pith. sign in

arxiv: 2606.01516 · v1 · pith:QL3JPVZPnew · submitted 2026-06-01 · 🌀 gr-qc · astro-ph.IM· physics.atom-ph· physics.ins-det

Gravitational-wave astronomy with a space-based optical clock network

Pith reviewed 2026-06-28 14:00 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.IMphysics.atom-phphysics.ins-det
keywords gravitational wavesoptical clocksDoppler trackingspace-based detectorsbinary sourcesparameter estimationLISA
0
0 comments X

The pith

Space-based optical clock networks extract astrophysical information from binary gravitational-wave sources using one-way Doppler tracking.

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

The paper explores the use of space-based optical clock networks for gravitational-wave detection through one-way Doppler tracking in combination with LISA-like detectors. It develops protocols for measurements, analyzes noise sources, and performs parameter estimation on simulated signals from binary sources. This is proposed as a complementary approach that can tune sensitivity from the millihertz to hertz range. Sympathetic readers would care because it could provide new ways to study binary black hole systems in frequency bands not accessible otherwise.

Core claim

By using one-way Doppler tracking in space-based atomic clock networks, critical astrophysical information about binary gravitational-wave sources can be extracted, as shown by the development of measurement protocols, noise analysis, and parameter estimation on simulated signals.

What carries the argument

One-way Doppler tracking in space-based optical clock networks, enabling tunable sensitivity from millihertz to hertz frequencies.

If this is right

  • The detectors can access the millihertz band inaccessible to ground-based instruments.
  • Sensitivity can be tuned across a broad band up to the hertz regime.
  • They provide complementary capabilities to optical interferometers like LISA.
  • Parameter estimation can yield astrophysical details on binary sources.

Where Pith is reading between the lines

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

  • Combining such networks with ground-based detectors could enable multi-band gravitational wave astronomy.
  • The approach might improve source localization for electromagnetic follow-up.

Load-bearing premise

Dominant noise sources can be characterized and mitigated sufficiently for reliable parameter estimation based on simulations.

What would settle it

Experimental data from a space-based clock network demonstrating that noise mitigation allows accurate recovery of binary parameters from real signals.

Figures

Figures reproduced from arXiv: 2606.01516 by Dhruva Ganapathy, Divya Singh, Sammith Singamsetty, Shimon Kolkowitz.

Figure 1
Figure 1. Figure 1: FIG. 1. Differential clock comparisons across separated [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Coordinate system to establish the geometry of a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Antenna pattern for a one-way link of length L = 1 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Detector response for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Laser noise suppression from finite Rabi frequency [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Power spectral density of acceleration noise modeled [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Allan deviation for various noise sources in a spin [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Phase/Amplitude Estimation Protocol. Spin-echo [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Phase and amplitude estimation uncertainty as [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Phase and amplitude estimation uncertainty as a [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Frequency evolution of gravitational waves from [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Example clock-detector network, with 6 one-way [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Posterior distributions for simulated binary inspiral signal at [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Evolution of sky localization for an binary inspiral at [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Sky localization posteriors for a binary inspiral at [PITH_FULL_IMAGE:figures/full_fig_p014_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Laser noise suppression from finite Rabi frequency [PITH_FULL_IMAGE:figures/full_fig_p016_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Filter function, [PITH_FULL_IMAGE:figures/full_fig_p016_20.png] view at source ↗
read the original abstract

Since the first detection of a merging binary black hole system a decade ago, gravitational-wave astronomy has emerged as a powerful tool for astrophysics. Future space-based observatories, such as the Laser Interferometer Space Antenna (LISA), will unlock the millihertz (mHz) band, which remains entirely inaccessible to ground-based detectors due to terrestrial noise. In parallel, proposed atom-based gravitational-wave detectors, specifically those based on space-based optical clocks and atom interferometers, offer capabilities that are unique and complementary to traditional optical interferometers. Their highly tunable character enable sensitive measurements across a broad frequency band extending from the mHz up to and possibly even above the Hz regime. In this work, we investigate the use of one-way Doppler tracking in space-based atomic clock networks operating in concert with detectors like LISA. We develop dedicated measurement protocols, analyze dominant noise sources, and perform preliminary parameter estimation on simulated gravitational-wave signals. Ultimately, we demonstrate how these detectors could be used to extract critical astrophysical information about binary gravitational-wave sources.

