pith. sign in

arxiv: 2607.02320 · v1 · pith:IOUIDPWDnew · submitted 2026-07-02 · 🪐 quant-ph · physics.atom-ph

Time-Reversal and Reversible Dynamics in Cavity QED for Quantum Metrology

Pith reviewed 2026-07-03 11:57 UTC · model grok-4.3

classification 🪐 quant-ph physics.atom-ph
keywords quantum metrologycavity QEDtime-reversalentanglement decodinginteraction-based readoutquantum sensing
0
0 comments X

The pith

Reversible many-body dynamics in cavity QED decode entangled signals for quantum metrology.

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

The paper argues that many-body interactions can serve dual purposes in quantum metrology: generating entanglement and decoding the encoded information through time-reversal. Cavity QED is highlighted as an ideal platform for implementing these reversible dynamics due to its collective enhancement and tunable interactions. This review positions the ability to decode quantum information as equally important as generating it, making reversible many-body dynamics a key resource for quantum-enhanced sensing.

Core claim

Time-reversal protocols, including signal amplification through a time-reversed interaction (SATIN) and scrambling-enhanced metrology, use controlled nonlinear dynamics in cavity QED to transform weakly encoded signals into accessible observables, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.

What carries the argument

Time-reversal of many-body interactions enabling interaction-based readout and signal amplification.

If this is right

  • Time-reversal protocols amplify metrological signals beyond the standard quantum limit.
  • Decoding via reversible dynamics extracts advantage from entangled states.
  • Cavity QED enables controllable reversibility for these protocols.
  • Nonlinear decoding extends metrology to complex entangled states.

Where Pith is reading between the lines

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

  • These methods could be adapted to other platforms like optical lattices or ion traps for broader quantum sensing applications.
  • Hybrid systems might integrate generation and decoding in one setup to optimize overall sensitivity.
  • Experimental tests in larger atom numbers could quantify the scaling benefits of reversible dynamics.

Load-bearing premise

Cavity QED provides collective enhancement, tunable interactions, and controllable reversibility within a single platform.

What would settle it

Demonstration that applying time-reversed interactions in a cavity QED system fails to improve the sensitivity or accessibility of metrological information compared to direct measurement.

read the original abstract

Quantum-enhanced metrology relies on entanglement to achieve sensitivities beyond the standard quantum limit. While remarkable progress has been made in generating highly entangled many-body states, extracting their metrological advantage remains a central challenge because the encoded information is often inaccessible to realistic measurements. A key development of the past decade has been the realization that many-body interactions can play a dual role: they can be used not only to generate entanglement, but also to decode it. This idea underlies interaction-based readout and time-reversal protocols, in which controlled non-linear dynamics transform weakly encoded signals into experimentally accessible observables. Cavity quantum electrodynamics (QED) provides a particularly powerful setting for these approaches because it combines collective enhancement, tunable interactions, and controllable reversibility within a single platform. In this review, we discuss the emergence of time-reversal protocols in cavity QED, from their conceptual roots in Loschmidt echoes to modern implementations of signal amplification through a time-reversed interaction (SATIN), scrambling-enhanced metrology, and more general interaction-based readout schemes. We examine the physical mechanisms that enable reversible many-body dynamics, review key experimental demonstrations, and discuss future directions involving complex entangled states, nonlinear decoding, and emerging quantum platforms. Together, these developments suggest that the ability to decode quantum information may become as important as the ability to generate it, establishing reversible many-body dynamics as a central resource for quantum-enhanced sensing.

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

0 major / 1 minor

Summary. This review paper surveys the use of time-reversal and reversible many-body dynamics in cavity QED for quantum metrology. It argues that many-body interactions serve a dual role in both generating entanglement and decoding encoded information through protocols such as interaction-based readout and signal amplification through a time-reversed interaction (SATIN). The manuscript traces conceptual roots to Loschmidt echoes, covers scrambling-enhanced metrology and related schemes, highlights cavity QED advantages (collective enhancement, tunable interactions, reversibility), reviews experimental demonstrations, and outlines future directions with complex states and nonlinear decoding. The central perspectival claim is that the ability to decode quantum information may become as important as generating it, positioning reversible dynamics as a key resource alongside entanglement generation.

