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Rydberg photon recoil splits atoms into macroscopic Bell states

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2026-07-09 18:22 UTC pith:NGOKIE5A

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arxiv 2607.07167 v1 pith:NGOKIE5A submitted 2026-07-08 quant-ph physics.atom-ph

Macroscopic position-position entanglement by photon recoil in Rydberg atoms

Xiao-Feng Shi This is my paper
classification quant-ph physics.atom-ph PACS 03.67.Bg32.80.Ee37.10.Gh
keywords atomsatomentanglementrydbergseparatespatiallyblockadeparticles
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper proposes a deterministic protocol to entangle two spatially separated neutral atoms not in their internal spin states but in their physical positions. The mechanism works as follows. Two atoms (a control and a target) sit in separate optical traps. The control atom is placed in a superposition of two internal states, one of which can be excited to a Rydberg state (a high-lying energy level with a large orbital radius). A sequence of laser pulses then attempts to excite the target atom to a Rydberg state and immediately de-excite it, using counter-propagating beams so that the atom receives a net momentum kick from photon recoil. Crucially, if the control atom was excited to the Rydberg state, the strong Rydberg-Rydberg interaction blocks the target atom's excitation, so the target receives no kick. If the control was not excited, the target completes the full excitation-de-excitation cycle and gets pushed. After a free-flight period of tens to hundreds of microseconds, the atoms are recaptured in optical tweezers at their new locations. The result is a Bell state where each atom's position is entangled with the other's: if atom A is found displaced, atom B is found at its original spot, and vice versa. Using rubidium with a single Rabi cycle, the displacement is a few microns after 100 microseconds of free flight. Using ten Rabi cycles reduces the flight time to about 10 microseconds for the same displacement. Switching to metastable helium-3, whose mass is roughly 29 times lighter than rubidium, the displacement can reach roughly 100 microns after 100 microseconds of flight, entering a genuinely macroscopic regime where the two possible locations of each atom are separated by a distance visible to the naked eye. The author also shows an intermediate step where one atom's internal state is entangled with the other atom's position, which is then promoted to full position-position entanglement by applying the same recoil protocol to both atoms.

Core claim

The central mechanism is that Rydberg blockade, which is normally used to create entanglement in internal spin states, can instead be repurposed to make photon recoil conditional on the state of a partner atom. When a control atom is in a Rydberg state, it blocks the target atom from absorbing and re-emitting photons, so the target stays put. When the control atom is in a ground state, the target absorbs and re-emits, receiving a net momentum kick from the counter-propagating laser geometry. After free flight, the momentum difference becomes a position difference, and recapture in optical tweezers converts the momentum superposition into a stable position superposition. By applying the same踢

What carries the argument

Rydberg blockade (state-dependent conditional excitation suppression), counter-propagating two-photon Rydberg excitation (net momentum transfer 2ℏk per Rabi cycle), free-flight wavepacket evolution, and optical tweezer recapture at displaced positions.

Load-bearing premise

The protocol assumes that atoms can be recaptured with unit efficiency after up to 100 microseconds of free flight and that their Gaussian wavepacket spreading remains negligible during that time. If recapture fidelity is substantially below unity or wavepacket expansion is significant, the quality of the entangled state degrades.