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 / 1 minor

Summary. The manuscript proposes combining one-way Doppler tracking in space-based optical clock networks with LISA-like interferometers for gravitational-wave detection. It develops dedicated measurement protocols, analyzes dominant noise sources, and performs parameter estimation on simulated signals from binary sources, claiming this enables extraction of critical astrophysical information about those sources across a tunable mHz-to-Hz band.

Significance. If the noise models and mitigation strategies hold under realistic conditions, the work could provide a complementary channel to LISA with tunable sensitivity, potentially improving parameter recovery for millihertz binaries. The simulation-based demonstration of parameter estimation is a positive step, but its value depends on the fidelity of the unshown noise budgets.

major comments (2)
  1. [Abstract / parameter estimation section] Abstract and results sections: the central claim that the network 'could be used to extract critical astrophysical information' rests on parameter estimation performed solely on simulated signals. No quantitative error budgets, residual noise levels after mitigation, or tests against unmodeled systematics are provided, which is load-bearing for whether simulated recovery translates to real observability.
  2. [Noise analysis] Noise analysis section: the dominant noise sources are stated to be analyzed and mitigated, yet the manuscript supplies no explicit equations for the noise power spectral densities, no comparison of mitigated versus unmitigated residuals, and no validation against independent constraints (e.g., existing clock or LISA noise data). This leaves the efficacy of the protocols unverified.
minor comments (1)
  1. [Abstract] The abstract refers to 'preliminary parameter estimation' without specifying the waveform model, priors, or recovered parameters; adding these details would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback. We address the major comments point by point below, indicating planned revisions where appropriate. The manuscript presents a conceptual proposal with preliminary simulations; we agree that additional quantitative details will strengthen the presentation.

read point-by-point responses
  1. Referee: [Abstract / parameter estimation section] Abstract and results sections: the central claim that the network 'could be used to extract critical astrophysical information' rests on parameter estimation performed solely on simulated signals. No quantitative error budgets, residual noise levels after mitigation, or tests against unmodeled systematics are provided, which is load-bearing for whether simulated recovery translates to real observability.

    Authors: We agree that the parameter estimation is performed on simulated signals and constitutes a preliminary demonstration rather than a full observability study. The simulations incorporate the dominant noise sources discussed in the noise analysis, but we acknowledge the absence of explicit quantitative error budgets and residual levels. In revision we will add these budgets and clarify the scope as a proof-of-concept for the proposed protocols. Tests against unmodeled systematics lie beyond the present scope and will be noted as future work. revision: yes

  2. Referee: [Noise analysis] Noise analysis section: the dominant noise sources are stated to be analyzed and mitigated, yet the manuscript supplies no explicit equations for the noise power spectral densities, no comparison of mitigated versus unmitigated residuals, and no validation against independent constraints (e.g., existing clock or LISA noise data). This leaves the efficacy of the protocols unverified.

    Authors: The referee correctly notes that explicit PSD equations, mitigated-versus-unmitigated comparisons, and direct validation against external data are not provided. The current text discusses the dominant sources and mitigation strategies at a descriptive level. We will incorporate the requested explicit equations, residual comparisons, and relevant cross-checks with published LISA and optical-clock noise models in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity; analysis relies on simulations of established concepts without self-referential reduction

full rationale

The paper develops dedicated measurement protocols for one-way Doppler tracking in clock networks, analyzes dominant noise sources, and performs parameter estimation on simulated gravitational-wave signals. No equations or derivations are shown that reduce outputs to inputs by construction, nor are there fitted parameters renamed as predictions. Claims build on prior LISA and optical clock literature without load-bearing self-citations or uniqueness theorems imported from the authors' own work. The derivation chain is self-contained against external benchmarks and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; assessment limited to surface claims.

pith-pipeline@v0.9.1-grok · 5728 in / 1029 out tokens · 28802 ms · 2026-06-28T14:00:21.018618+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

80 extracted references · 41 canonical work pages

  1. [1]

    xXudh0yQRR4AvHDAHAthBhQ70sU=

    and the Einstein Telescope [13], hold immense promise for the advancement of gravitational-wave astronomy, the detection band of ground-based interferometers is fundamentally limited by seismic and technical noise at low frequencies [ 14, 15]. To overcome this limitation, space-based observatories such as the Laser Interferometer Space Antenna (LISA) are ...