Significance. If the synthesis is accurate, the review could help consolidate an emerging perspective in quantum metrology by linking disparate protocols under the umbrella of reversible dynamics. As a review without new derivations, theorems, or primary data, its value lies in coherent aggregation of existing literature rather than novel predictions or proofs; this may guide experimental design in cavity QED platforms but does not itself constitute a falsifiable advance.

minor comments (1)
  1. The abstract and introduction could more explicitly distinguish review content from forward-looking speculation to help readers calibrate expectations for a survey paper.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and their recommendation to accept. The referee's summary accurately reflects the scope of the review, which synthesizes the role of reversible many-body dynamics in cavity QED metrology without introducing new derivations or data.

Circularity Check

0 steps flagged

No circularity: review aggregates external concepts without internal derivations

full rationale

This is a review paper that surveys time-reversal and interaction-based readout protocols in cavity QED, drawing on established ideas such as Loschmidt echoes and SATIN without presenting new equations, theorems, or quantitative predictions. The central claim is a forward-looking synthesis about the importance of reversible dynamics, supported by citations to prior independent work rather than any self-referential fitting or definitional loop. No load-bearing step reduces by construction to the paper's own inputs, making the derivation chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No new free parameters, axioms, or invented entities are introduced; the work summarizes existing literature on cavity QED metrology.

pith-pipeline@v0.9.1-grok · 5784 in / 950 out tokens · 41810 ms · 2026-07-03T11:57:59.458650+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

103 extracted references · 86 canonical work pages · 5 internal anchors

  1. [1]

    Wineland, D.J., Bollinger, J.J., Itano, W.M., Moore, F.L., Heinzen, D.J.: Spin squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A46, 6797– 6800 (1992) https://doi.org/10.1103/PhysRevA.46.R6797

  2. [2]

    Wineland, D.J., Bollinger, J.J., Itano, W.M., Heinzen, D.J.: Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A50, 67–88 (1994) https://doi.org/10.1103/PhysRevA.50.67

  3. [3]

    Science306(5700), 1330–1336 (2004) https://doi.org/10.1126/science.1104149

    Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science306(5700), 1330–1336 (2004) https://doi.org/10.1126/science.1104149

  4. [4]

    Tóth, G., Apellaniz, I.: Quantum metrology from a quantum information science perspective. J. Phys. A: Math. Theor.47(42), 424006 (2014) https://doi.org/ 10.1088/1751-8113/47/42/424006

  5. [5]

    Nature455(7217), 1216–1219 (2008) https://doi.org/10.1038/nature07332

    Estève, J., Gross, C., Weller, A., Giovanazzi, S., Oberthaler, M.K.: Squeezing and entanglement in a bose–einstein condensate. Nature455(7217), 1216–1219 (2008) https://doi.org/10.1038/nature07332

  6. [6]

    Nature464(7292), 1165–1169 (2010) https://doi.org/10.1038/nature08919

    Gross, C., Zibold, T., Nicklas, E., Esteve, J., Oberthaler, M.K.: Nonlinear atom interferometer surpasses classical precision limit. Nature464(7292), 1165–1169 (2010) https://doi.org/10.1038/nature08919

  7. [7]

    Hamley,C.D.,Gerving,C.,Hoang,T.M.,Bookjans,E.M.,Chapman,M.S.:Spin- nematic squeezed vacuum in a quantum gas. Nat. Phys.8(4), 305–308 (2012) https://doi.org/10.1038/nphys2245

  8. [8]

    Ma, J., Wang, X., Sun, C.-P., Nori, F.: Quantum spin squeezing. Phys. Rep. 509(2-3), 89–165 (2011) https://doi.org/10.1016/j.physrep.2011.08.003

