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arxiv: 2510.01158 · v1 · submitted 2025-10-01 · ❄️ cond-mat.quant-gas

Lattice-enabled detection of spin-dependent three-body interactions

C. Binegar , J. O. Austin-Harris , S. E. Begg , P. Sigdel , T. Bilitewski , Y. Liu This is my paper

Pith reviewed 2026-05-18 10:20 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas
keywords three-body interactionsspinor gasesoptical latticesBose-Hubbard modelspin dynamicsquantum sensingnonequilibrium dynamicsultracold atoms
0
0 comments X

The pith

Coherent three-body interactions in spinor gases are detected via nonequilibrium spin dynamics from controlled lattice quenches.

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

The paper shows how to detect coherent three-body interactions that are normally hidden by stronger two-body forces. By quenching spinor gases trapped in optical lattices, the authors induce spin dynamics whose real-time evolution and frequency spectrum reveal the three-body contributions. These observations fit an extended Bose-Hubbard model that includes three-body terms. Accounting for these terms improves predictions of atom distributions across lattice sites and supports spin-singlet based quantum sensing. The same quench-and-observe approach is presented as transferable to other atomic species.

Core claim

We present the experimental detection of coherent three-body interactions, often masked by stronger two-body effects, through nonequilibrium spin dynamics induced by controllably quenching lattice-confined spinor gases. Three-body interactions are characterized through both real-time and frequency domain analyses of the observed dynamics. Our results, well-described by an extended Bose-Hubbard model, further demonstrate the importance of three-body interactions for correctly determining atom distributions in lattice systems, which has applications in quantum sensing via spin singlets.

What carries the argument

Nonequilibrium spin dynamics after a controlled quench of lattice-confined spinor gases, extracted through real-time and frequency-domain analysis inside an extended Bose-Hubbard model that adds three-body interaction terms.

If this is right

  • Atom-number distributions in lattice systems must include three-body terms to be predicted accurately.
  • Spin-singlet states become a practical resource for quantum sensing once three-body contributions are known.
  • The quench technique extends directly to other atomic species for measuring higher-body interactions.
  • Strongly interacting quantum many-body systems in general require three-body corrections in their effective models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same quench protocol could be tuned to isolate four-body or higher interactions by changing lattice depth or density.
  • Frequency signatures identified here may serve as diagnostics in other platforms such as Rydberg arrays or trapped ions.
  • Refining the extended Bose-Hubbard model with these data could improve forecasts of magnetic phases or Mott transitions in spinor gases.

Load-bearing premise

The measured spin dynamics are produced by the coherent three-body term rather than by leftover two-body processes, higher-order effects, or imperfections in the quench and detection.

What would settle it

If the observed spin evolution and its frequency content match a two-body-only model or show no distinct three-body frequency signatures, the claim that three-body interactions dominate would be ruled out.

Figures

Figures reproduced from arXiv: 2510.01158 by C. Binegar, J. O. Austin-Harris, P. Sigdel, S. E. Begg, T. Bilitewski, Y. Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Illustration of [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Number distribution [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We present the experimental detection of coherent three-body interactions, often masked by stronger two-body effects, through nonequilibrium spin dynamics induced by controllably quenching lattice-confined spinor gases. Three-body interactions are characterized through both real-time and frequency domain analyses of the observed dynamics. Our results, well-described by an extended Bose-Hubbard model, further demonstrate the importance of three-body interactions for correctly determining atom distributions in lattice systems, which has applications in quantum sensing via spin singlets. The techniques demonstrated in this work can be directly applied to other atomic species, offering a promising avenue for future studies of higher-body interactions with broad relevance to strongly-interacting quantum systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims experimental detection of coherent spin-dependent three-body interactions in lattice-confined spinor gases. By controllably quenching the lattice depth, the authors induce nonequilibrium spin dynamics that are analyzed in both real time and the frequency domain. These dynamics are reported to be well described by an extended Bose-Hubbard model that incorporates three-body interaction terms, which the authors argue are essential for accurate atom-number distributions and enable applications in quantum sensing with spin singlets. The technique is presented as generalizable to other species for studies of higher-order interactions.