  2. [2]

    source frame

    While atom numbers of this magnitude in one- dimensional optical lattices typically introduce density- dependent frequency shifts, the time-varying fluctuations of these shifts, which are the primary concern for AC 6 10 3 10 2 10 1 100 f [Hz] 10 1 100 Favg L = 1 × 1010 m L = 3 × 109 m L = 1 × 109 m FIG. 5. Sky and polarization averaged frequency response ...

  3. [3]

    Landa, P

    B. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett.116, 061102 (2016), URL http://dx.doi.org/10.1103/PhysRevLett. 116.061102

  4. [4]

    D., Acernese , F., et al

    R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, C. Adams, N. Adhikari, R. X. Adhikari, V. B. Adya, C. Affeldt, D. Agarwal, et al. (LIGO Scientific Collabora- tion, Virgo Collaboration, and KAGRA Collaboration), Phys. Rev. X13, 041039 (2023), URL https://link.aps. org/doi/10.1103/PhysRevX.13.041039

  5. [5]

    LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration (2025), 2508.18082, URL https: //arxiv.org/abs/2508.18082

  6. [6]

    LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration,Gravitational-Wave Candidate Event Database (GraceDB): O4 Public Superevents, https://gracedb.ligo.org/superevents/public/O4/ (2024), accessed: 2026-05-29

  7. [7]

    Abbott, T

    R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, A. Adams, C. Adams, R. X. Adhikari, V. B. Adya, C. Affeldt, et al., The Astrophysical Journal Letters913, L7 (2021), URL https://dx.doi.org/10. 3847/2041-8213/abe949

  8. [8]

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett.122, 061104 (2019), URL https://link.aps.org/doi/10. 1103/PhysRevLett.122.061104

  9. [9]

    Abbott et al., Physical Review Letters121(2018), URL https://doi.org/10.1103\%2Fphysrevlett.121

    B. Abbott et al., Physical Review Letters121(2018), URL https://doi.org/10.1103\%2Fphysrevlett.121. 161101

  10. [10]

    Kasen, B

    D. Kasen, B. Metzger, J. Barnes, E. Quataert, and E. Ramirez-Ruiz, Nature551, 80 (2017), URL https: 18 //doi.org/10.1038/nature24453

  11. [11]

    D., Acernese , F., et al

    Abbott, R., Abbott, T. D., Acernese, F., Ackley, K., Adams, C., Adhikari, N., Adhikari, R. X., Adya, V. B., Affeldt, C., Agarwal, D., et al., A&A659, A84 (2022), URLhttps://doi.org/10.1051/0004-6361/202141452

  12. [12]

    Abbott and others

    R. Abbott and others. (LIGO Scientific Collabora- tion and Virgo Collaboration), Phys. Rev. D103, 122002 (2021), URL https://link.aps.org/doi/10. 1103/PhysRevD.103.122002

  13. [13]

    Dirirsa, S

    R. Abbott, H. Abe, F. Acernese, K. Ackley, N. Adhikari, R. X. Adhikari, V. K. Adkins, V. B. Adya, C. Affeldt, D. Agarwal, et al., The Astrophysical Journal949, 76 (2023), URL https://dx.doi.org/10.3847/1538-4357/ ac74bb

  14. [14]

    Evans, R

    M. Evans, R. X. Adhikari, C. Afle, S. W. Ballmer, S. Biscoveanu, S. Borhanian, D. A. Brown, Y. Chen, R. Eisenstein, A. Gruson, et al.,A horizon study for cosmic explorer: Science, observatories, and community (2021), 2109.09882, URL https://doi.org/10.48550/ arXiv.2109.09882

  15. [15]

    Punturo, M

    M. Punturo, M. Abernathy, F. Acernese, B. Allen, N. Andersson, K. Arun, F. Barone, B. Barr, M. Barsuglia, M. Beker, et al., Classical and Quantum Gravity 27, 194002 (2010), URL https://dx.doi.org/10.1088/ 0264-9381/27/19/194002

  16. [16]