What would settle it

The most direct test would be to implement the protocol with rubidium atoms in optical tweezers, apply the Rydberg pulse sequence, let the target atom fly freely, recapture it in a tweezer at the predicted displaced position, and measure the correlation between the control atom's internal state and the target atom's position. If the position of the target atom does not correlate with the control atom's internal state at the level predicted, or if recapture fidelity is too low to maintain coherence, the protocol fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If position-position entanglement of atoms can be transferred to photons via cavity coupling, it would yield deterministic photon-photon position entanglement, in contrast to the probabilistic position entanglement from spontaneous parametric down-conversion.
  • Using lighter atoms like metastable helium-3 would push the spatial separation into the hundred-micron regime, making the entanglement macroscopically visible and potentially testable against decoherence models for large spatial superpositions.
  • Multiple Rabi cycles trade fidelity for speed: the paper calculates roughly 95% fidelity with 10 cycles versus 99.9% with 1 cycle, quantifying a concrete speed-accuracy frontier for this protocol.
  • The protocol adds a position-based encoding dimension to the Rydberg quantum toolkit, which has almost exclusively used internal-state qubits.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript proposes a protocol for generating position-position entanglement between two spatially separate neutral atoms using photon recoil during Rydberg excitation. The core idea is that state-dependent Rydberg blockade controls whether a target atom receives a net momentum kick from counter-propagating Rydberg laser pulses, and by applying the same scheme to a control atom, both atoms end up in a superposition of two spatially separated positions. The protocol is analyzed for 87Rb (with single and multiple Rabi cycles) and for metastable 3He*, the latter yielding spatial separations approaching 100 µm. The Hamiltonian analysis in Secs. II–III is standard and the physical mechanism is plausible.

Significance. The proposal introduces a genuinely novel form of entanglement—macroscopic position-position entanglement between individual ground-state atoms—that goes beyond the usual internal-state or motional-state entanglement in Rydberg systems. The hundred-micron regime for 3He* is a concrete, falsifiable prediction. The use of photon recoil as a resource rather than a nuisance is conceptually appealing. However, the quantitative claims rest on an untested assumption of unit recapture efficiency and a fidelity formula that omits motional decoherence, which limits the current significance.

major comments (3)
  1. Section II: The assumption of unit recapture efficiency after free flight up to 100 µs is load-bearing for all quantitative claims, yet it is stated as an axiom ('Below, we assume that the recapture of the atomic wavepacket has unit efficiency') without any estimate of the actual recapture fidelity. For a 10 kHz trap with 87Rb, the ground-state wavepacket size is σ ≈ 0.2 µm, and after 100 µs of free flight the wavepacket expands by a factor sqrt(1 + ω²t²) ≈ sqrt(1 + (2π·10⁴·10⁻⁴)²) ≈ 6.3, giving σ ≈ 1.3 µm. This is comparable to the displacement ℓ ≈ 3.1 µm for the single-cycle Rb case, meaning the two wavepackets (displaced and undisplaced) have non-negligible overlap. The paper should quantify the recapture fidelity and the wavepacket overlap, and show that the resulting state still qualifies as a Bell state (i.e., that the two branches are sufficiently orthogonal).
  2. Section IV, Eq. for F and surrounding text: The fidelity formula F = p_c·p_t·(1−ε_decay)·(1−ε_leak) does not account for motional decoherence. The Doppler phases φ₀ and φ₁ are described as 'random' and the paper states there is 'no need to have a definite phase in the internal state for the desired entanglement to emerge.' However, the atomic velocity v is correlated with the final position (since the momentum kick causes both displacement and Doppler phase), so tracing over the thermal distribution of v will reduce the purity of the position Bell state. The paper should include this effect in the fidelity estimate, or at minimum provide an upper bound on the associated infidelity.
  3. Section III (unnumbered equation after the H_c definition): The final position-entangled state is written with the control atom's wavepacket at r_c or r_c ± ℓe_z, but the phases φ₀ and φ₁ are carried over from the internal-state entanglement protocol of Sec. II without a clear derivation of how they transform when both atoms undergo the full pulse sequence. The claim that this constitutes a Bell state in the position basis requires that the internal states factor out cleanly; the paper should explicitly show the full state after all pulses and verify that the internal states are disentangled from the positions.
minor comments (6)
  1. Equation (1): The ket notation |↑_a↓_b⟩ is used for position states later, but here it appears to denote internal states. Clarifying the notation early would help readers.
  2. Section II, below Eq. (5): The drift speed V = 2ℏk_t/m ≈ 30.9 nm/µs is given for Rb, but the symbol V is also used for the blockade interaction. Consider using a different symbol for velocity (e.g., v_d).
  3. Section III: The final state of the position-position entanglement protocol is given in an unnumbered equation. Consider numbering it for reference.
  4. Section V: The 3He* two-photon transition wavelengths (389 nm and 785 nm) are given but the resulting effective k is not explicitly stated. Including this would make the ℓ ≈ 102 µm estimate easier to verify.
  5. References [40, 41, 48, 65] appear to be from 2026 and may be preprints. Verify that final publication details are available or cite as preprints consistently.
  6. Section VI: The quantum networking proposal involving transfer of position entanglement to photonic qubits in fibers is sketched very briefly. A sentence or two on the mechanism (e.g., cavity-mediated readout) would make this more concrete.

