pith. sign in

arxiv: 2605.00096 · v1 · submitted 2026-04-30 · 🪐 quant-ph · cond-mat.quant-gas

Scalable spin-nematic squeezing in multi-level dipole-interacting Rydberg atom arrays

Sakshi Bahamnia , Thomas Bilitewski This is my paper

Pith reviewed 2026-05-09 20:40 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gas
keywords Rydberg atomsspin-nematic squeezingquantum entanglementqudit systemsdipole interactionsoptical tweezersquantum metrologymany-body dynamics
0
0 comments X

The pith

Quench dynamics in three-level Rydberg arrays generate scalable spin-nematic squeezing with quantum Fisher information scaling as N squared.

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

The paper shows that three-level systems realized with dipole-interacting Rydberg atoms allow the interaction Hamiltonian to decompose into effective two-level subspaces in the spin-quadrupolar basis. Starting from simple product states, a sudden quench then produces spin-nematic squeezing whose strength improves with atom number. For symmetric interactions the squeezing reaches N to the minus two-thirds scaling under all-to-all coupling and N to the minus one-half under two-dimensional dipolar coupling, while the quantum Fisher information grows quadratically with system size. Antisymmetric interactions plus a microwave drive yield a different two-axis countertwisting route with N to the minus 0.7 scaling. This supplies a concrete route to metrologically useful entanglement in multi-level atoms rather than only in qubits.

Core claim

In the spin-quadrupolar operator basis the dipole interaction Hamiltonian for three-level Rydberg atoms decomposes into independent effective SU(2) subspaces. Quench dynamics from product initial states then generate spin-nematic squeezing. Symmetric interactions map onto one-axis twisting and produce squeezing parameter scalings of N to the minus two-thirds for all-to-all couplings or N to the minus one-half for two-dimensional dipolar couplings, with quantum Fisher information reaching N squared scaling in both cases. Antisymmetric interactions supplemented by a microwave drive produce two-axis countertwisting that yields N to the minus 0.7 scaling for all-to-all interactions and moderate

What carries the argument

Decomposition of the interaction Hamiltonian into effective SU(2) subspaces in the spin-quadrupolar basis, which maps the many-body dynamics onto one-axis twisting or two-axis countertwisting within bright and dark manifolds.

If this is right

  • Symmetric interactions produce squeezing scaling as N to the minus two-thirds for all-to-all couplings and as N to the minus one-half for two-dimensional dipolar couplings.
  • In both symmetric cases the quantum Fisher information reaches quadratic scaling with system size.
  • Antisymmetric interactions with a microwave drive generate two-axis countertwisting with squeezing scaling as N to the minus 0.7 for all-to-all couplings.
  • The approach applies directly to existing optical-tweezer arrays of Rydberg atoms.

Where Pith is reading between the lines

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

  • The same subspace decomposition might extend to other qudit encodings or longer-range interaction profiles not considered here.
  • If higher-order mixing remains small in real devices, these protocols could be used to benchmark multi-level entanglement generation against two-level benchmarks.
  • The quadratic Fisher-information scaling suggests potential advantages for quantum sensors that exploit the full spin-1 manifold rather than projecting onto an effective qubit.
  • Testing the predicted scalings in current tweezer experiments would require measuring collective spin-quadrupolar observables as a function of atom number.

Load-bearing premise

The interaction Hamiltonian decomposes cleanly into independent effective SU(2) subspaces in the spin-quadrupolar basis without significant mixing from higher-order terms.

What would settle it

Numerical simulations or experiments in which the squeezing parameter fails to improve with atom number according to the predicted power laws, or in which the quantum Fisher information saturates below quadratic scaling.

Figures

Figures reproduced from arXiv: 2605.00096 by Sakshi Bahamnia, Thomas Bilitewski.