    Aasi et al

    J. Aasi et al. (LIGO Scientific), Classical and Quantum Gravity32, 074001 (2015), URL https://doi.org/10. 1088/0264-9381/32/7/074001

  17. [17]

    Harms, Living Reviews in Relativity22, 6 (2019), URL https://doi.org/10.1007/s41114-019-0022-2

    J. Harms, Living Reviews in Relativity22, 6 (2019), URL https://doi.org/10.1007/s41114-019-0022-2

  18. [18]

    Colpi, K

    M. Colpi, K. Danzmann, M. Hewitson, K. Holley- Bockelmann, P. Jetzer, G. Nelemans, A. Petiteau, D. Shoemaker, C. Sopuerta, R. Stebbins, et al.,Lisa definition study report(2024), 2402.07571, URL https: //arxiv.org/abs/2402.07571

  19. [19]

    Robson, N

    T. Robson, N. J. Cornish, and C. Liu, Classical and Quantum Gravity36, 105011 (2019), URL https://doi. org/10.1088/1361-6382/ab1101

  20. [20]

    M. A. Sedda, C. P. L. Berry, K. Jani, P. Amaro-Seoane, P. Auclair, J. Baird, T. Baker, E. Berti, K. Breivik, A. Burrows, et al., Classical and Quantum Gravity 37, 215011 (2020), URL https://doi.org/10.1088/ 1361-6382/abb5c1

  21. [21]

    Kawamura et al., Classical and Quantum Gravity 28, 094011 (2011), URL https://doi.org/10.1088/ 0264-9381/28/9/094011

    S. Kawamura et al., Classical and Quantum Gravity 28, 094011 (2011), URL https://doi.org/10.1088/ 0264-9381/28/9/094011

  22. [22]

    G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner, and E. S. Phinney, Classical and Quantum Gravity 23, 4887 (2006), URL https://doi.org/10.1088/ 0264-9381/23/15/008

  23. [23]

    M. A. Norcia, J. R. K. Cline, and J. K. Thompson, Phys. Rev. A96, 042118 (2017), URL https://link.aps.org/ doi/10.1103/PhysRevA.96.042118

  24. [24]

    Kolkowitz, I

    S. Kolkowitz, I. Pikovski, N. Langellier, M. D. Lukin, R. L. Walsworth, and J. Ye, Phys. Rev. D94, 124043 (2016), URL https://link.aps.org/doi/10. 1103/PhysRevD.94.124043

  25. [25]

    M. Abe, P. Adamson, M. Borcean, D. Bortoletto, K. Bridges, S. P. Carman, S. Chattopadhyay, J. Coleman, N. M. Curfman, K. DeRose, et al., Quantum Science and Technology6, 044003 (2021), URL https://dx.doi.org/ 10.1088/2058-9565/abf719

  26. [26]

    Vutha, New Journal of Physics17, 063030 (2015), ISSN 1367-2630, URL http://stacks.iop.org/1367-2630/ 17/i=6/a=063030

    A. Vutha, New Journal of Physics17, 063030 (2015), ISSN 1367-2630, URL http://stacks.iop.org/1367-2630/ 17/i=6/a=063030

  27. [27]

    Yu and M

    N. Yu and M. Tinto, General Relativity and Gravitation 43, 1943 (2011), URL https://doi.org/10.1007/ s10714-010-1055-8

  28. [28]

    F. B. Estabrook and H. D. Wahlquist, General Relativity and Gravitation6, 439 (1975), URL https://doi.org/ 10.1007/BF00762449

  29. [29]

    R. W. Hellings and G. S. Downs, Apjl265, L39 (1983), URL https://ui.adsabs.harvard.edu/abs/1983ApJ... 265L..39H

  30. [30]

    Agazie et al

    G. Agazie et al. (NANOGrav), The Astrophysical Journal Letters951, L8 (2023), URL https://doi.org/10.3847/ 2041-8213/acdac6

  31. [31]

    Antoniadis et al

    J. Antoniadis et al. (EPTA and InPTA), Astronomy & Astrophysics678, A50 (2023), URL https://doi.org/ 10.1051/0004-6361/202346844

  32. [32]