  9. [9]

    Pezze, L., Smerzi, A., Oberthaler, M.K., Schmied, R., Treutlein, P.: Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys.90(3), 035005 (2018) https://doi.org/10.1103/RevModPhys.90.035005

  10. [10]

    Huang, J., Zhuang, M., Lee, C.: Entanglement-enhanced quantum metrology: From standard quantum limit to heisenberg limit. Appl. Phys. Rev.11(3), 031302 (2024) https://doi.org/10.1063/5.0204102

  11. [11]

    Nature581(7807), 159–163 (2020) https://doi

    Bao, H., Duan, J., Jin, S., Lu, X., Li, P., Qu, W., Wang, M., Novikova, I., Mikhailov, E.E., Zhao, K.-F.,et al.: Spin squeezing of1011 atoms by prediction and retrodiction measurements. Nature581(7807), 159–163 (2020) https://doi. org/10.1038/s41586-020-2243-7 23

  12. [12]

    arXiv preprint arXiv:2512.02202 (2025) https: //doi.org/10.48550/arXiv.2512.02202

    Kaubruegger, R., Kaufman, A.M.: Progress in quantum metrology and appli- cations for optical atomic clocks. arXiv preprint arXiv:2512.02202 (2025) https: //doi.org/10.48550/arXiv.2512.02202

  13. [13]

    Ludlow, A.D., Boyd, M.M., Ye, J., Peik, E., Schmidt, P.O.: Optical atomic clocks. Rev. Mod. Phys.87, 637–701 (2015) https://doi.org/10.1103/ RevModPhys.87.637

  14. [14]

    Gil, L.I.R., Mukherjee, R., Bridge, E.M., Jones, M.P.A., Pohl, T.: Spin squeezing in a rydberg lattice clock. Phys. Rev. Lett.112, 103601 (2014) https://doi.org/ 10.1103/PhysRevLett.112.103601

  15. [15]

    Nature588(7838), 414–418 (2020) https: //doi.org/10.1038/s41586-020-3006-1

    Pedrozo-Peñafiel, E., Colombo, S., Shu, C., Adiyatullin, A.F., Li, Z., Mendez, E., Braverman, B., Kawasaki, A., Akamatsu, D., Xiao, Y.,et al.: Entanglement on an optical atomic-clock transition. Nature588(7838), 414–418 (2020) https: //doi.org/10.1038/s41586-020-3006-1

  16. [16]

    Schulte, M., Lisdat, C., Schmidt, P.O., Sterr, U., Hammerer, K.: Prospects and challenges for squeezing-enhanced optical atomic clocks. Nat. Commun.11(1), 5955 (2020) https://doi.org/10.1038/s41467-020-19403-7

  17. [17]

    Colombo, S., Pedrozo-Peñafiel, E., Vuletić, V.: Entanglement-enhanced opti- cal atomic clocks. Appl. Phys. Lett.121(21) (2022) https://doi.org/10.1063/5. 0121372

  18. [18]

    Science304(5676), 1476–1478 (2004) https://doi.org/10.1126/science.1097576

    Leibfried, D., Barrett, M.D., Schaetz, T., Britton, J., Chiaverini, J., Itano, W.M., Jost, J.D., Langer, C., Wineland, D.J.: Toward heisenberg-limited spec- troscopy with multiparticle entangled states. Science304(5676), 1476–1478 (2004) https://doi.org/10.1126/science.1097576

  19. [19]

    Nature609(7928), 689–694 (2022) https://doi.org/10

    Nichol, B.C., Srinivas, R., Nadlinger, D.P., Drmota, P., Main, D., Araneda, G., Ballance, C.J., Lucas, D.M.: An elementary quantum network of entangled optical atomic clocks. Nature609(7928), 689–694 (2022) https://doi.org/10. 1038/s41586-022-05088-z

  20. [20]