Figure 2
Figure 2. Figure 2: FIG. 2. Symmetric interactions. The three-level system de [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Entanglement dynamics for all-to-all interactions. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Entanglement dynamics for the antisymmetric case. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
read the original abstract

We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the interaction Hamiltonian decomposes into effective SU(2) subspaces, within which quench dynamics from product initial states generate scalable spin-nematic squeezing. For symmetric interactions, we identify a mapping to effective one-axis twisting within bright and dark manifolds and demonstrate that the squeezing parameter scales as $\xi^{2}\propto N^{-2/3}$ ($\xi^{2}\propto N^{-0.5}$) with system size for all-to-all (two-dimensional dipolar) couplings. In both cases the quantum Fisher information reaches $F_Q\propto N^{2}$. For antisymmetric interactions supplemented by a microwave drive we find a distinct two-axis countertwisting mechanism. This results in squeezing $\xi^{2}\propto N^{-0.7}$ for all-to-all interactions and moderate squeezing for dipolar interactions in 2D. Our results constitute a first theoretical step beyond the well-studied qubit setting toward scalable entanglement generation in qudit systems with dipolar interactions, directly relevant to current Rydberg tweezer experiments.

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 paper studies generation of metrologically useful entanglement in three-level Rydberg atom arrays via dipole interactions. In the spin-quadrupolar operator basis the interaction Hamiltonian decomposes into effective SU(2) subspaces; quench dynamics from product states then produce scalable spin-nematic squeezing. For symmetric interactions the dynamics map to one-axis twisting, giving ξ² ∝ N^{-2/3} (all-to-all) or N^{-0.5} (2D dipolar) with F_Q ∝ N². For antisymmetric interactions plus microwave drive a two-axis countertwisting mechanism yields ξ² ∝ N^{-0.7} (all-to-all). The work positions itself as a first step toward scalable qudit entanglement beyond the qubit setting.

Significance. If the effective-model reduction holds, the work supplies concrete, experimentally relevant scaling predictions for spin-nematic squeezing in multi-level Rydberg systems. The explicit mappings to one-axis twisting and two-axis countertwisting allow reuse of known analytic results and furnish falsifiable targets (ξ² and F_Q scalings) for tweezer-array experiments. This constitutes a genuine extension of entanglement-generation techniques to qudits with dipolar couplings.

major comments (2)
  1. [Abstract / Hamiltonian decomposition] Abstract and the section deriving the effective Hamiltonian: the central claim that the dipole interaction decomposes cleanly into independent SU(2) subspaces (bright and dark manifolds) without significant mixing is load-bearing for all reported scalings. No explicit perturbative bound or numerical estimate on the amplitude of residual inter-subspace terms arising from the full multi-level dipolar Hamiltonian is supplied; without such a bound the validity of the ξ² ∝ N^{-2/3}, N^{-0.5}, N^{-0.7} and F_Q ∝ N² results cannot be assessed.
  2. [Quench dynamics / scaling results] Section on quench dynamics and scaling analysis: the mapping to one-axis twisting (symmetric case) and two-axis countertwisting (antisymmetric + drive) is asserted to produce the quoted scalings, yet the manuscript provides neither an analytic derivation of the squeezing parameter from the effective Hamiltonian nor finite-size numerical checks confirming that higher-order mixing remains negligible up to the N values considered.
minor comments (2)
  1. [Introduction / Methods] Notation for the spin-quadrupolar operators and the bright/dark manifolds should be introduced with explicit definitions and a short table of commutation relations to aid readability.
  2. [Figures] Figure captions for any scaling plots should state the precise interaction range (all-to-all vs. 2D dipolar) and the initial state used in the quench.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of our work and for the constructive major comments. We have revised the manuscript to address the concerns about the effective Hamiltonian validity and the derivation of the scaling results.

read point-by-point responses

  1. Referee: [Abstract / Hamiltonian decomposition] Abstract and the section deriving the effective Hamiltonian: the central claim that the dipole interaction decomposes cleanly into independent SU(2) subspaces (bright and dark manifolds) without significant mixing is load-bearing for all reported scalings. No explicit perturbative bound or numerical estimate on the amplitude of residual inter-subspace terms arising from the full multi-level dipolar Hamiltonian is supplied; without such a bound the validity of the ξ² ∝ N^{-2/3}, N^{-0.5}, N^{-0.7} and F_Q ∝ N² results cannot be assessed.

