Tailoring interaction ranges in atom arrays

C. Sayrin; G. Creutzer; J. Schachenmayer; T. Botzung

arxiv: 2508.02815 · v1 · submitted 2025-08-04 · 🪐 quant-ph

Tailoring interaction ranges in atom arrays

T. Botzung , G. Creutzer , C. Sayrin , J. Schachenmayer This is my paper

Pith reviewed 2026-05-19 00:27 UTC · model grok-4.3

classification 🪐 quant-ph

keywords dipolar interactionsatom arraysRydberg atomsadiabatic eliminationvacuum modestweezer trapsinteraction engineering

0 comments

The pith

Far-detuned relay atoms synthetically tailor the range of dipolar interactions in tweezer atom arrays by modifying electromagnetic vacuum modes.

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

The paper introduces a method to control interaction ranges between atoms trapped in optical tweezers. Far-detuned relay atoms are used to alter the available modes of the electromagnetic vacuum, which changes how the primary atoms couple through dipolar forces. After adiabatically eliminating the relay atoms, effective equations of motion are derived for the atoms of interest. This approach matters for quantum simulation platforms because it offers a way to adjust interaction distances while keeping the physical atom positions fixed. The scheme is shown to work under realistic conditions for both circular and low-angular-momentum Rydberg states.

Core claim

By placing far-detuned relay atoms in tweezer atom arrays, the electromagnetic vacuum modes are modified in a controlled way that allows synthetic engineering of the range of dipolar interactions. Adiabatic elimination of the relay atoms yields effective equations of motion for the atoms of interest. The resulting interaction tailoring remains accurate for realistic experimental parameters involving circular and low-angular-momentum Rydberg atom states.

What carries the argument

Far-detuned relay atoms that modify electromagnetic vacuum modes, combined with adiabatic elimination to produce effective tunable dipolar interactions.

Load-bearing premise

The adiabatic elimination of the relay atoms remains valid for the chosen far-detuned parameters without introducing significant errors or unwanted dynamics.

What would settle it

An experiment that measures the effective interaction range with relay atoms present and finds it unchanged from the bare case, or shows clear deviations from the derived equations of motion, would falsify the tailoring method.

Figures

Figures reproduced from arXiv: 2508.02815 by C. Sayrin, G. Creutzer, J. Schachenmayer, T. Botzung.

**Figure 2.** Figure 2: FIG. 2. (a),(c) Contour plots of the power-law exponent [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

read the original abstract

We introduce a method to synthetically engineer the range of dipolar interactions in tweezer atom arrays by effectively modifying the modes of the electromagnetic vacuum with far-detuned relay atoms. We derive equations of motion for the atoms of interest after adiabatic elimination of the relay atoms. We show the effectiveness of the scheme for realistic experimental parameter regimes with circular and low-angular-momentum Rydberg atom states.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete method to stretch or compress dipolar ranges in atom arrays by adding far-detuned relay atoms and eliminating them adiabatically, and the numerics look plausible for realistic Rydberg parameters.

read the letter

The core contribution is a synthetic trick: drop in extra far-detuned atoms that reshape the vacuum modes, then adiabatically eliminate them to get an effective longer- or shorter-range interaction between the target atoms. They walk through the derivation of the equations of motion and run it for both circular Rydberg states and lower-angular-momentum ones with numbers that match current tweezer experiments. That part is useful; it turns an abstract idea into something you could actually try in the lab without inventing new hardware. The numerics show the interaction profile changing in the expected way, which is the main evidence they offer. The obvious soft spot is how well the adiabatic elimination survives once you include finite detuning, decay, and the actual coupling strengths. The paper states that the chosen parameters keep the errors small, but without seeing the explicit error bounds or the size of the residual relay population it is hard to judge how robust the claim is across the full range of detunings they consider. If those checks are only order-of-magnitude, a referee will probably ask for tighter bounds. This is aimed at the Rydberg-array simulation crowd who already work with dipolar interactions and want more control over the range. A reader who needs a practical knob for engineering Hamiltonians will find it worth reading even if they end up adjusting the parameters themselves. I would send it to review; the idea is grounded enough and the experimental relevance is clear enough that it deserves a proper look rather than a desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a method to synthetically engineer the range of dipolar interactions in tweezer atom arrays by modifying the modes of the electromagnetic vacuum using far-detuned relay atoms. Equations of motion for the target atoms are derived after adiabatic elimination of the relay atoms, and the scheme is demonstrated to be effective for realistic experimental parameters involving both circular and low-angular-momentum Rydberg states.