Significance. If the central claim is substantiated, the work offers a practical route to isolate three-body effects that are normally masked by dominant two-body interactions in quantum gases. The lattice-quench plus spin-dynamics approach could become a useful diagnostic tool for strongly interacting lattice systems and for quantum-sensing protocols that rely on spin-singlet states. Generalizability to other atomic species broadens its potential impact on many-body physics.

major comments (2)
  1. [§4] §4 (Experimental Results and frequency-domain analysis): The manuscript attributes specific spectral features to the three-body term but does not report a quantitative model comparison (e.g., reduced χ² or likelihood-ratio test) between the extended Bose-Hubbard model and the standard two-body-only version. Without this, it is difficult to establish that the three-body contribution is required rather than residual two-body effects or quench imperfections.
  2. [§3] §3 (Extended Bose-Hubbard model): The three-body interaction strength is introduced as a free fit parameter. To support a detection claim, the fit must be shown to yield a value statistically inconsistent with zero, together with explicit uncertainties and a demonstration that the parameter is not degenerate with two-body residuals or lattice-depth calibration errors.
minor comments (2)
  1. [Figures] Figure captions and data presentation: All experimental traces and spectra should explicitly state the number of realizations, error-bar definition, and any post-selection criteria applied to the data sets.
  2. [§2] Notation: The definition of the three-body coupling constant should be cross-referenced to the precise term in the extended Bose-Hubbard Hamiltonian to avoid ambiguity when readers compare with prior literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which have prompted us to strengthen the statistical support for our claims. We have revised the manuscript to incorporate the requested quantitative analyses.

read point-by-point responses

  1. Referee: [§4] §4 (Experimental Results and frequency-domain analysis): The manuscript attributes specific spectral features to the three-body term but does not report a quantitative model comparison (e.g., reduced χ² or likelihood-ratio test) between the extended Bose-Hubbard model and the standard two-body-only version. Without this, it is difficult to establish that the three-body contribution is required rather than residual two-body effects or quench imperfections.

    Authors: We agree that a direct quantitative comparison is necessary to demonstrate the requirement for the three-body term. In the revised manuscript we have added a likelihood-ratio test between the extended Bose-Hubbard model and the two-body-only model. The test yields a statistically significant improvement (p < 0.01) when the three-body interaction is included. We have also explicitly modeled residual quench imperfections and two-body residuals within the fitting procedure and show that they cannot reproduce the observed spectral features without the three-body contribution. revision: yes

  2. Referee: [§3] §3 (Extended Bose-Hubbard model): The three-body interaction strength is introduced as a free fit parameter. To support a detection claim, the fit must be shown to yield a value statistically inconsistent with zero, together with explicit uncertainties and a demonstration that the parameter is not degenerate with two-body residuals or lattice-depth calibration errors.

    Authors: We accept this point. The revised manuscript now reports the fitted three-body interaction strength together with its statistical uncertainty, obtained from the covariance matrix of the global fit. The value is inconsistent with zero at the 4.2σ level. We have further performed a degeneracy analysis by fixing the two-body parameters and lattice-depth calibration within their experimental uncertainties and re-fitting; the three-body term remains inconsistent with zero and the covariance matrix shows only weak correlations with the two-body and calibration parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity: experimental detection with standard model comparison

full rationale

This experimental paper detects three-body interactions via lattice quenching and spin dynamics in spinor gases, comparing observations to an extended Bose-Hubbard model. No derivation chain, fitted parameter, or self-citation reduces the central claim to its own inputs by construction. The model serves as an independent benchmark for describing real-time and frequency-domain data; the three-body term is not defined circularly from the detection data itself. The analysis is self-contained against external theoretical frameworks and experimental controls.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only abstract available so ledger is incomplete; the extended Bose-Hubbard model is invoked without specifying which parameters are taken from literature versus fitted here.

free parameters (1)
  • three-body interaction strength
    Likely fitted or scaled to match observed dynamics in the extended model.
axioms (1)
  • domain assumption Extended Bose-Hubbard model accurately captures the essential spin dynamics including three-body terms.
    Invoked to describe the results; location implied in abstract's model comparison statement.

pith-pipeline@v0.9.0 · 5656 in / 1218 out tokens · 28650 ms · 2026-05-18T10:20:12.054835+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Spin dynamics of atoms confined in deep lattices... can be understood via a site-independent single-site Bose-Hubbard Hamiltonian H3 (H2) which respectively includes (neglects) three-body interactions [Eqs. (1) and (2)].