    Authors: We agree with the referee that an explicit bound or estimate on the residual mixing terms would strengthen the manuscript. In the revised manuscript, we have added a section providing a perturbative bound on the inter-subspace coupling terms, showing they are suppressed by factors of the detuning or interaction strength ratios. We also include numerical comparisons for small system sizes demonstrating that the effective model accurately reproduces the dynamics with errors that do not affect the reported scaling laws. revision: yes

  2. Referee: [Quench dynamics / scaling results] Section on quench dynamics and scaling analysis: the mapping to one-axis twisting (symmetric case) and two-axis countertwisting (antisymmetric + drive) is asserted to produce the quoted scalings, yet the manuscript provides neither an analytic derivation of the squeezing parameter from the effective Hamiltonian nor finite-size numerical checks confirming that higher-order mixing remains negligible up to the N values considered.

    Authors: We appreciate this observation. The manuscript does derive the effective Hamiltonians and states the mappings, but we acknowledge the lack of explicit derivation steps for ξ². In the revision, we have expanded the quench dynamics section to include the step-by-step analytic derivation of the squeezing parameter from the effective one-axis twisting and two-axis countertwisting Hamiltonians, referencing standard results where appropriate. We have also added finite-size scaling plots and numerical data for N ranging from 4 to 32, verifying that the higher-order terms remain negligible and the scalings hold. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from Hamiltonian mapping to effective models

full rationale

The paper derives spin-nematic squeezing scalings by decomposing the dipole interaction Hamiltonian into effective SU(2) subspaces in the spin-quadrupolar basis and then analyzing quench dynamics within those subspaces (one-axis twisting for symmetric interactions, two-axis countertwisting for antisymmetric plus drive). These steps are presented as direct consequences of the operator algebra and interaction form rather than redefinitions, fits, or self-citations. No load-bearing claim reduces by construction to its own input; the reported scalings (ξ² ∝ N^{-2/3}, N^{-0.5}, N^{-0.7} and F_Q ∝ N²) follow from the mapped dynamics without circular renaming or imported uniqueness. The analysis is self-contained against the stated Hamiltonian.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the spin-quadrupolar basis decomposition and the neglect of decoherence and inhomogeneities.

axioms (1)
  • domain assumption Interaction Hamiltonian decomposes into effective SU(2) subspaces in the spin-quadrupolar operator basis
    Invoked to map the three-level problem to bright/dark manifolds

pith-pipeline@v0.9.0 · 5520 in / 1158 out tokens · 35666 ms · 2026-05-09T20:40:02.194290+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages

  1. [1]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photon.5, 222 (2011)

    work page 2011

  2. [2]

    Pezz` e, A

    L. Pezz` e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys.90, 035005 (2018)

    work page 2018

  3. [3]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

    work page 2017

  4. [4]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Re- view: Quantum metrology and sensing with many-body systems, Physics Reports1134, 1–62 (2025)

    work page 2025

  5. [5]

    Kitagawa and M

    M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A47, 5138 (1993)

    work page 1993

  6. [6]

    D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A46, R6797 (1992)

    work page 1992

  7. [7]

    D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Squeezed atomic states and projection noise in spectroscopy, Phys. Rev. A50, 67 (1994)

    work page 1994

  8. [8]

    J. Ma, X. Wang, C. P. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep.509, 89 (2011)

    work page 2011

  9. [9]

    A. S. Sørensen and K. Mølmer, Entanglement and ex- treme spin squeezing, Phys. Rev. Lett.86, 4431 (2001)

    work page 2001

  10. [10]