Circularity Check

0 steps flagged

No significant circularity; protocol is derived from standard Rydberg physics with no fitted parameters forcing the result

full rationale

The paper proposes a protocol for generating position-position entanglement using photon recoil in Rydberg atoms. The derivation chain proceeds from standard ingredients: (1) the Rydberg blockade Hamiltonian (Eqs. 3-4), (2) photon recoil imparting momentum 2ℏk per Rabi cycle (Eq. 5), (3) free-flight displacement ℓ = V·T where V = 2ℏk/m (Sec. II, Sec. V), and (4) recapture into spatially separated traps (Eq. 6). No parameter is fitted to data and then presented as a prediction. The momentum kick, drift velocity, and displacement all follow directly from physical constants (laser wavevector k, atomic mass m, flight time T) via elementary mechanics. The fidelity formula F = p_c·p_t·(1-ε_decay)·(1-ε_leak) (Sec. IV) uses independently defined error sources (Rydberg decay, blockade leakage, Doppler-induced population loss), none of which are defined in terms of the target entangled state. Self-citations (Refs. 54, 56, 62) are for related prior results on Doppler dephasing suppression and gate fidelity analysis; they provide independent physical analysis rather than circularly defining the present result. The numerical simulation in Fig. 1 samples from Gaussian distributions of initial velocity and position, then computes population transfer — this is a forward simulation, not a fit-then-predict structure. The unit recapture efficiency assumption (Sec. II) is an explicitly stated idealization, not a hidden circular definition. The protocol's output (position-position entanglement) is not equivalent to its inputs by construction; it depends on the physical correctness of the Rydberg blockade mechanism and photon recoil, which are independently established physical phenomena. The score of 2 reflects minor self-citations that are not load-bearing for the central claim.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities, particles, or forces. It uses established Rydberg atom physics, standard laser-atom interactions, and known atomic species (Rb, 3He*). The protocol is constructed from known components in a new configuration.

free parameters (5)
  • Rabi frequency Ω = 2π×15 MHz
    Chosen from experimental availability (Ref. 41), not fitted to data.
  • Trap frequency ωz = 2π×10 kHz
    Assumed shallow trap parameter for ground-state cooling.
  • Number of Rabi cycles N = 10
    Chosen to demonstrate time-efficiency tradeoff in Sec. IV.
  • Rydberg lifetime τ = 80 µs
    Taken from experimental reference (Ref. 41).
  • Blockade strength V/ℏ = 2π×0.95 GHz
    Taken from experimental reference (Ref. 41).
axioms (5)
  • domain assumption Rydberg blockade prevents excitation of the target atom when the control atom is in the Rydberg state, with leakage error bounded by ℏ²Ω²/(2V²).
    Standard Rydberg blockade physics (Refs. 9, 56); invoked in Sec. II.
  • standard math Photon recoil imparts momentum ℏk to the atom during ground-Rydberg transition.
    Standard momentum conservation; used throughout.
  • ad hoc to paper Recapture of the atomic wavepacket by optical traps has unit efficiency after free flight up to 100 µs.
    Explicitly assumed in Sec. II: 'Below, we assume that the recapture of the atomic wavepacket has unit efficiency.'
  • domain assumption Wavepacket expansion during free flight is negligible for flight times ~10-100 µs with ωz~2π×10 kHz.
    Stated in Sec. II using σj/σj0 formula; depends on trap parameters.
  • domain assumption Gravitational acceleration is negligible during free flight up to 100 µs.
    Stated in Sec. II: 'the gravitation-induced atomic speed can be neglected.'