    D. J. Reardon et al. (PPTA), The Astrophysical Journal Letters951, L6 (2023), URL https://doi.org/10.3847/ 2041-8213/acdd02

  33. [33]

    Xu et al

    H. Xu et al. (CPTA), Research in Astronomy and Astrophysics23, 075024 (2023), URL https://doi.org/ 10.1088/1674-4527/acdfa5

  34. [34]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, Rev. Mod. Phys.87, 637 (2015), URL https: //link.aps.org/doi/10.1103/RevModPhys.87.637

  35. [35]

    Aeppli, K

    A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Phys. Rev. Lett.133, 023401 (2024), URL https:// link.aps.org/doi/10.1103/PhysRevLett.133.023401

  36. [36]

    Oelker, R

    E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, et al., Nature Photonics 13, 714 (2019), URL https://doi.org/10.1038/ s41566-019-0493-4

  37. [37]

    Courtillot, A

    I. Courtillot, A. Quessada, R. P. Kovacich, A. Brusch, D. Kolker, J.-J. Zondy, G. D. Rovera, and P. Lemonde, Phys. Rev. A68, 030501 (2003), URL https://link.aps. org/doi/10.1103/PhysRevA.68.030501

  38. [38]

    Zheng, J

    X. Zheng, J. Dolde, V. Lochab, B. N. Merriman, H. Li, and S. Kolkowitz, Nature602, 425 (2022), URL https: //doi.org/10.1038/s41586-021-04344-y

  39. [39]

    Zheng, J

    X. Zheng, J. Dolde, M. C. Cambria, H. M. Lim, and S. Kolkowitz, Nature Communications14, 4886 (2023), ISSN 2041-1723, URL https://doi.org/10. 1038/s41467-023-40629-8

  40. [40]

    F. Guo, W. Tan, C.-h. Zhou, J. Xia, Y.-x. Chen, T. Liang, Q. Liu, Y. Liu, D.-j. He, Y.-z. Zhou, et al., AIP Advances 11(2021)

  41. [41]

    Xia et al., Review of Scientific Instruments96, 093201 (2025)

    J. Xia et al., Review of Scientific Instruments96, 093201 (2025)

  42. [42]

    N. Yu, Z. Pan, and H. Zheng, inThird Advanced Imaging and Information Processing Conference (AIIP 2025) (SPIE, 2025), vol. 13817, p. 138170D

  43. [43]

    McNamara, S

    P. McNamara, S. Vitale, K. Danzmann, and (on behalf of the LISA Pathfinder Science Working Team), Classical and Quantum Gravity25, 114034 (2008), URL https: //doi.org/10.1088/0264-9381/25/11/114034

  44. [44]

    Armano, H

    M. Armano, H. Audley, G. Auger, J. T. Baird, M. Bassan, P. Binetruy, M. Born, D. Bortoluzzi, N. Brandt, M. Caleno, et al., Phys. Rev. Lett.116, 231101 (2016), URL https://link.aps.org/doi/10. 1103/PhysRevLett.116.231101

  45. [45]

    Armano, H

    M. Armano, H. Audley, J. Baird, P. Binetruy, M. Born, D. Bortoluzzi, E. Castelli, A. Cavalleri, A. Cesarini, A. M. Cruise, et al., Phys. Rev. Lett. 19 120, 061101 (2018), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.120.061101

  46. [46]

    Zheng, J

    X. Zheng, J. Dolde, and S. Kolkowitz, Phys. Rev. X 14, 011006 (2024), URL https://link.aps.org/doi/10. 1103/PhysRevX.14.011006

  47. [47]

    Katori, Applied Physics Express14, 072006 (2021), URLhttps://doi.org/10.35848/1882-0786/ac0e16

    H. Katori, Applied Physics Express14, 072006 (2021), URLhttps://doi.org/10.35848/1882-0786/ac0e16

  48. [48]

    Okaba, R

    S. Okaba, R. Takeuchi, S. Tsuji, and H. Katori, Phys. Rev. Appl.21, 034006 (2024), URL https://link.aps. org/doi/10.1103/PhysRevApplied.21.034006

  49. [49]

    Niroula, J

    P. Niroula, J. Dolde, X. Zheng, J. Bringewatt, A. Ehrenberg, K. C. Cox, J. Thompson, M. J. Gullans, S. Kolkowitz, and A. V. Gorshkov, Phys. Rev. Lett. 133, 080801 (2024), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.133.080801