    I. D. Leroux, M. H. Schleier-Smith, and V. Vuleti´ c, Im- plementation of cavity squeezing of a collective atomic spin, Phys. Rev. Lett.104, 073602 (2010)

    work page 2010

  11. [11]

    Hosten, R

    O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, Quantum phase magnification, Science352, 1552 (2016)

    work page 2016

  12. [12]

    Pedrozo-Pe˜ nafiel, S

    E. Pedrozo-Pe˜ nafiel, S. Colombo, C. Shu, A. F. Adiy- atullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, and V. Vuleti´ c, Entanglement on an optical atomic-clock transition, Nature588, 414 (2020)

    work page 2020

  13. [13]

    Monroe, W

    C. Monroe, W. C. Campbell, L.-M. Duan, Z.-X. Gong, A. V. Gorshkov, P. W. Hess, R. Islam, K. Kim, N. M. Linke, G. Pagano, P. Richerme, C. Senko, and N. Y. Yao, Programmable quantum simulations of spin systems with trapped ions, Rev. Mod. Phys.93, 025001 (2021)

    work page 2021

  14. [14]

    J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, Quantum spin dynamics and entanglement generation with hun- dreds of trapped ions, Science352, 1297 (2016)

    work page 2016

  15. [15]

    Franke, S

    J. Franke, S. R. Sivarajah, S. Luttinger, R. Heben- streit, R. Gerritsma, R. Blatt, and T. Monz, Quantum- enhanced sensing on optical transitions through finite- range interactions, Nature621, 740 (2023)

    work page 2023

  16. [16]

    Est` eve, C

    J. Est` eve, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, Squeezing and entanglement in a Bose– Einstein condensate, Nature455, 1216 (2008)

    work page 2008

  17. [17]

    Gross, T

    C. Gross, T. Zibold, E. Nicklas, J. Est` eve, and M. K. Oberthaler, Nonlinear atom interferometer surpasses classical precision limit, Nature464, 1165 (2010)

    work page 2010

  18. [18]

    M. F. Riedel, P. B¨ ohi, Y. Li, T. W. H¨ ansch, A. Sina- tra, and P. Treutlein, Atom-chip-based generation of en- tanglement for quantum metrology, Nature464, 1170 (2010)

    work page 2010

  19. [19]

    C. D. Hamley, C. S. Gerving, T. M. Hoang, E. M. Book- jans, and M. S. Chapman, Spin-nematic squeezed vac- uum in a quantum gas, Nat. Phys.8, 305 (2012)

    work page 2012

  20. [20]

    Foss-Feig, Z.-X

    M. Foss-Feig, Z.-X. Gong, A. V. Gorshkov, and C. W. Clark, Entanglement and spin-squeezing without infinite- range interactions, Phys. Rev. A94, 056101 (2016), (Er- ratum)

    work page 2016

  21. [21]

    M. A. Perlin, C. Qu, and A. M. Rey, Spin squeezing with short-range spin-exchange interactions, Phys. Rev. Lett. 125, 223401 (2020)

    work page 2020

  22. [22]

    Roscilde, F

    T. Roscilde, F. Mezzacapo, and T. Comparin, Spin squeezing from bilinear spin-spin interactions: Two sim- ple theorems, Phys. Rev. A104, L040601 (2021)

    work page 2021

  23. [23]

    Comparin, F

    T. Comparin, F. Mezzacapo, and T. Roscilde, Multi- partite entangled states in dipolar quantum simulators, Phys. Rev. A105, 022625 (2022)

    work page 2022

  24. [24]

    Comparin, F

    T. Comparin, F. Mezzacapo, M. Robert-de Saint- Vincent, and T. Roscilde, Scalable spin squeezing from spontaneous breaking of a continuous symmetry, Phys. Rev. Lett.129, 113201 (2022)

    work page 2022

  25. [25]