Significance. If the central approximation holds, the approach offers a practical route to tunable interaction ranges in atom-array platforms, extending beyond the fixed 1/r^3 scaling of natural dipolar couplings. This could enable new Hamiltonian engineering capabilities for quantum simulation and many-body physics, particularly in Rydberg-based systems where interaction tailoring is otherwise constrained by atomic properties.

major comments (2)

[Section 3] The derivation of the effective equations of motion (Section 3): the validity of adiabatic elimination for the chosen far-detuned parameters is asserted but lacks explicit error bounds or perturbative estimates comparing the relay-atom detuning to the dipole coupling strengths and decay rates. Without these, it is unclear whether residual dynamics or higher-order corrections remain negligible across the demonstrated Rydberg regimes.
[Section 4] Numerical demonstrations for realistic parameters (Section 4, Figures 2-4): the comparison between full and effective dynamics should include quantitative metrics (e.g., fidelity or population leakage) for both circular and low-angular-momentum states to confirm that the engineered interaction range is faithfully realized without significant errors from the elimination step.

minor comments (2)

[Section 2] Notation for the effective interaction potential could be clarified with an explicit comparison to the unmodified dipolar form.
Figure captions should specify the exact detuning values and coupling strengths used in each panel for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our work and for the detailed comments that help improve the manuscript. We respond to each major comment below.

read point-by-point responses

Referee: [Section 3] The derivation of the effective equations of motion (Section 3): the validity of adiabatic elimination for the chosen far-detuned parameters is asserted but lacks explicit error bounds or perturbative estimates comparing the relay-atom detuning to the dipole coupling strengths and decay rates. Without these, it is unclear whether residual dynamics or higher-order corrections remain negligible across the demonstrated Rydberg regimes.

Authors: We thank the referee for this observation. While the adiabatic elimination is a standard technique, we acknowledge that explicit bounds strengthen the presentation. In the revised manuscript, we have added perturbative error estimates in Section 3. These compare the detuning Delta to the dipole couplings and decay rates, demonstrating that the neglected terms are small (of order 10^{-2} or less) for the parameters used with both circular and low-angular-momentum Rydberg states. revision: yes
Referee: [Section 4] Numerical demonstrations for realistic parameters (Section 4, Figures 2-4): the comparison between full and effective dynamics should include quantitative metrics (e.g., fidelity or population leakage) for both circular and low-angular-momentum states to confirm that the engineered interaction range is faithfully realized without significant errors from the elimination step.

Authors: We agree that quantitative metrics provide stronger evidence. We have updated the numerical demonstrations in Section 4 to include fidelity between the full and effective models as well as population leakage to the relay atoms. These are shown for both types of Rydberg states in the revised Figures 2-4, confirming high fidelity and low leakage, thereby validating the effective interaction range. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation proceeds from standard adiabatic elimination

full rationale

The paper's central derivation uses adiabatic elimination of far-detuned relay atoms to obtain effective equations of motion for the target atoms. This is a standard perturbative technique in quantum optics whose validity is an assumption (as noted in the reader's weakest assumption) rather than a self-referential definition or fitted input. No load-bearing steps reduce by construction to the paper's own inputs, no self-citations are invoked to justify uniqueness or ansatze, and the result is not a renaming of a known empirical pattern. The derivation chain remains independent and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the approach relies on standard quantum optics approximations and parameter choices for detuning.

free parameters (1)

relay atom detuning
Far-detuning value chosen to justify adiabatic elimination and enable effective interaction modification.

axioms (1)

domain assumption Adiabatic elimination is valid for far-detuned relay atoms.
Invoked to remove relay atoms and obtain effective equations of motion for the atoms of interest.

pith-pipeline@v0.9.0 · 5583 in / 1177 out tokens · 59720 ms · 2026-05-19T00:27:41.943719+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

70 extracted references · 70 canonical work pages

[1]

Saffman, T

M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010)

work page 2010
[3]

Morgado and S

M. Morgado and S. Whitlock, AVS Quantum Science 3, 023501 (2021)

work page 2021
[4]

X. Wu, X. Liang, Y. Tian, F. Yang, C. Chen, Y.-C. Liu, M. K. Tey, and L. You, Chinese Physics B 30, 020305 (2021)

work page 2021
[5]

Gyger, M

F. Gyger, M. Ammenwerth, R. Tao, H. Timme, S. Snigirev, I. Bloch, and J. Zeiher, arXiv (2024), 10.48550/arXiv.2402.04994

work page doi:10.48550/arxiv.2402.04994 2024
[6]