  50. [50]

    S. Ma, J. Dolde, X. Zheng, D. Ganapathy, A. Shtov, J. Chen, A. St¨ oltzel, B. J. Christensen, and S. Kolkowitz, PRX Quantum6, 040340 (2025), URL https://link. aps.org/doi/10.1103/2rqf-r9gw

  51. [51]

    Dolde, D

    J. Dolde, D. Ganapathy, X. Zheng, S. Ma, K. Beloy, and S. Kolkowitz, Phys. Rev. A112, 023121 (2025), URL https://link.aps.org/doi/10.1103/f6pt-flnt

  52. [52]

    K. Kim, A. Aeppli, W. Warfield, A. Chu, A. M. Rey, and J. Ye, Phys. Rev. Lett.135, 103601 (2025), URL https://link.aps.org/doi/10.1103/3wtv-sty2

  53. [53]

    G. W. Biedermann, K. Takase, X. Wu, L. Deslauriers, S. Roy, and M. A. Kasevich, Phys. Rev. Lett.111, 170802 (2013), URL https://link.aps.org/doi/10. 1103/PhysRevLett.111.170802

  54. [54]

    Schioppo, R

    M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, et al., Nature Photonics11, 48 (2017), URLhttps://doi.org/10.1038/nphoton.2016.231

  55. [55]

    J. D. Romano and N. J. Cornish, Living Reviews in Relativity20, 2 (2017), URL https://doi.org/10.1007/ s41114-017-0004-1

  56. [56]

    N. J. Cornish and S. L. Larson, Classical and Quantum Gravity18, 3473 (2001), URL https://doi.org/10. 1088/0264-9381/18/17/308

  57. [57]

    A. G. Polnarev and D. Baskaran, Phys. Rev. D77, 124013 (2008), URL https://link.aps.org/doi/10. 1103/PhysRevD.77.124013

  58. [58]

    Baskaran, A

    D. Baskaran, A. G. Polnarev, M. S. Pshirkov, and K. A. Postnov, Phys. Rev. D78, 044018 (2008), URL https: //link.aps.org/doi/10.1103/PhysRevD.78.044018

  59. [59]

    W. J. Eckner, N. Darkwah Oppong, A. Cao, A. W. Young, W. R. Milner, J. M. Robinson, J. Ye, and A. M. Kaufman, Nature621, 734 (2023), URL https: //doi.org/10.1038/s41586-023-06360-6

  60. [60]

    J. M. Robinson, M. Miklos, Y. M. Tso, C. J. Kennedy, T. Bothwell, D. Kedar, J. K. Thompson, and J. Ye, Nature Physics20, 208 (2024), URL https://doi.org/10.1038/ s41567-023-02310-1

  61. [61]

    Bishof, X

    M. Bishof, X. Zhang, M. J. Martin, and J. Ye, Phys. Rev. Lett.111, 093604 (2013), URL https://link.aps.org/ doi/10.1103/PhysRevLett.111.093604

  62. [62]

    S. L. Larson, W. A. Hiscock, and R. W. Hellings, Phys. Rev. D62, 062001 (2000), URL https://link.aps.org/ doi/10.1103/PhysRevD.62.062001

  63. [63]

    Batkis et al., Classical and Quantum Gravity42, 235007 (2025)

    M. Batkis et al., Classical and Quantum Gravity42, 235007 (2025)

  64. [64]

    Lisdat, S

    C. Lisdat, S. D¨ orscher, I. Nosske, and U. Sterr, Phys. Rev. Res.3, L042036 (2021), URL https://link.aps. org/doi/10.1103/PhysRevResearch.3.L042036

  65. [65]

    M. S. Safronova, S. G. Porsev, U. I. Safronova, M. G. Kozlov, and C. W. Clark, Phys. Rev. A87, 012509 (2013), URL https://link.aps.org/doi/10. 1103/PhysRevA.87.012509

  66. [66]

    Y. S. Hassan, K. Beloy, J. L. Siegel, T. Kobayashi, E. Swiler, T. Grogan, R. C. Brown, T. Rojo, T. Bothwell, B. D. Hunt, et al., Phys. Rev. Lett.135, 063402 (2025), URLhttps://link.aps.org/doi/10.1103/4tky-jmsm