pith-pipeline@v1.1.0-glm · 16222 in / 2393 out tokens · 316396 ms · 2026-07-09T18:22:46.201062+00:00 · methodology

0 comments
read the original abstract

Entanglement between two spatially separate matter particles can be generated via many means and often resides in the internal states of particles. Here, via Rydberg blockade in two spatially separate neutral atoms, we find that the photon recoil in Rydberg excitation can push one atom microns away provided the other atom exerts a state-dependent Rydberg-mediated blockade. When the atoms are recaptured by optical traps, a position-position entangled state between two spatially separate atoms can emerge. This realizes a Bell state of two atoms, where the entanglement exists in the position of each atom and the distance between the two possible locations of each atom can be in the hundred-micron regime.

Figures

Figures reproduced from arXiv: 2607.07167 by Xiao-Feng Shi.

Figure 1
Figure 1. Figure 1: FIG. 1. Influence of Doppler effect on the restoration of the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Works this paper leans on

66 extracted references · 66 canonical work pages · 2 internal anchors

  1. [1]

    Horodecki, P

    R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009)

    work page 2009

  2. [2]

    J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique1, 195 (1964)

    work page 1964

  3. [3]

    J. M. Raimond, M. Brune, and S. Haroche, Manipulat- ing quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys.73, 565 (2001)

    work page 2001

  4. [4]

    Zhang, Y.-K

    H. Zhang, Y.-K. Wang, Y. Zheng, H.-T. Bai, and B. Yang, Scalable generation of massive schr¨ odinger cat states via quantum tunnelling, Nat. Phys. (2026), 10.1038/s41567-026-03281-9

    work page doi:10.1038/s41567-026-03281-9 2026

  5. [5]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys.80, 885 (2008)

    work page 2008

  6. [6]

    Lange, J

    K. Lange, J. Peise, B. L¨ ucke, I. Kruse, G. Vitagliano, I. Apellaniz, M. Kleinmann, G. T´ oth, and C. Klempt, Entanglement between two spatially separated atomic modes, Science360, 416 (2018)

    work page 2018

  7. [7]

    A. L. Shaw, P. Scholl, R. Finkelstein, R. B.-S. Tsai, J. Choi, and M. Endres, Erasure cooling, control, and hyperentanglement of motion in optical tweezers, Science 388, 845 (2025)

    work page 2025

  8. [8]

    J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, Realization of the einstein-podolsky-rosen para- dox using momentum- and position-entangled photons from spontaneous parametric down conversion, Phys. Rev. Lett.92, 210403 (2004)

    work page 2004

  9. [9]

    Saffman, T

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

    work page 2010

  10. [10]

    Jaksch, J

    D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cote, and M. D. Lukin, Fast Quantum Gates for Neutral Atoms, Phys. Rev. Lett.85, 2208 (2000)

    work page 2000

  11. [11]

    M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles, Phys. Rev. Lett.87, 037901 (2001)

    work page 2001

  12. [12]

    Saffman, Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges, J

    M. Saffman, Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges, J. Phys. B49, 202001 (2016)

    work page 2016

  13. [13]

    Saffman, Quantum computing with neutral atoms, Nat

    M. Saffman, Quantum computing with neutral atoms, Nat. Sci. Rev.6, 24 (2019)

    work page 2019

  14. [14]