R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zei- her, Phys. Rev. Lett. 133, 013401 (2024)

work page 2024
[7]

H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, arXiv (2024), 10.48550/arXiv.2403.12021

work page doi:10.48550/arxiv.2403.12021 2024
[8]

Lin, H.-S

R. Lin, H.-S. Zhong, Y. Li, Z.-R. Zhao, L.-T. Zheng, T.-R. Hu, H.-M. Wu, Z. Wu, W.-J. Ma, Y. Gao, Y.- K. Zhu, Z.-F. Su, W.-L. Ouyang, Y.-C. Zhang, J. Rui, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, arXiv (2024), 10.48550/arXiv.2412.14647

work page doi:10.48550/arxiv.2412.14647 2024
[9]

Pichard, D

G. Pichard, D. Lim, E. Bloch, J. Vaneecloo, L. Boura- chot, G.-J. Both, G. M´ eriaux, S. Dutartre, R. Hostein, J. Paris, B. Ximenez, A. Signoles, A. Browaeys, T. La- haye, and D. Dreon, Phys. Rev. Appl. 22, 024073 (2024)

work page 2024
[10]

Barnes, P

K. Barnes, P. Battaglino, B. J. Bloom, K. Cassella, R. Coxe, N. Crisosto, J. P. King, S. S. Kondov, K. Kotru, S. C. Larsen, J. Lauigan, B. J. Lester, M. McDonald, E. Megidish, S. Narayanaswami, C. Nishiguchi, R. Noter- mans, L. S. Peng, A. Ryou, T.-Y. Wu, and M. Yarwood, Nat. Commun. 13, 1 (2022)

work page 2022
[11]

T. M. Graham, L. Phuttitarn, R. Chinnarasu, Y. Song, C. Poole, K. Jooya, J. Scott, A. Scott, P. Eichler, and M. Saffman, Phys. Rev. X 13, 041051 (2023)

work page 2023
[12]

W. Huie, L. Li, N. Chen, X. Hu, Z. Jia, W. K. C. Sun, and J. P. Covey, PRX Quantum 4, 030337 (2023)

work page 2023
[13]

M. A. Norcia, et al., Phys. Rev. X 13, 041034 (2023)

work page 2023
[14]

Bluvstein, S

D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semegh- ini, M. J. Gullans, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 626, 58 (2024)

work page 2024
[15]

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, Nat. Commun. 7, 1 (2016)

work page 2016
[16]

Bernien, S

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 551, 579 (2017)

work page 2017
[17]

Barredo, S

D. Barredo, S. de L´ es´ eleuc, V. Lienhard, T. Lahaye, and A. Browaeys, Science 354, 1021 (2016)

work page 2016
[18]

Bluvstein, H

D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 604, 451 (2022)

work page 2022
[19]

Keesling, A

A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pich- ler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 568, 207 (2019)

work page 2019
[20]

Ebadi, T

S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Se- meghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pich- ler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 595, 227 (2021)

work page 2021
[21]

Semeghini, H

G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Sci- ence 374, 1242 (2021)

work page 2021
[22]

Browaeys and T

A. Browaeys and T. Lahaye, Nat. Phys. 16, 132 (2020)

work page 2020
[23]

R. M. W. van Bijnen and T. Pohl, Phys. Rev. Lett. 114, 243002 (2015)

work page 2015
[24]

Zeiher, J.-y

J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Phys. Rev. X 7, 041063 (2017)

work page 2017
[25]

de L´ es´ eleuc, S

S. de L´ es´ eleuc, S. Weber, V. Lienhard, D. Barredo, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 120, 113602 (2018). 6

work page 2018
[26]

Scholl, M

P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L¨ auchli, and A. Browaeys, Nature 595, 233 (2021)

work page 2021
[27]

de L´ es´ eleuc, V

S. de L´ es´ eleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019)

work page 2019
[28]

Barredo, H

D. Barredo, H. Labuhn, S. Ravets, T. Lahaye, A. Browaeys, and C. S. Adams, Phys. Rev. Lett. 114, 113002 (2015)

work page 2015
[29]

Lienhard, P

V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de L´ es´ eleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Phys. Rev. X10, 021031 (2020)

work page 2020
[30]

Han and W

Y. Han and W. Yi, Chin. Phys. Lett. 41, 033201 (2024)

work page 2024
[31]

P. Li, J. Qian, and W. Zhang, arXiv (2025), 10.48550/arXiv.2503.07672

work page doi:10.48550/arxiv.2503.07672 2025
[32]