    Dietze, K., Pelzer, L., Krinner, L., Dawel, F., Kramer, J., Spethmann, N.C.H., Kielinski, T., Hammerer, K., Stahl, K., Klose, J., Dörscher, S., Lisdat, C., Ben- kler, E., Schmidt, P.O.: Entanglement-enhanced optical ion clock. Phys. Rev. Lett.136, 073601 (2026) https://doi.org/10.1103/dyqm-k8p6

  21. [21]

    Robinson, J.M., Miklos, M., Tso, Y.M., Kennedy, C.J., Bothwell, T., Kedar, D., Thompson, J.K., Ye, J.: Direct comparison of two spin-squeezed optical clock ensembles at the10 −17 level. Nat. Phys.20(2), 208–213 (2024) https: //doi.org/10.1038/s41567-023-02310-1

  22. [22]

    Yang, Y., Miklos, M., Tso, Y.M., Kraus, S., Hur, J., Ye, J.: Clock precision beyond the standard quantum limit at10−18 level. Phys. Rev. Lett.135(19), 24 193202 (2025) https://doi.org/10.1103/6v93-whwq

  23. [23]

    Nature621(7980), 734–739 (2023) https: //doi.org/10.1038/s41586-023-06360-6

    Eckner, W.J., Darkwah Oppong, N., Cao, A., Young, A.W., Milner, W.R., Robinson, J.M., Ye, J., Kaufman, A.M.: Realizing spin squeezing with ryd- berg interactions in an optical clock. Nature621(7980), 734–739 (2023) https: //doi.org/10.1038/s41586-023-06360-6

  24. [24]

    Nature634(8033), 315–320 (2024) https://doi.org/10.1038/s41586-024-07913-z

    Cao, A., Eckner, W.J., Lukin Yelin, T., Young, A.W., Jandura, S., Yan, L., Kim, K., Pupillo, G., Ye, J., Darkwah Oppong, N.,et al.: Multi-qubit gates and schrödinger cat states in an optical clock. Nature634(8033), 315–320 (2024) https://doi.org/10.1038/s41586-024-07913-z

  25. [25]

    Szigeti, S.S., Hosten, O., Haine, S.A.: Improving cold-atom sensors with quan- tum entanglement: Prospects and challenges. Appl. Phys. Lett.118(14) (2021) https://doi.org/10.1063/5.0050235

  26. [26]

    Nature610(7932), 472–477 (2022) https://doi.org/10.1038/s41586-022-05197-9

    Greve, G.P., Luo, C., Wu, B., Thompson, J.K.: Entanglement-enhanced matter- wave interferometry in a high-finesse cavity. Nature610(7932), 472–477 (2022) https://doi.org/10.1038/s41586-022-05197-9

  27. [27]

    DeMille, D., Hutzler, N.R., Rey, A.M., Zelevinsky, T.: Quantum sensing and metrology for fundamental physics with molecules. Nat. Phys.20(5), 741–749 (2024) https://doi.org/10.1038/s41567-024-02499-9

  28. [28]

    Quantum Sci

    Terrano, W., Romalis, M.: Comagnetometer probes of dark matter and new physics. Quantum Sci. Technol.7(1), 014001 (2022) https://doi.org/10.1088/ 2058-9565/ac1ae0

  29. [29]

    Budker, D., Romalis, M.: Optical magnetometry. Nat. Phys.3(4), 227–234 (2007) https://doi.org/10.1038/nphys566

  30. [30]

    Degen, C.L., Reinhard, F., Cappellaro, P.: Quantum sensing. Rev. Mod. Phys. 89(3), 035002 (2017) https://doi.org/10.1103/RevModPhys.89.035002

  31. [31]

    Ye, J., Zoller, P.: Essay: Quantum sensing with atomic, molecular, and optical platforms for fundamental physics. Phys. Rev. Lett.132(19), 190001 (2024) https://doi.org/10.1103/PhysRevLett.132.190001

  32. [32]