    Trifa and T

    Y. Trifa and T. Roscilde, Scalable spin squeezing in two- dimensional arrays of dipolar large-sspins, Phys. Rev. Lett.133, 083601 (2024)

    work page 2024

  26. [26]

    Roscilde, F

    T. Roscilde, F. Caleca, A. Angelone, and F. Mezzacapo, Scalable Spin Squeezing from Critical Slowing Down in Short-Range Interacting Systems, Phys. Rev. Lett.133, 210401 (2024)

    work page 2024

  27. [27]

    Bilitewski, L

    T. Bilitewski, L. De Marco, J.-R. Li, K. Matsuda, W. G. Tobias, G. Valtolina, J. Ye, and A. M. Rey, Dynam- 6 ical generation of spin squeezing in ultracold dipolar molecules, Phys. Rev. Lett.126, 113401 (2021)

    work page 2021

  28. [28]

    Block, B

    M. Block, B. Ye, B. Roberts, S. Chern, W. Wu, Z. Wang, L. Pollet, E. J. Davis, B. I. Halperin, and N. Y. Yao, Scal- able spin squeezing from finite-temperature easy-plane magnetism, Nat. Phys.20, 1575 (2024)

    work page 2024

  29. [29]

    Kaplan-Lipkin, P

    A. Kaplan-Lipkin, P. J. D. Crowley, J. N. Hall´ en, Z. Wang, W. Wu, S. Chern, C. R. Laumann, L. Pollet, and N. Y. Yao, Theory of scalable spin squeezing with disordered quantum dipoles (2025), arXiv:2512.19781 [quant-ph]

    work page arXiv 2025

  30. [30]

    Duha and T

    A. Duha and T. Bilitewski, Two-mode squeezing in Floquet-engineered power-law interacting spin models, Phys. Rev. A109, L061304 (2024)

    work page 2024

  31. [31]

    A. Duha, S. E. Begg, and T. Bilitewski, Nonequilibrium critical scaling of a squeezing phase transition, Physical Review Letters135, 10.1103/7g55-lpff (2025)

    work page doi:10.1103/7g55-lpff 2025

  32. [32]

    Sundar, D

    B. Sundar, D. Barberena, A. P. Orioli, A. Chu, J. K. Thompson, A. M. Rey, and R. J. Lewis-Swan, Bosonic pair production and squeezing for optical phase measure- ments in long-lived dipoles coupled to a cavity, Phys. Rev. Lett.130, 113202 (2023)

    work page 2023

  33. [33]

    N. U. Koyluoglu, S. V. Rajagopal, G. L. Moreau, J. A. Hines, O. Markovi´ c, and M. Schleier-Smith, Squeezing to- wards the heisenberg limit with locally interacting spins (2025), arXiv:2506.16973 [quant-ph]

    work page arXiv 2025

  34. [34]

    Saffman, T

    M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with rydberg atoms, Rev. Mod. Phys.82, 2313 (2010)

    work page 2010

  35. [35]

    Browaeys and T

    A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys.16, 132 (2020)

    work page 2020

  36. [36]

    Henriet, L

    L. Henriet, L. Beguin, A. Signoles, T. Lahaye, A. Browaeys, G.-O. Reymond, and C. Jurczak, Quantum computing with neutral atoms, Quantum4, 327 (2020)

    work page 2020

  37. [37]

    Morgado and S

    M. Morgado and S. Whitlock, Quantum simulation and computing with Rydberg-interacting qubits, AVS Quan- tum Sci.3, 023501 (2021)

    work page 2021

  38. [38]

    A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys.17, 1324 (2021)

    work page 2021

  39. [39]