    Shi, Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity, Quantum Sci

    X.-F. Shi, Quantum logic and entanglement by neutral Rydberg atoms: methods and fidelity, Quantum Sci. Technol.7, 023002 (2022)

    work page 2022

  15. [15]

    Browaeys and T

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

    work page 2020

  16. [16]

    C. S. Adams, J. D. Pritchard, and J. P. Shaffer, Ryd- berg atom quantum technologies, J. Phys. B53, 012002 (2020)

    work page 2020

  17. [17]

    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

  18. [18]

    X. Wu, X. Liang, Y. Tian, F. Yang, C. Chen, Y. C. Liu, M. K. Tey, and L. You, A concise review of Rydberg atom based quantum computation and quantum simula- tion, Chin. Phys. B30, 020305 (2021)

    work page 2021

  19. [19]

    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

  20. [20]

    Shao, S.-L

    X.-Q. Shao, S.-L. Su, L. Li, R. Nath, J.-H. Wu, and W. Li, Rydberg superatoms: An artificial quantum sys- tem for quantum information processing and quantum optics, Appl. Phys. Rev.11, 031320 (2024)

    work page 2024

  21. [21]

    Verstraten, K

    J. Verstraten, K. Dai, M. Dixmerias, B. Peaudecerf, T. de Jongh, and T. Yefsah, In situ imaging of a single- atom wave packet in continuous space, Phys. Rev. Phys. 134, 083403 (2025)

    work page 2025

  22. [22]

    T. Wilk, A. Gaetan, C. Evellin, J. Wolters, Y. Miroshny- chenko, P. Grangier, and A. Browaeys, Entanglement of Two Individual Neutral Atoms Using Rydberg Blockade, Phys. Rev. Lett.104, 010502 (2010)

    work page 2010

  23. [23]

    Isenhower, E

    L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, Demonstration of a Neutral Atom Controlled-NOT Quantum Gate, Phys. Rev. Lett.104, 010503 (2010)

    work page 2010

  24. [24]

    X. L. Zhang, L. Isenhower, A. T. Gill, T. G. Walker, and M. Saffman, Deterministic entanglement of two neutral atoms via Rydberg blockade, Phys. Rev. A82, 030306(R) (2010)

    work page 2010

  25. [25]

    K. M. Maller, M. T. Lichtman, T. Xia, Y. Sun, M. J. Piotrowicz, A. W. Carr, L. Isenhower, and M. Saffman, Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits, Phys. Rev. A92, 022336 (2015)

    work page 2015

  26. [26]

    Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydberg-dressed spin-flip blockade, Nat. Phys.12, 71 (2016)

    work page 2016

  27. [27]

    Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. J. Papoular, G. V. Shlyapnikov, and M. Zhan, Entangling Two Individual Atoms of Different Isotopes via Rydberg Blockade, Phys. Rev. Lett.119, 160502 (2017)

    work page 2017

  28. [28]

    Levine, A

    H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, High-fidelity control and 6 entanglement of Rydberg atom qubits, Phys. Rev. Lett. 121, 123603 (2018)

    work page 2018

  29. [29]

    C. J. Picken, R. Legaie, K. McDonnell, and J. D. Pritchard, Entanglement of neutral-atom qubits with long ground-Rydberg coherence times, Quantum Sci. Technol.4, 015011 (2019)

    work page 2019

  30. [30]

    Omran, H

    A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Mon- tangero, T. Calarco, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Generation and manipulation of Schr¨ odinger cat states in Rydberg atom arrays, Science 365, 570–574 (2019)

    work page 2019

  31. [31]

    Levine, A

    H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuleti´ c, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multi-qubit gates with neutral atoms, Phys. Rev. Lett.123, 170503 (2019)

    work page 2019

  32. [32]

    T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, Rydberg mediated entanglement in a two- dimensional neutral atom qubit array, Phys. Rev. Lett. 123, 230501 (2019)

    work page 2019

  33. [33]