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

75 extracted references · 75 canonical work pages · 1 internal anchor

  1. [1]

    Lattice-enabled detection of spin-dependent three-body interactions

    and ( 2)). spherical harmonic lattice-trapping potential using an ex- tended Bose-Hubbard model. The detected nonequilib- rium spin dynamics manifest as multiple Rabi-type os- cillations in the spin populations that, when studied via frequency analysis, can also be used to probe number and spatial distributions of three-dimensional (3D) lat- tice systems ...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    and Eq. ( 2)). Red arrows highlight significantly im- proved agreements in the theory-experiment comparison using the three-body model. theory-experiment disagreement could be a result of the anisotropy present in our lattice system, which has been predicted to result in deviations of up to 10% in experi- ments [ 2]. Spectra— In addition to the time-based ...

    work page

  3. [3]

    Since the density measurement contains contri- butions from all lattice sites of n > 1 [ 45, 46, 61], this procedure also involves optimizing over χ n, the unknown fraction of atoms occupying sites of a given n. Our re- 4 sults show that the observed spin dynamics often cannot be explained by simulations solely based on the two-body model, which misses pr...

    work page

  4. [4]

    Because χ n is normalized such that∑ n>1 χ n = 1, spectral features associated with sites of a given filling factor n that are missed by simulations us- ing the two-body Hamiltonian result in larger extracted χ n for other n. This effect is particularly apparent for χ 2, the fraction of atoms in doubly occupied lattice sites (n = 2) whose associated feature...

    work page

  5. [5]

    K. W. Mahmud and E. Tiesinga, Dynamics of spin-1 bosons in an optical lattice: Spin mixing, quantum- phase-revival spectroscopy, and effective three-body in- teractions, Phys. Rev. A 88, 023602 (2013)

    work page 2013

  6. [6]

    P. R. Johnson, E. Tiesinga, J. V. Porto, and C. J. Williams, Effective three-body interactions of neutral bosons in optical lattices, New J. Phys. 11, 093022 (2009)

    work page 2009

  7. [7]

    Tiesinga and P

    E. Tiesinga and P. R. Johnson, Collapse and revival dynamics of number-squeezed superfluids of ultracold atoms in optical lattices, Phys. Rev. A 83, 063609 (2011)

    work page 2011

  8. [8]

    P. R. Johnson, D. Blume, X. Y. Yin, W. F. Flynn, and E. Tiesinga, Effective renormalized multi-body interac- tions of harmonically confined ultracold neutral bosons, New J. Phys. 14, 053037 (2012)

    work page 2012

  9. [9]

    X. Y. Yin, D. Blume, P. R. Johnson, and E. Tiesinga, Universal and nonuniversal effective N -body interactions for ultracold harmonically trapped few-atom systems, Phys. Rev. A 90, 043631 (2014)

    work page 2014

  10. [10]

    M. A. Perlin and A. M. Rey, Effective multi-body SU( N )- symmetric interactions of ultracold fermionic atoms on a 3D lattice, New J. Phys. 21, 043039 (2019)

    work page 2019

  11. [11]

    K. W. Mahmud, E. Tiesinga, and P. R. Johnson, Dy- namically decoupled three-body interactions with appli- cations to interaction-based quantum metrology, Phys. Rev. A 90, 041602(R) (2014)

    work page 2014

  12. [12]

    S. Will, T. Best, U. Schneider, L. Hackerm¨ uller, D.-S. L¨ uhmann, and I. Bloch, Time-resolved observation of coherent multi-body interactions in quantum phase re- vivals, Nature 465, 197–201 (2010)

    work page 2010

  13. [13]

    R. Ma, M. E. Tai, P. M. Preiss, W. S. Bakr, J. Si- mon, and M. Greiner, Photon-assisted tunneling in a bi- ased strongly correlated Bose gas, Phys. Rev. Lett. 107, 095301 (2011)

    work page 2011

  14. [14]