  67. [67]

    Ohmae, F

    N. Ohmae, F. Bregolin, N. Nemitz, and H. Katori, Opt. Express28, 15112 (2020), URL https://opg.optica. org/oe/abstract.cfm?URI=oe-28-10-15112

  68. [68]

    P. G. Westergaard, J. Lodewyck, L. Lorini, A. Lecallier, E. A. Burt, M. Zawada, J. Millo, and P. Lemonde, Phys. Rev. Lett.106, 210801 (2011), URLhttps://link.aps. org/doi/10.1103/PhysRevLett.106.210801

  69. [69]

    Ushijima, M

    I. Ushijima, M. Takamoto, and H. Katori, Phys. Rev. Lett.121, 263202 (2018), URL https://link.aps.org/ doi/10.1103/PhysRevLett.121.263202

  70. [70]

    Arvanitaki and A

    A. Arvanitaki and A. A. Geraci, Phys. Rev. Lett. 110, 071105 (2013), URL https://link.aps.org/doi/ 10.1103/PhysRevLett.110.071105

  71. [71]

    Aggarwal, G

    N. Aggarwal, G. P. Winstone, M. Teo, M. Baryakhtar, S. L. Larson, V. Kalogera, and A. A. Geraci, Phys. Rev. Lett.128, 111101 (2022), URL https://link.aps.org/ doi/10.1103/PhysRevLett.128.111101

  72. [72]

    Goryachev and M

    M. Goryachev and M. E. Tobar, Phys. Rev. D90, 102005 (2014), URL https://link.aps.org/doi/10. 1103/PhysRevD.90.102005

  73. [73]

    Saini, S

    P. Saini, S. A. Bhat, and K. G. Arun, Phys. Rev. D 106, 104015 (2022), URL https://link.aps.org/doi/ 10.1103/PhysRevD.106.104015

  74. [74]

    P. W. Graham and S. Jung, Phys. Rev. D97, 024052 (2018), URL https://link.aps.org/doi/10. 1103/PhysRevD.97.024052

  75. [75]

    Zhang, T

    C. Zhang, T. Ooi, J. S. Higgins, J. F. Doyle, L. von der Wense, K. Beeks, A. Leitner, G. A. Kazakov, P. Li, P. G. Thirolf, et al., Nature633, 63 (2024), URL https://doi. org/10.1038/s41586-024-07839-6

  76. [76]

    Derevianko, K

    A. Derevianko, K. Gibble, L. Hollberg, N. R. Newbury, C. Oates, M. S. Safronova, L. C. Sinclair, and N. Yu, Quantum Science and Technology7, 044002 (2022), URL https://dx.doi.org/10.1088/2058-9565/ac7df9

  77. [77]

    Alonso, C

    I. Alonso, C. Alpigiani, B. Altschul, H. Ara´ ujo, G. Arduini, J. Arlt, L. Badurina, A. Balaˇ z, S. Bandarupally, B. C. Barish, et al., EPJ Quantum Technology9, 30 (2022), ISSN 2196-0763, URL https://doi.org/10. 1140/epjqt/s40507-022-00147-w

  78. [78]

    B. M. Roberts, G. Blewitt, C. Dailey, M. Murphy, M. Pospelov, A. Rollings, J. Sherman, W. Williams, and A. Derevianko, Nature Communications8, 1195 (2017), ISSN 2041-1723, URL https://doi.org/10. 1038/s41467-017-01440-4

  79. [79]

    J. S. Speagle, Monthly Notices of the Royal Astronomical Society493, 3132 (2020), ISSN 0035-8711, https://academic.oup.com/mnras/article- pdf/493/3/3132/32890730/staa278.pdf, URL https://doi.org/10.1093/mnras/staa278

  80. [80]

    D., et al

    G. Ashton, M. H¨ ubner, P. D. Lasky, C. Talbot, K. Ackley, S. Biscoveanu, Q. Chu, A. Divakarla, P. J. Easter, B. Goncharov, et al., The Astrophysical Journal Supplement Series241, 27 (2019), URL https://doi. org/10.3847/1538-4365/ab06fc