    H. Jo, Y. Song, M. Kim, and J. Ahn, Rydberg atom entanglements in the weak coupling regime, Phys. Rev. Lett.124, 033603 (2020)

    work page 2020

  34. [34]

    Z. Fu, P. Xu, Y. Sun, Y.-Y. Liu, X.-D. He, X. Li, M. Liu, R.-B. Li, J. Wang, L. Liu, and M.-S. Zhan, High-fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled- PHASE gate, Phys. Rev. A105, 042430 (2022)

    work page 2022

  35. [35]

    McDonnell, L

    K. McDonnell, L. F. Keary, and J. D. Pritchard, Demon- stration of a Quantum Gate using Electromagnetically Induced Transparency, Phys. Rev. Lett.129, 200501 (2022)

    work page 2022

  36. [36]

    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, A quantum processor based on coherent transport of en- tangled atom arrays, Nature604, 451 (2022)

    work page 2022

  37. [37]

    T. M. Graham, Y. Song, J. Scott, C. Poole, L. Phutti- tarn, K. Jooya, P. Eichler, X. Jiang, A. Marra, B. Grinke- meyer, M. Kwon, M. Ebert, J. Cherek, M. T. Licht- man, M. Gillette, J. Gilbert, D. Bowman, T. Ballance, C. Campbell, E. D. Dahl, O. Crawford, N. S. Blunt, B. Rogers, T. Noel, and M. Saffman, Multi-qubit en- tanglement and algorithms on a neutra...

    work page 2022

  38. [38]

    S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuletic, and M. D. Lukin, High-fidelity parallel entan- gling gates on a neutral-atom quantum computer, Nature 622, 268 (2023)

    work page 2023

  39. [39]

    Bluvstein, A

    D. Bluvstein, A. A. Geim, S. H. Li, S. J. Evered, J. P. Bonilla Ataides, G. Baranes, A. Gu, T. Manovitz, M. Xu, M. Kalinowski, S. Majidy, C. Kokail, N. Maskara, E. C. Trapp, L. M. Stewart, S. Hollerith, H. Zhou, M. J. Gullans, S. F. Yelin, M. Greiner, V. Vuleti´ c, M. Cain, and M. D. Lukin, A fault-tolerant neutral-atom architec- ture for universal quantu...

    work page 2025

  40. [40]

    R. Lin, Y. Li, L.-T. Zheng, T.-R. Hu, S.-Y. Chen, H.- M. Wu, Y.-C. Zhang, H.-W. Cheng, Y.-H. Deng, Z. Wu, M.-C. Chen, J. Rui, C.-Y. Lu, and J.-W. Pan, Sustain- ing high-fidelity quantum logic in neutral-atom circuits via mid-circuit operations, arxiv:2603.01612 (2026), arXiv:2603.01612 [quant-ph]

    work page arXiv 2026

  41. [41]

    S. J. Evered, M. Xu, S. H. Li, A. A. Geim, J. P. B. Ataides, M. Kalinowski, D. Bluvstein, N. Maskara, C. Kokail, M. Greiner, V. Vuletic, and M. D. Lukin, High-fidelity entangling gates and nonlocal circuits with neutral atoms, (2026), arXiv:2604.25987 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  42. [42]

    Miles, M

    J. Miles, M. T. Lichtman, A. M. Scott, J. Scott, S. A. Norrell, M. J. Bedalov, D. A. Belknap, D. C. Cole, S. Y. Eubanks, M. Gillette, P. Gokhale, J. Goldwin, M. Iliev, R. A. Jones, K. W. Kuper, D. Mason, P. T. Mitchell, J. D. Murphree, N. A. Neff-Mallon, T. W. Noel, A. G. Radnaev, I. V. Vinogradov, and M. Saffman, Qubit syn- drome measurements with a high...

    work page arXiv 2026

  43. [43]