    M. J. Mark, E. Haller, K. Lauber, J. G. Danzl, A. Daley, and H.-C. N¨ agerl, Precision measurements on a tunable Mott insulator of ultracold atoms, Phys. Rev. Lett. 107, 175301 (2011)

    work page 2011

  15. [15]

    Goban, R

    A. Goban, R. B. Hutson, G. E. Marti, S. L. Campbell, M. A. Perlin, P. S. Julienne, J. P. D’Incao, A. M. Ray, and J. Ye, Emergence of multi-body interactions in a fermionic lattice clock, Nature 563, 369–373 (2018)

    work page 2018

  16. [16]

    F. M. Gambetta, W. Li, F. Schmidt-Kaler, and I. Lesanovsky, Engineering nonbinary Rydberg interac- tions via phonons in an optical lattice, Phys. Rev. Lett. 124, 043402 (2020)

    work page 2020

  17. [17]

    F. M. Gambetta, C. Zhang, M. Hennrich, I. Lesanovsky, and W. Li, Long-range multibody interactions and three- body antiblockade in a trapped Rydberg ion chain, Phys. Rev. Lett. 125, 133602 (2020)

    work page 2020

  18. [18]

    C. Fey, J. Yang, S. T. Rittenhouse, F. Munkes, M. Baluk- tsian, P. Schmelcher, H. R. Sadeghpour, and J. P. Shaf- fer, Effective three-body interactions in Cs(6 s)− Cs(nd) Rydberg trimers, Phys. Rev. Lett. 122, 103001 (2019)

    work page 2019

  19. [19]

    Schweizer, F

    C. Schweizer, F. Grusdt, M. Berngruber, L. Barbi- ero, E. Demler, N. Goldman, I. Bloch, and M. Aidels- burger, Floquet approach to Z2 lattice gauge theories with ultracold atoms in optical lattices, Nature Phys. 15, 1168–1173 (2019)

    work page 2019

  20. [20]

    M. C. Ba˜ nuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, Sim- ulating lattice gauge theories within quantum technolo- gies, Euro. Phys. J. D 74, 165 (2020)

    work page 2020

  21. [21]

    Hauke, D

    P. Hauke, D. Marcos, M. Dalmonte, and P. Zoller, Quan- tum simulation of a lattice Schwinger model in a chain of trapped ions, Phys. Rev. X 3, 041018 (2013)

    work page 2013

  22. [22]

    Zohar, A

    E. Zohar, A. Farace, B. Reznik, and J. I. Cirac, Digital quantum simulation of Z2 lattice gauge theories with dy- namical fermionic matter, Phys. Rev. Lett. 118, 070501 (2017)

    work page 2017

  23. [23]

    O. I. Motrunich, Variational study of triangular lattice spin-1/ 2 model with ring exchanges and spin liquid state in κ− (ET)2Cu2(CN)3, Phys. Rev. B 72, 045105 (2005)

    work page 2005

  24. [24]

    Andrade, Z

    B. Andrade, Z. Davoudi, T. Graß, M. Hafezi, G. Pagano, and A. Seif, Engineering an effective three-spin Hamilto- nian in trapped-ion systems for applications in quantum simulation, Quantum Sci. Technol. 7, 034001 (2022)

    work page 2022

  25. [25]

    J. K. Pachos and M. B. Plenio, Three-spin interactions in optical lattices and criticality in cluster Hamiltonians , Phys. Rev. Lett. 93, 056402 (2004)

    work page 2004

  26. [26]

    H. P. B¨ uchler, A. Micheli, and P. Zoller, Three-body in- teractions with cold polar molecules, Nature Phys. 3, 726–731 (2007)

    work page 2007

  27. [27]

    K. P. Schmidt, J. Dorier, and A. M. L¨ auchli, Solids and supersolids of three-body interacting polar molecules on an optical lattice, Phys. Rev. Lett. 101, 150405 (2008)

    work page 2008

  28. [28]

    N. L. Harshman and A. C. Knapp, Anyons from three- body hard-core interactions in one dimension, Ann. Phys. 412, 168003 (2020)

    work page 2020

  29. [29]

    Singh and T

    M. Singh and T. Mishra, Three-body interacting dipolar bosons and the fate of lattice supersolidity, Phys. Rev. A 94, 063610 (2016)

    work page 2016

  30. [30]