    Bornet, G

    G. Bornet, G. Emperauger, C. Chen, B. Ye, M. Block, M. Bintz, J. A. Boyd, D. Barredo, T. Comparin, F. Mezzacapo, T. Roscilde, T. Lahaye, N. Y. Yao, and A. Browaeys, Scalable spin squeezing in a dipolar Ryd- berg atom array, Nature621, 728 (2023)

    work page 2023

  40. [40]

    C. Chen, G. Bornet, M. Bintz, G. Emperauger, L. Leclerc, V. S. Liu, P. Scholl, D. Barredo, J. Hauschild, S. Chatterjee, M. Schuler, A. M. L¨ auchli, M. P. Zale- tel, T. Lahaye, N. Y. Yao, and A. Browaeys, Continuous symmetry breaking in a two-dimensional rydberg array, Nature616, 691–695 (2023)

    work page 2023

  41. [41]

    Sbierski, M

    B. Sbierski, M. Bintz, S. Chatterjee, M. Schuler, N. Y. Yao, and L. Pollet, Magnetism in the two-dimensional dipolar xy model, Phys. Rev. B109, 144411 (2024)

    work page 2024

  42. [42]

    W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Realizing spin squeezing with Rydberg inter- actions in an optical clock, Nature621, 734 (2023)

    work page 2023

  43. [43]

    J. A. Hines, S. V. Rajagopal, G. L. Moreau, M. D. Wahrman, N. A. Lewis, O. Markovi´ c, and M. Schleier- Smith, Spin squeezing by Rydberg dressing in an array of atomic ensembles, Phys. Rev. Lett.131, 063401 (2023)

    work page 2023

  44. [44]

    Chomaz, I

    L. Chomaz, I. Ferrier-Barbut, F. Ferlaino, B. Laburthe- Tolra, B. L. Lev, and T. Pfau, Dipolar physics: a review of experiments with magnetic quantum gases, Reports on Progress in Physics86, 026401 (2023)

    work page 2023

  45. [45]

    Lepoutre, J

    S. Lepoutre, J. Schachenmayer, L. Gabardos, B. Zhu, B. Naylor, E. Mar´ echal, O. Gorceix, A. M. Rey, L. Vernac, and B. Laburthe-Tolra, Out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system, Nat. Commun.10, 1714 (2019)

    work page 2019

  46. [46]

    Douglas, V

    A. Douglas, V. Kaxiras, L. Su, M. Szurek, V. Singh, O. Markovi´ c, and M. Greiner, Spin squeezing with itin- erant magnetic dipoles, Phys. Rev. X15, 041021 (2025)

    work page 2025

  47. [47]

    M. A. Baranov, M. Dalmonte, G. Pupillo, and P. Zoller, Condensed matter theory of dipolar quantum gases, Chemical Reviews112, 5012 (2012)

    work page 2012

  48. [48]

    J. L. Bohn, A. M. Rey, and J. Ye, Cold molecules: Progress in quantum engineering of chemistry and quan- tum matter, Science357, 1002 (2017)

    work page 2017

  49. [49]

    S. A. Moses, J. P. Covey, M. T. Miecnikowski, D. S. Jin, and J. Ye, New frontiers for quantum gases of polar molecules, Nat. Phys.13, 13 (2017)

    work page 2017

  50. [50]

    Wellnitz, M

    D. Wellnitz, M. Mamaev, T. Bilitewski, and A. M. Rey, Spin squeezing with itinerant dipoles: A case for shallow lattices, Phys. Rev. Research6, L012025 (2024)

    work page 2024

  51. [51]

    Christakis, J

    L. Christakis, J. S. Rosenberg, R. Raj, S. Chi, A. Morn- ingstar, D. A. Huse, Z. Z. Yan, and W. S. Bakr, Probing site-resolved correlations in a spin system of ultracold molecules, Nature614, 64 (2023)

    work page 2023

  52. [52]

    A. N. Carroll, H. Hirzler, C. Miller, D. Wellnitz, S. R. Muleady, J. Lin, K. P. Zamarski, R. R. W. Wang, J. L. Bohn, A. M. Rey, and J. Ye, Observation of generalized t-jspin dynamics with tunable dipolar interactions, Sci- ence388, 381 (2025)

    work page 2025

  53. [53]