    Unnikrishnan, P

    G. Unnikrishnan, P. Ilzh¨ ofer, A. Scholz, C. H¨ olzl, A. G¨ otzelmann, R. Gupta, J. Zhao, J. Krauter, S. We- ber, N. Makki, H. B¨ uchler, T. Pfau, and F. Meinert, Coherent control of the fine-structure qubit in a single alkaline-earth atom, Phys. Rev. Lett.132, 150606 (2024)

    work page 2024

  44. [44]

    K. Kim, A. Aeppli, W. Warfield, A. Chu, A. M. Rey, and J. Ye, Atomic coherence of 2 minutes and instability of 1.5×10 −18 at 1 s in a wannier-stark lattice clock, Phys. Rev. Lett.135, 103601 (2025)

    work page 2025

  45. [45]

    I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, High-fidelity entanglement and detection of alkaline-earth Rydberg atoms, Nat. Phys.16, 857 (2020)

    work page 2020

  46. [46]

    R. B.-S. Tsai, X. Sun, A. L. Shaw, R. Finkelstein, and M. Endres, Benchmarking and fidelity response theory of high-fidelity rydberg entangling gates, PRX Quantum6, 010331 (2025)

    work page 2025

  47. [47]

    Finkelstein, R

    R. Finkelstein, R. B.-S. Tsai, X. Sun, P. Scholl, S. Di- rekci, T. Gefen, J. Choi, A. L. Shaw, and M. Endres, Universal quantum operations and ancilla-based read-out for tweezer clocks, Nature634, 321 (2024)

    work page 2024

  48. [48]

    O. Lib, H. Timme, M. Ammenwerth, F. Gyger, R. Tao, S. Sun, I. Bloch, and J. Zeiher, Velocity-enabled quan- tum computing with neutral atoms, arxiv:2603.15561 (2026), arXiv:2603.15561 [quant-ph]

    work page arXiv 2026

  49. [49]

    S. Ma, A. P. Burgers, G. Liu, J. Wilson, B. Zhang, and J. D. Thompson, Universal gate operations on nuclear spin qubits in an optical tweezer array of 171Yb atoms, Phys. Rev. X12, 021028 (2022)

    work page 2022

  50. [50]

    S. Ma, G. Liu, P. Peng, B. Zhang, S. Jandura, A. P. Burgers, G. Pupillo, S. Puri, and J. D. Thompson, High- fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit, Nature622, 279 (2023)

    work page 2023

  51. [51]

    J. A. Muniz, M. Stone, D. T. Stack, M. Jaffe, J. M. Kindem, L. Wadleigh, E. Zalys-Geller, X. Zhang, C.-A. Chen, M. A. Norcia, J. Epstein, E. Halperin, F. Hum- mel, T. Wilkason, M. Li, K. Barnes, P. Battaglino, T. C. Bohdanowicz, G. Booth, A. Brown, M. O. Brown, W. B. Cairncross, K. Cassella, R. Coxe, D. Crow, M. Feldkamp, C. Griger, A. Heinz, A. M. W. Jon...

    work page 2025

  52. [52]

    Peper, Y

    M. Peper, Y. Li, D. Y. Knapp, M. Bileska, S. Ma, G. Liu, P. Peng, B. Zhang, S. P. Horvath, A. P. Burgers, and J. D. Thompson, Spectroscopy and modeling of 171yb ry- dberg states for high-fidelity two-qubit gates, Phys. Rev. X15, 011009 (2025)

    work page 2025

  53. [53]

    Senoo, A

    A. Senoo, A. Baumg¨ artner, J. W. Lis, G. M. Vaidya, Z. Zeng, G. Giudici, H. Pichler, and A. M. Kauf- man, High-fidelity entanglement and coherent multi- qubit mapping in an atom array, Nat. Phys.22, 903 (2026)

    work page 2026

  54. [54]