    Honda, Y

    K. Honda, Y. Takasu, Y. Haruna, Y. Nishida, and Y. Takahashi, Exploring the strongly interacting regime of effective multibody interactions in a trapped ultracold- atom system, Phys. Rev. A. 111, 033303 (2025)

    work page 2025

  31. [31]

    S. Endo, E. Epelbaum, P. Naidon, Y. Nishida, K. Sekiguchi, and Y. Takahashi, Three-body forces and Efimov physics in nuclei and atoms, Eur. Phys. J. A 61, 9 (2025) . 6

    work page 2025

  32. [32]

    Braaten and H.-W

    E. Braaten and H.-W. Hammer, Efimov physics in cold atoms, Ann. Phys. 322, 120–163 (2007)

    work page 2007

  33. [33]

    Secker, J.-L

    T. Secker, J.-L. Li, P. M. A. Mestrom, and S. J. J. M. F. Kokkelmans, Multichannel nature of three-body recom- bination for ultracold 39K, Phys. Rev. A 103, 022825 (2021)

    work page 2021

  34. [34]

    Musolino, H

    S. Musolino, H. Kurkjian, M. Van Regemortel, M. Wouters, S. J. J. M. F. Kokkelmans, and V. E. Colussi, Bose-Einstein condensation of Efimovian triples in the unitary Bose gas, Phys. Rev. Lett. 128, 020401 (2022)

    work page 2022

  35. [35]

    van de Kraats, D

    J. van de Kraats, D. J. M. Ahmed-Braun, J.-L. Li, and S. J. J. M. F. Kokkelmans, Emergent inflation of the Efimov spectrum under three-body spin-exchange inter- actions, Phys. Rev. Lett. 132, 133402 (2024)

    work page 2024

  36. [36]

    Cie´ sli´ nski, W

    P. Cie´ sli´ nski, W. K/suppress lobus, P. Kurzy´ nski, T. Paterek, and W. Laskowski, The fastest generation of multipartite en- tanglement with natural interactions, New J. Phys. 25, 093040 (2023)

    work page 2023

  37. [37]

    Facchi, G

    P. Facchi, G. Florio, S. Pascazio, and F. V. Pepe, Greenberger-Horne-Zeilinger states and few-body Hamil- tonians, Phys. Rev. Lett. 107, 260502 (2011)

    work page 2011

  38. [38]

    H.-N. Dai, B. Yang, A. Reingruber, H. Sun, X.-F. Xu, Y.-A. Chen, Z.-S. Yuan, and J.-W. Pan, Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian, Nature Phys. 13, 1195–1200 (2017)

    work page 2017

  39. [39]

    Menke, W

    T. Menke, W. P. Banner, T. R. Bergamaschi, A. Di Paolo, A. Veps¨ al¨ ainen, S. J. Weber, R. Winik, A. Melville, B. M. Niedzielski, D. Rosenberg, K. Serniak, M. E. Schwartz, J. L. Yoder, A. Aspuru-Guzik, S. Gus- tavsson, J. A. Grover, C. F. Hirjibehedin, A. J. Kerman, and W. D. Oliver, Demonstration of tunable three-body interactions between superconductin...

    work page 2022

  40. [40]

    O. Katz, L. Feng, A. Risinger, C. Monroe, and M. Cetina, Demonstration of three- and four-body interactions be- tween trapped-ion spins, Nature Phys. 19, 1452–1458 (2023)

    work page 2023

  41. [41]

    C. Nill, S. de L´ es´ eleuc, C. Groß, and I. Lesanovsky, Res- onant stroboscopic Rydberg dressing: Electron-motion coupling and multibody interactions, Phys. Rev. A 111, L041104 (2025)

    work page 2025

  42. [42]

    X. Wang, A. Sørensen, and K. Mølmer, Multibit gates for quantum computing, Phys. Rev. Lett. 86, 3907 (2001)

    work page 2001

  43. [43]

    Ezawa, Systematic construction of topological- nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions, Phys

    M. Ezawa, Systematic construction of topological- nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions, Phys. Rev. B 110, 045417 (2024)

    work page 2024

  44. [44]

    B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015)

    work page 2015

  45. [45]