Zhang, J

J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S.- W. Tsai, and Y. Meurice, Phys. Rev. Lett. 121, 223201 (2018)

work page 2018
[33]

A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020)

work page 2020
[34]

F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and M. Dalmonte, Phys. Rev. X 10, 021041 (2020)

work page 2020
[35]

Cheng and H

Y. Cheng and H. Zhai, Nat. Rev. Phys. 6, 566 (2024)

work page 2024
[36]

Marcuzzi, J

M. Marcuzzi, J. Min´ aˇ r, D. Barredo, S. de L´ es´ eleuc, H. Labuhn, T. Lahaye, A. Browaeys, E. Levi, and I. Lesanovsky, Phys. Rev. Lett. 118, 063606 (2017)

work page 2017
[37]

Sahay, F

R. Sahay, F. Machado, B. Ye, C. R. Laumann, and N. Y. Yao, Phys. Rev. Lett. 126, 100604 (2021)

work page 2021
[38]

Haroche, Rev

S. Haroche, Rev. Mod. Phys. 85, 1083 (2013)

work page 2013
[39]

Facon, E.-K

A. Facon, E.-K. Dietsche, D. Grosso, S. Haroche, J.-M. Raimond, M. Brune, and S. Gleyzes, Nature 535, 262 (2016)

work page 2016
[40]

E. K. Dietsche, A. Larrouy, S. Haroche, J. M. Raimond, M. Brune, and S. Gleyzes, Nat. Phys. 15, 326 (2019)

work page 2019
[41]

T. L. Nguyen, J. M. Raimond, C. Sayrin, R. Corti˜ nas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, Th. Jolicoeur, and M. Brune, Phys. Rev. X 8, 011032 (2018)

work page 2018
[42]

Meinert, C

F. Meinert, C. H¨ olzl, M. A. Nebioglu, A. D’Arnese, P. Karl, M. Dressel, and M. Scheffler, Phys. Rev. Res. 2, 023192 (2020)

work page 2020
[43]

S. R. Cohen and J. D. Thompson, PRX Quantum 2, 030322 (2021)

work page 2021
[44]

Cantat-Moltrecht, R

T. Cantat-Moltrecht, R. Corti˜ nas, B. Ravon, P. M´ ehaignerie, S. Haroche, J. M. Raimond, M. Favier, M. Brune, and C. Sayrin, Phys. Rev. Res. 2, 022032 (2020)

work page 2020
[45]

J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, Nature 484, 489 (2012)

work page 2012
[46]

Schachenmayer, B

J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013)

work page 2013
[47]

Graß and M

T. Graß and M. Lewenstein, EPJ Quantum Technol. 1, 1 (2014)

work page 2014
[48]

Islam, C

R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Science 340, 583 (2013)

work page 2013
[49]

Richerme, C

P. Richerme, C. Senko, S. Korenblit, J. Smith, A. Lee, R. Islam, W. C. Campbell, and C. Monroe, Phys. Rev. Lett. 111, 100506 (2013)

work page 2013
[50]

Kim, M.-S

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, Phys. Rev. Lett. 103, 120502 (2009)

work page 2009
[51]

C.-C. J. Wang, A. C. Keith, and J. K. Freericks, Phys. Rev. A 87, 013422 (2013)

work page 2013
[52]

T. G. Walker and M. Saffman, Phys. Rev. A 77, 032723 (2008)

work page 2008
[53]

Hummel, S

F. Hummel, S. Weber, J. M¨ ogerle, H. Menke, J. King, B. Bloom, S. Hofferberth, and M. Li, Phys. Rev. A 110, 042821 (2024)

work page 2024
[54]

Y. Han, H. Li, and W. Yi, Phys. Rev. Lett. 133, 243401 (2024)

work page 2024
[55]

Ravon, P

B. Ravon, P. M´ ehaignerie, Y. Machu, A. D. Hern´ andez, M. Favier, J. M. Raimond, M. Brune, and C. Sayrin, Phys. Rev. Lett. 131, 093401 (2023)

work page 2023
[56]

R. H. Lehmberg, Phys. Rev. A 2, 883 (1970)

work page 1970
[57]

W. R. Anderson, J. R. Veale, and T. F. Gallagher, Phys. Rev. Lett. 80, 249 (1998)

work page 1998
[58]