    Shi, Suppressing Motional Dephasing of Ground- Rydberg Transition for High-Fidelity Quantum Control with Neutral Atoms, Phys

    X.-F. Shi, Suppressing Motional Dephasing of Ground- Rydberg Transition for High-Fidelity Quantum Control with Neutral Atoms, Phys. Rev. Appl.13, 024008 (2020)

    work page 2020

  55. [55]

    In tweezer-based neutral atom quantum computing, the phase of the qubit state is supposed to be definite, where the Doppler phase is a noise [54], in contrast to the case here

    work page

  56. [56]

    Shi, Accurate Quantum Logic Gates by Spin Echo in Rydberg Atoms, Phys

    X.-F. Shi, Accurate Quantum Logic Gates by Spin Echo in Rydberg Atoms, Phys. Rev. Appl.10, 034006 (2018)

    work page 2018

  57. [57]

    [56] that the error is aboutℏ 2Ω2/V 2 times a sine factor, where the sine factor is a function of V π/(ℏΩ)

    It was shown in Ref. [56] that the error is aboutℏ 2Ω2/V 2 times a sine factor, where the sine factor is a function of V π/(ℏΩ). Given thatVcan fluctuate, one can see that the the error is bounded belowℏ 2Ω2/V 2. Half of the final state does not experience the blockade, so the average blockade error is bounded belowℏ 2Ω2/(2V 2)

    work page

  58. [58]

    H. J. Manetsch, G. Nomura, E. Bataille, X. Lv, K. H. Leung, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, Nature647, 60–67 (2025)

    work page 2025

  59. [59]

    [44, 58] are the coherence times

    The quoted times from Refs. [44, 58] are the coherence times. However, the relaxation timeT 1 is longer than the coherence time of the qubit for the atoms under study because the coherence between the two qubit states in- cludes the relaxation effect

    work page

  60. [60]

    Schymik, S

    K.-N. Schymik, S. Pancaldi, F. Nogrette, D. Barredo, J. Paris, A. Browaeys, and T. Lahaye, Single atoms with 6000-second trapping lifetimes in optical-tweezer arrays at cryogenic temperatures, Phys. Rev. Appl.16, 034013 (2021)

    work page 2021

  61. [61]

    Zhang, T.-W

    Z. Zhang, T.-W. Hsu, T. Y. Tan, D. H. Slichter, A. M. Kaufman, M. Marinelli, and C. A. Regal, High opti- cal access cryogenic system for rydberg atom arrays with a 3000-second trap lifetime, PRX Quantum6, 020337 (2025)

    work page 2025

  62. [62]

    X.-F. Shi, Y. Lu, Y. Jiao, and J. Zhao, Coherence en- hancement of rydberg polaritons, Phys. Rev. Appl.24, 044028 (2025)

    work page 2025

  63. [63]

    B. M. Spar, E. Guardado-Sanchez, S. Chi, Z. Z. Yan, and W. S. Bakr, Realization of a fermi-hubbard optical tweezer array, Phys. Rev. Lett.128, 223202 (2022)

    work page 2022

  64. [64]

    S. A. Saakyan, V. A. Sautenkov, S. V. Klimov, A. A. Nazarov, A. A. Bobrov, and B. B. Zelener, Excita- tion dynamics of interacting rydberg atoms in lithium magneto-optical trap, J. Russ. Laser. Res.44, 264 (2023)

    work page 2023

  65. [65]

    Z. Li, R. De, R. Sivakumar, W. Huie, H.-T. Wei, J. D. Piel, C. H. Greene, K. R. A. Hazzard, Z. Z. Yan, and J. P. Covey, Quantum science with arrays of metastable helium-3 atoms, (2026), arXiv:2601.06763 [quant-ph]

    work page internal anchor Pith review arXiv 2026

  66. [66]

    Here, 3He∗ instead of 3He is used to distinguish that the atom we take here is not in the ground state but in the 2 3S1 state

    work page