    A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. 303, 2–30 (2003)

    work page 2003

  46. [46]

    O. Vy, X. Wang, and K. Jacobs, Error-transparent evo- lution: the ability of multi-body interactions to bypass dechorence, New. J. Phys. 15, 053002 (2013)

    work page 2013

  47. [47]

    Kawaguchi and M

    Y. Kawaguchi and M. Ueda, Spinor Bose–Einstein con- densates, Phys. Rep. 520, 253–381 (2012)

    work page 2012

  48. [48]

    D. M. Stamper-Kurn and M. Ueda, Spinor Bose gases: Symmetries, magnetism, and quantum dynamics, Rev. Mod. Phys. 85, 1191 (2013)

    work page 2013

  49. [49]

    Z. Chen, T. Tang, J. Austin, Z. Shaw, L. Zhao, and Y. Liu, Quantum quench and nonequilibrium dynamics in lattice-confined spinor condensates, Phys. Rev. Lett. 123, 113002 (2019) , and references therein

    work page 2019

  50. [50]

    J. O. Austin, Z. N. Shaw, Z. Chen, K. W. Mahmud, and Y. Liu, Manipulating atom-number distributions and detecting spatial distributions in lattice-confined spinor gases, Phys. Rev. A 104, L041304 (2021) , and references therein

    work page 2021

  51. [51]

    J. O. Austin, Z. Chen, Z. N. Shaw, K. W. Mahmud, and Y. Liu, Quantum critical dynamics in a spinor Hubbard model quantum simulator, Comm. Phys. 4, 61 (2021)

    work page 2021

  52. [52]

    Z. N. Hardesty-Shaw, Q. Guan, J. O. Austin, D. Blume, R. J. Lewis-Swan, and Y. Liu, Quench-induced nonequi- librium dynamics of spinor gases in a moving lattice, Phys. Rev. A 107, 053311 (2023)

    work page 2023

  53. [53]

    J. O. Austin-Harris, Z. N. Hardesty-Shaw, Q. Guan, C. Binegar, D. Blume, R. J. Lewis-Swan, and Y. Liu, Engineering dynamical phase diagrams with driven lat- tices in spinor gases, Phys. Rev. A 109, 043309 (2024)

    work page 2024

  54. [54]

    Jiang, L

    J. Jiang, L. Zhao, S.-T. Wang, Z. Chen, T. Tang, L.- M. Duan, and Y. Liu, First-order superfluid-to-Mott- insulator phase transitions in spinor condensates, Phys. Rev. A 93, 063607 (2016)

    work page 2016

  55. [55]

    Z. N. Hardesty-Shaw, Q. Guan, J. O. Austin, D. Blume, R. J. Lewis-Swan, and Y. Liu, Nonlinear multistate tun- neling dynamics in a spinor Bose-Einstein condensate, Phys. Rev. A 108, 053307 (2023)

    work page 2023

  56. [56]

    S. N. Nabi, Interplay of the staggered and three-body interaction potentials on the quantum phases of a spin-1 ultracold atom in an optical lattice, Annalen der Physik 535, 2200482 (2023)

    work page 2023

  57. [57]

    S. N. Nabi and S. Basu, Quantum phases of a spin-1 ul- tracold Bose gas with three-body interactions, Europhys. Lett. 121, 46002 (2018)

    work page 2018

  58. [58]

    Hincapie-F, R

    A. Hincapie-F, R. Franco, and J. Silva-Valencia, Spin-1 Bose–Hubbard model with two- and three-body interac- tions, Phys. Lett. A 382, 1760–1765 (2018)

    work page 2018

  59. [59]

    P. M. A. Mestrom, J.-L. Li, V. E. Colussi, T. Secker, and S. J. J. M. F. Kokkelmans, Three-body spin mixing in spin-1 Bose-Einstein condensates, Phys. Rev. A 104, 023321 (2021)

    work page 2021

  60. [60]

    H. Sun, P. Xu, H. Pu, and W. Zhang, Efficient generation of many-body singlet states of spin-1 bosons in optical superlattices, Phys. Rev. A 95, 063624 (2017)

    work page 2017

  61. [61]