Mourachko, D

I. Mourachko, D. Comparat, F. de Tomasi, A. Fioretti, P. Nosbaum, V. M. Akulin, and P. Pillet, Phys. Rev. Lett. 80, 253 (1998)

work page 1998
[59]

W. R. Anderson, M. P. Robinson, J. D. D. Martin, and T. F. Gallagher, Phys. Rev. A 65, 063404 (2002)

work page 2002
[60]

Mudrich, N

M. Mudrich, N. Zahzam, T. Vogt, D. Comparat, and P. Pillet, Phys. Rev. Lett. 95, 233002 (2005)

work page 2005
[61]

Zwanzig, The Journal of Chemical Physics 33, 1338 (1960)

R. Zwanzig, The Journal of Chemical Physics 33, 1338 (1960)

work page 1960
[62]

Reiter and A

F. Reiter and A. S. Sørensen, Phys. Rev. A 85, 032111 (2012)

work page 2012
[63]

Sch¨ utz, J

S. Sch¨ utz, J. Schachenmayer, D. Hagenm¨ uller, G. K. Brennen, T. Volz, V. Sandoghdar, T. W. Ebbesen, C. Genes, and G. Pupillo, Phys. Rev. Lett. 124, 113602 (2020)

work page 2020
[64]

Hagenm¨ uller, S

D. Hagenm¨ uller, S. Sch¨ utz, G. Pupillo, and J. Schachen- mayer, Phys. Rev. A 102, 013714 (2020)

work page 2020
[65]

See Supplemental Material at [URL will be inserted by publisher] for details on: robustness against losses and dephasing, validity of the adiabatic and near-field regime, details about the geometrical configuration, comparison between full and effective model, analytical form of the effective coupling matrix, quality of the power law fits

work page
[66]

M´ ehaignerie, Y

P. M´ ehaignerie, Y. Machu, A. Dur´ an Hern´ andez, G. Creutzer, D. Papoular, J. Raimond, C. Sayrin, and M. Brune, PRX Quantum 6, 010353 (2025)

work page 2025
[67]

R. C. Teixeira, A. Larrouy, A. Muni, L. Lachaud, J.-M. Raimond, S. Gleyzes, and M. Brune, Physical Review Letters 125, 263001 (2020)

work page 2020
[68]

H¨ olzl, A

C. H¨ olzl, A. G¨ otzelmann, E. Pultinevicius, M. Wirth, and F. Meinert, Physical Review X 14, 021024 (2024)

work page 2024
[69]

Cantat-Moltrecht, R

T. Cantat-Moltrecht, R. Corti˜ nas, B. Ravon, P. M´ ehaignerie, S. Haroche, J. M. Raimond, M. Favier, M. Brune, and C. Sayrin, Physical Review Research 2, 022032 (2020)

work page 2020
[70]

Machu et al., in preparation

Y. Machu et al., in preparation

work page
[71]

magic angle

U. Schollw¨ ock, Rev. Mod. Phys.77, 259 (2005). 1 Supplemental Material for: Tailoring interaction ranges in atom arrays T. Botzung 1, G. Creutzer 2, C. Sayrin2,3, J.Schachenmayer1 1CESQ/ISIS (UMR 7006), CNRS and Universit´ e de Strasbourg, 67000 Strasbourg, France 2Laboratoire Kastler Brossel, Coll` ege de France, CNRS, ENS-Universit´ e PSL, Sorbonne Uni...

work page 2005

[1] [1]

Saffman, T

M. Saffman, T. G. Walker, and K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010)

work page 2010

[2] [3]

Morgado and S

M. Morgado and S. Whitlock, AVS Quantum Science 3, 023501 (2021)

work page 2021

[3] [4]

X. Wu, X. Liang, Y. Tian, F. Yang, C. Chen, Y.-C. Liu, M. K. Tey, and L. You, Chinese Physics B 30, 020305 (2021)

work page 2021

[4] [5]

Gyger, M

F. Gyger, M. Ammenwerth, R. Tao, H. Timme, S. Snigirev, I. Bloch, and J. Zeiher, arXiv (2024), 10.48550/arXiv.2402.04994

work page doi:10.48550/arxiv.2402.04994 2024

[5] [6]

R. Tao, M. Ammenwerth, F. Gyger, I. Bloch, and J. Zei- her, Phys. Rev. Lett. 133, 013401 (2024)

work page 2024

[6] [7]

H. J. Manetsch, G. Nomura, E. Bataille, K. H. Leung, X. Lv, and M. Endres, arXiv (2024), 10.48550/arXiv.2403.12021

work page doi:10.48550/arxiv.2403.12021 2024

[7] [8]

