, T. Bergmann, U. Näher, and T. Martin, Ionization energies of sodium clusters containing up to 22000 atoms, Chem. Phys. Lett.187, 67 (1991)

    1991

  42. [50]

    Wrigge, M

    G. Wrigge, M. A. Hoffmann, and B. v. Issendorff, Photoelec- tron spectroscopy of sodium clusters: Direct observation of the electronic shell structure, Phys. Rev. A65, 10.1103/Phys- RevA.65.063201 (2002)

    2002 doi

  43. [51]

    Schmidt, R

    M. Schmidt, R. Kusche, T. Hippler, J. Donges, W. Kronmüller, B. von Issendorff, and H. Haberland, Negative heat capacity for a cluster of 147 sodium atoms, Phys. Rev. Lett.86, 1191 (2001)

    2001

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