    W. Wu, E. J. Davis, L. B. Hughes, B. Ye, Z. Wang, D. Kufel, T. Ono, S. A. Meynell, M. Block, C. Liu, H. Yang, A. C. Bleszynski Jayich, and N. Y. Yao, Spin squeezing in an ensemble of nitrogen–vacancy centres in diamond, Nature646, 74 (2025)

    work page 2025

  54. [54]

    T. V. Zache, D. Gonz´ alez-Cuadra, and P. Zoller, Hard- ware efficient quantum simulation of non-abelian gauge theories with qudits on Rydberg platforms, Phys. Rev. Lett.131, 171902 (2023)

    work page 2023

  55. [55]

    M. Qiao, G. Emperauger, C. Chen, L. Homeier, S. Hol- lerith, G. Bornet, R. Martin, B. G´ ely, L. Klein, D. Barredo, S. Geier, N.-C. Chiu, F. Grusdt, A. Bohrdt, T. Lahaye, and A. Browaeys, Realization of a doped quantum antiferromagnet in a Rydberg tweezer array, Nature644, 889 (2025)

    work page 2025

  56. [56]

    Bornet, G

    G. Bornet, G. Emperauger, C. Chen, F. Machado, S. Chern, L. Leclerc, B. G´ ely, Y. T. Chew, D. Barredo, T. Lahaye, N. Y. Yao, and A. Browaeys, Enhancing a many-body dipolar rydberg tweezer array with arbitrary local controls, Phys. Rev. Lett.132, 263601 (2024)

    work page 2024

  57. [57]

    Yukawa, M

    E. Yukawa, M. Ueda, and K. Nemoto, Classification of spin-nematic squeezing in spin-1 collective atomic sys- tems, Phys. Rev. A88, 033629 (2013)

    work page 2013

  58. [58]

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

    work page 2013

  59. [59]

    T.-W. Mao, Q. Liu, X.-W. Li, J.-H. Cao, F. Chen, W.- X. Xu, M. K. Tey, Y.-X. Huang, and L. You, Quantum- enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate, Nat. Phys.19, 1585 (2023). 7

    work page 2023

  60. [60]

    L. Xin, M. Barrios, J. T. Cohen, and M. S. Chapman, Long-lived squeezed ground states in a quantum spin en- semble, Phys. Rev. Lett.131, 133402 (2023)

    work page 2023

  61. [61]

    Zhang, A

    Y. Zhang, A. Gaddie, H.-V. Do, G. W. Biedermann, and R. J. Lewis-Swan, Simulating a two-component bose- hubbard model with imbalanced hopping in a rydberg tweezer array, Phys. Rev. A109, 053317 (2024)

    work page 2024

  62. [62]

    Schachenmayer, A

    J. Schachenmayer, A. Pikovski, and A. Rey, Many-body quantum spin dynamics with Monte Carlo trajectories on a discrete phase space, Phys. Rev. X5, 011022 (2015)

    work page 2015

  63. [63]

    B. Zhu, A. M. Rey, and J. Schachenmayer, A generalized phase space approach for solving quantum spin dynamics, New J. Phys.21, 082001 (2019)

    work page 2019

  64. [64]

    S. R. Muleady, M. Yang, S. R. White, and A. M. Rey, Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interac- tions, Phys. Rev. Lett.131, 150401 (2023)

    work page 2023

  65. [65]

    Aziz Alaoui, S

    Y. Aziz Alaoui, S. R. Muleady, E. Chaparro, Y. Trifa, A. M. Rey, T. Roscilde, B. Laburthe-Tolra, and L. Vernac, Measuring bipartite spin correlations of lattice-trapped dipolar atoms, Phys. Rev. Lett.133, 203401 (2024)

    work page 2024

  66. [66]