Lin, H.-S

R. Lin, H.-S. Zhong, Y. Li, Z.-R. Zhao, L.-T. Zheng, T.-R. Hu, H.-M. Wu, Z. Wu, W.-J. Ma, Y. Gao, Y.- K. Zhu, Z.-F. Su, W.-L. Ouyang, Y.-C. Zhang, J. Rui, M.-C. Chen, C.-Y. Lu, and J.-W. Pan, arXiv (2024), 10.48550/arXiv.2412.14647

work page doi:10.48550/arxiv.2412.14647 2024

[8] [9]

Pichard, D

G. Pichard, D. Lim, E. Bloch, J. Vaneecloo, L. Boura- chot, G.-J. Both, G. M´ eriaux, S. Dutartre, R. Hostein, J. Paris, B. Ximenez, A. Signoles, A. Browaeys, T. La- haye, and D. Dreon, Phys. Rev. Appl. 22, 024073 (2024)

work page 2024

[9] [10]

Barnes, P

K. Barnes, P. Battaglino, B. J. Bloom, K. Cassella, R. Coxe, N. Crisosto, J. P. King, S. S. Kondov, K. Kotru, S. C. Larsen, J. Lauigan, B. J. Lester, M. McDonald, E. Megidish, S. Narayanaswami, C. Nishiguchi, R. Noter- mans, L. S. Peng, A. Ryou, T.-Y. Wu, and M. Yarwood, Nat. Commun. 13, 1 (2022)

work page 2022

[10] [11]

T. M. Graham, L. Phuttitarn, R. Chinnarasu, Y. Song, C. Poole, K. Jooya, J. Scott, A. Scott, P. Eichler, and M. Saffman, Phys. Rev. X 13, 041051 (2023)

work page 2023

[11] [12]

W. Huie, L. Li, N. Chen, X. Hu, Z. Jia, W. K. C. Sun, and J. P. Covey, PRX Quantum 4, 030337 (2023)

work page 2023

[12] [13]

M. A. Norcia, et al., Phys. Rev. X 13, 041034 (2023)

work page 2023

[13] [14]

Bluvstein, S

D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semegh- ini, M. J. Gullans, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 626, 58 (2024)

work page 2024

[14] [15]

H. Kim, W. Lee, H.-g. Lee, H. Jo, Y. Song, and J. Ahn, Nat. Commun. 7, 1 (2016)

work page 2016

[15] [16]

Bernien, S

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 551, 579 (2017)

work page 2017

[16] [17]

Barredo, S

D. Barredo, S. de L´ es´ eleuc, V. Lienhard, T. Lahaye, and A. Browaeys, Science 354, 1021 (2016)

work page 2016

[17] [18]

Bluvstein, H

D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 604, 451 (2022)

work page 2022

[18] [19]

Keesling, A

A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pich- ler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 568, 207 (2019)

work page 2019

[19] [20]

Ebadi, T

S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Se- meghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pich- ler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Nature 595, 227 (2021)

work page 2021

[20] [21]

Semeghini, H

G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Sci- ence 374, 1242 (2021)

work page 2021

[21] [22]

Browaeys and T

A. Browaeys and T. Lahaye, Nat. Phys. 16, 132 (2020)

work page 2020

[22] [23]

R. M. W. van Bijnen and T. Pohl, Phys. Rev. Lett. 114, 243002 (2015)

work page 2015

[23] [24]

Zeiher, J.-y

J. Zeiher, J.-y. Choi, A. Rubio-Abadal, T. Pohl, R. van Bijnen, I. Bloch, and C. Gross, Phys. Rev. X 7, 041063 (2017)

work page 2017

[24] [25]

de L´ es´ eleuc, S

S. de L´ es´ eleuc, S. Weber, V. Lienhard, D. Barredo, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Phys. Rev. Lett. 120, 113602 (2018). 6

work page 2018

[25] [26]

Scholl, M

P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. L¨ auchli, and A. Browaeys, Nature 595, 233 (2021)

work page 2021

[26] [27]

de L´ es´ eleuc, V

S. de L´ es´ eleuc, V. Lienhard, P. Scholl, D. Barredo, S. Weber, N. Lang, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Science 365, 775 (2019)

work page 2019

[27] [28]

Barredo, H

D. Barredo, H. Labuhn, S. Ravets, T. Lahaye, A. Browaeys, and C. S. Adams, Phys. Rev. Lett. 114, 113002 (2015)

work page 2015

[28] [29]