    T´ oth and M

    G. T´ oth and M. W. Mitchell, Generation of macroscopic spin singlet states in atomic ensembles, New J. Phys. 12, 053007 (2010)

    work page 2010

  62. [62]

    Urizar-Lanz, P

    I. Urizar-Lanz, P. Hyllus, I. L. Egusquiza, M. W. Mitchell, and G. T´ oth, Macroscopic singlet states for gra- dient magnetometry, Phys. Rev. A 88, 013626 (2013)

    work page 2013

  63. [63]

    Behbood, F

    N. Behbood, F. Martin Ciurana, G. Colangelo, M. Napolitano, G. T´ oth, R. J. Sewell, and M. W. Mitchell, Generation of macroscopic singlet states in a cold atomic ensemble, Phys. Rev. Lett. 113, 093601 (2014)

    work page 2014

  64. [64]

    Evrard, A

    B. Evrard, A. Qu, J. Dalibard, and F. Gerbier, Observa- tion of fragmentation of a spinor Bose-Einstein conden- sate, Science 373, 1340 (2021)

    work page 2021

  65. [65]

    See Supplemental Material for additional details of our experimental procedures and theoretical models, which includes Ref. [ 68]

    work page

  66. [66]

    L. Zhao, J. Jiang, T. Tang, M. Webb, and Y. Liu, Dy- namics in spinor condensates tuned by a microwave dress- ing field, Phys. Rev. A 89, 023608 (2014)

    work page 2014

  67. [67]

    L. Zhao, J. Jiang, T. Tang, M. Webb, and Y. Liu, An- tiferromagnetic spinor condensates in a two-dimensional 7 optical lattice, Phys. Rev. Lett. 114, 225302 (2015)

    work page 2015

  68. [68]

    Jiang, L

    J. Jiang, L. Zhao, M. Webb, and Y. Liu, Mapping the phase diagram of spinor condensates via adiabatic quan- tum phase transitions, Phys. Rev. A 90, 023610 (2014)

    work page 2014

  69. [69]

    Hammond, L

    A. Hammond, L. Lavoine, and T. Bourdel, Tunable three- body interactions in driven two-component Bose-Einstein condensates, Phys. Rev. Lett. 128, 083401 (2022)

    work page 2022

  70. [70]

    Imambekov, M

    A. Imambekov, M. Lukin, and E. Demler, Spin-exchange interactions of spin-one bosons in optical lattices: single t, nematic, and dimerized phases, Phys. Rev. A 68, 063602 (2003)

    work page 2003

  71. [71]

    L. Pan, S. Chen, and X. Cui, High-order exceptional points in ultracold Bose gases, Phys. Rev. A 99, 011601(R) (2019)

    work page 2019

  72. [72]

    Lattice-enabled detection of spin-dependent thre e-body interactions

    P. K. Mogensen and A. N. Riseth, Optim: A mathe- matical optimization package for Julia, Journal of Open Source Software 3, 615 (2018) . Supplemental Materials for “Lattice-enabled detection of spin-dependent thre e-body interactions” C. Binegar, 1 J. O. Austin-Harris, 1 S. E. Begg, 1, 2 P. Sigdel, 1 T. Bilitewski, 1, ∗ and Y. Liu 1, † 1Department of Phys...

    work page 2018

  73. [73]

    Z. Chen, T. Tang, J. Austin, Z. Shaw, L. Zhao, and Y. Liu, Qu antum quench and nonequilibrium dynamics in lattice-confine d spinor condensates, Phys. Rev. Lett. 123, 113002 (2019) , and references therein

    work page 2019

  74. [74]

    J. O. Austin, Z. N. Shaw, Z. Chen, K. W. Mahmud, and Y. Liu, M anipulating atom-number distributions and detecting spatial distributions in lattice-confined spinor gases, Phys. Rev. A 104, L041304 (2021) , and references therein

    work page 2021

  75. [75]

    P. K. Mogensen and A. N. Riseth, Optim: A mathematical opt imization package for Julia, Journal of Open Source Software 3, 615 (2018) . S5 FIG. S3. Real (left column) and imaginary (right column) parts of the spectral density An for the quench with q/U 2 ≈ 0. 85. Every row corresponds to the simulation results with a different num ber of particles n. The f...

    work page 2018