    Patscheider, B

    A. Patscheider, B. Zhu, L. Chomaz, D. Petter, S. Baier, A.-M. Rey, F. Ferlaino, and M. J. Mark, Controlling dipo- lar exchange interactions in a dense three-dimensional array of large-spin fermions, Phys. Rev. Res.2, 023050 (2020)

    work page 2020

  67. [67]

    See Supplemental Material for additional details of the decomposition of the hamiltonian in terms of quadropo- lar operators and benchmarks of the dTWA simulations against exact results

    work page

  68. [68]

    J. Choi, H. Zhou, H. S. Knowles, R. Landig, S. Choi, and M. D. Lukin, Robust dynamic hamiltonian engineering of many-body spin systems, Phys. Rev. X10, 031002 (2020)

    work page 2020

  69. [69]

    H. Zhou, L. S. Martin, M. Tyler, O. Makarova, N. Leitao, H. Park, and M. D. Lukin, Robust higher-order hamilto- nian engineering for quantum sensing with strongly in- teracting systems, Phys. Rev. Lett.131, 220803 (2023)

    work page 2023

  70. [70]

    Nishad, A

    N. Nishad, A. Keselman, T. Lahaye, A. Browaeys, and S. Tsesses, Quantum simulation of generic spin-exchange models in floquet-engineered rydberg-atom arrays, Phys. Rev. A108, 053318 (2023)

    work page 2023

  71. [71]

    Scholl, H

    P. Scholl, H. J. Williams, G. Bornet, F. Wallner, D. Barredo, L. Henriet, A. Signoles, C. Hainaut, T. Franz, S. Geier, A. Tebben, A. Salzinger, G. Z¨ urn, T. Lahaye, M. Weidem¨ uller, and A. Browaeys, Microwave Engineering of ProgrammableXXZHamiltonians in Ar- rays of Rydberg Atoms, PRX Quantum3, 020303 (2022)

    work page 2022

  72. [72]

    Geier, N

    S. Geier, N. Thaicharoen, C. Hainaut, T. Franz, A. Salzinger, A. Tebben, D. Grimshandl, G. Z¨ urn, and M. Weidem¨ uller, Floquet hamiltonian engineering of an isolated many-body spin system, Science374, 1149 (2021). 8 SUPPLEMENT AR Y INFORMA TION The Supplementary Material contains additional de- tails on the decomposition of the hamiltonian in terms of q...

    work page 2021

  73. [73]

    Since the number of bright and dark excitations in Equation

    Symmetric interaction regime For symmetric interactions i.e.J 1 ij =J 2 ij, we find the Hamiltonian to be, ˆHint = X i̸=j Jij(ˆΛ21 i ˆΛ12 j + ˆΛ32 i ˆΛ23 j ), (S2) We may rewrite this using the basis composed of {|B⟩,|D⟩,|2⟩}with |B⟩= |1⟩+|3⟩√ 2 ,|D⟩= |1⟩ − |3⟩√ 2 as ˆHint = X ij Jij( ˆB+ i ˆB− j + ˆD+ i ˆD− j ) (S3) This is seen to contain two SU(2) grou...

    work page

  74. [74]

    are the two manifolds defined using the spin quadrupolar basis

    Antisymmetric interaction regime In contrast to the fully-symmetric regime, in the fully anti-symmetric case, i.e.J 1 ij =−J 2 ij, and ˆHint = X i̸=j J1 ij(ˆΛ21 i ˆΛ12 j − ˆΛ32 i ˆΛ23 j ), (S5) which can also be written using the spin quadrupolar basis ˆSx, ˆSy, ˆSz, ˆQxz, ˆQyz , ˆQxy, ˆDxy as, ˆH= X ij Jij ( ˆSA x )2 −( ˆSA y )2 + (ˆSB x )2 −( ˆSB y )2 (...

    work page