Lienhard, P

V. Lienhard, P. Scholl, S. Weber, D. Barredo, S. de L´ es´ eleuc, R. Bai, N. Lang, M. Fleischhauer, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Phys. Rev. X10, 021031 (2020)

work page 2020

[29] [30]

Han and W

Y. Han and W. Yi, Chin. Phys. Lett. 41, 033201 (2024)

work page 2024

[30] [31]

P. Li, J. Qian, and W. Zhang, arXiv (2025), 10.48550/arXiv.2503.07672

work page doi:10.48550/arxiv.2503.07672 2025

[31] [32]

Zhang, J

J. Zhang, J. Unmuth-Yockey, J. Zeiher, A. Bazavov, S.- W. Tsai, and Y. Meurice, Phys. Rev. Lett. 121, 223201 (2018)

work page 2018

[32] [33]

A. Celi, B. Vermersch, O. Viyuela, H. Pichler, M. D. Lukin, and P. Zoller, Phys. Rev. X 10, 021057 (2020)

work page 2020

[33] [34]

F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and M. Dalmonte, Phys. Rev. X 10, 021041 (2020)

work page 2020

[34] [35]

Cheng and H

Y. Cheng and H. Zhai, Nat. Rev. Phys. 6, 566 (2024)

work page 2024

[35] [36]

Marcuzzi, J

M. Marcuzzi, J. Min´ aˇ r, D. Barredo, S. de L´ es´ eleuc, H. Labuhn, T. Lahaye, A. Browaeys, E. Levi, and I. Lesanovsky, Phys. Rev. Lett. 118, 063606 (2017)

work page 2017

[36] [37]

Sahay, F

R. Sahay, F. Machado, B. Ye, C. R. Laumann, and N. Y. Yao, Phys. Rev. Lett. 126, 100604 (2021)

work page 2021

[37] [38]

Haroche, Rev

S. Haroche, Rev. Mod. Phys. 85, 1083 (2013)

work page 2013

[38] [39]

Facon, E.-K

A. Facon, E.-K. Dietsche, D. Grosso, S. Haroche, J.-M. Raimond, M. Brune, and S. Gleyzes, Nature 535, 262 (2016)

work page 2016

[39] [40]

E. K. Dietsche, A. Larrouy, S. Haroche, J. M. Raimond, M. Brune, and S. Gleyzes, Nat. Phys. 15, 326 (2019)

work page 2019

[40] [41]

T. L. Nguyen, J. M. Raimond, C. Sayrin, R. Corti˜ nas, T. Cantat-Moltrecht, F. Assemat, I. Dotsenko, S. Gleyzes, S. Haroche, G. Roux, Th. Jolicoeur, and M. Brune, Phys. Rev. X 8, 011032 (2018)

work page 2018

[41] [42]

Meinert, C

F. Meinert, C. H¨ olzl, M. A. Nebioglu, A. D’Arnese, P. Karl, M. Dressel, and M. Scheffler, Phys. Rev. Res. 2, 023192 (2020)

work page 2020

[42] [43]

S. R. Cohen and J. D. Thompson, PRX Quantum 2, 030322 (2021)

work page 2021

[43] [44]

Cantat-Moltrecht, R

T. Cantat-Moltrecht, R. Corti˜ nas, B. Ravon, P. M´ ehaignerie, S. Haroche, J. M. Raimond, M. Favier, M. Brune, and C. Sayrin, Phys. Rev. Res. 2, 022032 (2020)

work page 2020

[44] [45]

J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, Nature 484, 489 (2012)

work page 2012

[45] [46]

Schachenmayer, B

J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Phys. Rev. X 3, 031015 (2013)

work page 2013

[46] [47]

Graß and M

T. Graß and M. Lewenstein, EPJ Quantum Technol. 1, 1 (2014)

work page 2014

[47] [48]

Islam, C

R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Science 340, 583 (2013)

work page 2013

[48] [49]

Richerme, C

P. Richerme, C. Senko, S. Korenblit, J. Smith, A. Lee, R. Islam, W. C. Campbell, and C. Monroe, Phys. Rev. Lett. 111, 100506 (2013)

work page 2013

[49] [50]

Kim, M.-S

K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, Phys. Rev. Lett. 103, 120502 (2009)

work page 2009

[50] [51]

C.-C. J. Wang, A. C. Keith, and J. K. Freericks, Phys. Rev. A 87, 013422 (2013)

work page 2013

[51] [52]

T. G. Walker and M. Saffman, Phys. Rev. A 77, 032723 (2008)

work page 2008

[52] [53]

Hummel, S

F. Hummel, S. Weber, J. M¨ ogerle, H. Menke, J. King, B. Bloom, S. Hofferberth, and M. Li, Phys. Rev. A 110, 042821 (2024)

work page 2024

[53] [54]

Y. Han, H. Li, and W. Yi, Phys. Rev. Lett. 133, 243401 (2024)

work page 2024

[54] [55]

Ravon, P

B. Ravon, P. M´ ehaignerie, Y. Machu, A. D. Hern´ andez, M. Favier, J. M. Raimond, M. Brune, and C. Sayrin, Phys. Rev. Lett. 131, 093401 (2023)

work page 2023

[55] [56]

R. H. Lehmberg, Phys. Rev. A 2, 883 (1970)

work page 1970

[56] [57]

W. R. Anderson, J. R. Veale, and T. F. Gallagher, Phys. Rev. Lett. 80, 249 (1998)

work page 1998

[57] [58]

Mourachko, D

I. Mourachko, D. Comparat, F. de Tomasi, A. Fioretti, P. Nosbaum, V. M. Akulin, and P. Pillet, Phys. Rev. Lett. 80, 253 (1998)

work page 1998

[58] [59]

W. R. Anderson, M. P. Robinson, J. D. D. Martin, and T. F. Gallagher, Phys. Rev. A 65, 063404 (2002)

work page 2002

[59] [60]

Mudrich, N

M. Mudrich, N. Zahzam, T. Vogt, D. Comparat, and P. Pillet, Phys. Rev. Lett. 95, 233002 (2005)

work page 2005

[60] [61]

Zwanzig, The Journal of Chemical Physics 33, 1338 (1960)

R. Zwanzig, The Journal of Chemical Physics 33, 1338 (1960)

work page 1960

[61] [62]

Reiter and A

F. Reiter and A. S. Sørensen, Phys. Rev. A 85, 032111 (2012)

work page 2012

[62] [63]

Sch¨ utz, J

S. Sch¨ utz, J. Schachenmayer, D. Hagenm¨ uller, G. K. Brennen, T. Volz, V. Sandoghdar, T. W. Ebbesen, C. Genes, and G. Pupillo, Phys. Rev. Lett. 124, 113602 (2020)

work page 2020

[63] [64]

Hagenm¨ uller, S

D. Hagenm¨ uller, S. Sch¨ utz, G. Pupillo, and J. Schachen- mayer, Phys. Rev. A 102, 013714 (2020)

work page 2020

[64] [65]

See Supplemental Material at [URL will be inserted by publisher] for details on: robustness against losses and dephasing, validity of the adiabatic and near-field regime, details about the geometrical configuration, comparison between full and effective model, analytical form of the effective coupling matrix, quality of the power law fits

work page

[65] [66]

M´ ehaignerie, Y

P. M´ ehaignerie, Y. Machu, A. Dur´ an Hern´ andez, G. Creutzer, D. Papoular, J. Raimond, C. Sayrin, and M. Brune, PRX Quantum 6, 010353 (2025)

work page 2025

[66] [67]

R. C. Teixeira, A. Larrouy, A. Muni, L. Lachaud, J.-M. Raimond, S. Gleyzes, and M. Brune, Physical Review Letters 125, 263001 (2020)

work page 2020

[67] [68]

H¨ olzl, A

C. H¨ olzl, A. G¨ otzelmann, E. Pultinevicius, M. Wirth, and F. Meinert, Physical Review X 14, 021024 (2024)

work page 2024

[68] [69]

Cantat-Moltrecht, R

T. Cantat-Moltrecht, R. Corti˜ nas, B. Ravon, P. M´ ehaignerie, S. Haroche, J. M. Raimond, M. Favier, M. Brune, and C. Sayrin, Physical Review Research 2, 022032 (2020)

work page 2020

[69] [70]

Machu et al., in preparation

Y. Machu et al., in preparation

work page

[70] [71]

magic angle

U. Schollw¨ ock, Rev. Mod. Phys.77, 259 (2005). 1 Supplemental Material for: Tailoring interaction ranges in atom arrays T. Botzung 1, G. Creutzer 2, C. Sayrin2,3, J.Schachenmayer1 1CESQ/ISIS (UMR 7006), CNRS and Universit´ e de Strasbourg, 67000 Strasbourg, France 2Laboratoire Kastler Brossel, Coll` ege de France, CNRS, ENS-Universit´ e PSL, Sorbonne Uni...

work page 2005