    Science345(6195), 424–427 (2014) https://doi.org/10

    Strobel, H., Muessel, W., Linnemann, D., Zibold, T., Hume, D.B., Pezzè, L., Smerzi, A., Oberthaler, M.K.: Fisher information and entanglement of non- gaussian spin states. Science345(6195), 424–427 (2014) https://doi.org/10. 1126/science.1250147

  33. [33]

    Fröwis, F., Sekatski, P., Dür, W.: Detecting large quantum fisher information with finite measurement precision. Phys. Rev. Lett.115(9) (2015) https://doi. org/10.1103/PhysRevLett.116.090801 25

  34. [34]

    Colombo, S., Pedrozo-Peñafiel, E., Adiyatullin, A.F., Li, Z., Mendez, E., Shu, C., Vuletić, V.: Time-reversal-based quantum metrology with many- body entangled states. Nat. Phys.18, 925–930 (2022) https://doi.org/10.1038/ s41567-022-01653-5

  35. [35]

    Davis, E., Bentsen, G., Schleier-Smith, M.: Approaching the heisenberg limit without single-particle detection. Phys. Rev. Lett.116(5) (2016) https://doi. org/10.1103/PhysRevLett.116.053601

  36. [36]

    Nature634(8033), 321–327 (2024) https://doi.org/ 10.1038/s41586-024-08005-8

    Finkelstein, R., Tsai, R.B.-S., Sun, X., Scholl, P., Direkci, S., Gefen, T., Choi, J., Shaw, A.L., Endres, M.: Universal quantum operations and ancilla-based read-out for tweezer clocks. Nature634(8033), 321–327 (2024) https://doi.org/ 10.1038/s41586-024-08005-8

  37. [37]

    Science352(6293), 1552–1555 (2016) https://doi.org/10.1126/ science.aaf3397

    Hosten, O., Krishnakumar, R., Engelsen, N.J., Kasevich, M.A.: Quantum phase magnification. Science352(6293), 1552–1555 (2016) https://doi.org/10.1126/ science.aaf3397

  38. [38]

    Nolan, S.P., Szigeti, S.S., Haine, S.A.: Optimal and robust quantum metrology using interaction-based readouts. Phys. Rev. Lett.119(19) (2017) https://doi. org/10.1103/PhysRevLett.119.193601

  39. [39]

    Haine, S.A.: Using interaction-based readouts to approach the ultimate limit of detection-noise robustness for quantum-enhanced metrology in collective spin systems. Phys. Rev. A98(3) (2018) https://doi.org/10.1103/PhysRevA. 98.030303

  40. [40]

    Quantum4, 268–286 (2020) https://doi.org/10.22331/q-2020-05-15-268

    Schulte, M., Martínez-Lahuerta, V.J., Scharnagl, M.S., Hammerer, K.: Ramsey interferometry with generalized one-axis twisting echoes. Quantum4, 268–286 (2020) https://doi.org/10.22331/q-2020-05-15-268

  41. [41]

    Macrì, T., Smerzi, A., Pezzè, L.: Loschmidt echo for quantum metrology. Phys. Rev. A94(1) (2016) https://doi.org/10.1103/PhysRevA.94.010102

  42. [42]

    Scholarpedia7(8), 11687 (2012) https://doi.org/10.4249/scholarpedia.11687

    Goussev, A., Jalabert, R.A., Pastawski, H.M., Wisniacki, D.: Loschmidt echo. Scholarpedia7(8), 11687 (2012) https://doi.org/10.4249/scholarpedia.11687

  43. [43]

    Science380(6652), 1381–1384 (2023) https://doi.org/10

    Li, Z., Colombo, S., Shu, C., Velez, G., Pilatowsky-Cameo, S., Schmied, R., Choi, S., Lukin, M., Pedrozo-Peñafiel, E., Vuletić, V.: Improving metrology with quantum scrambling. Science380(6652), 1381–1384 (2023) https://doi.org/10. 1126/science.adg9500

  44. [44]

    Linnemann, D., Strobel, H., Muessel, W., Schulz, J., Lewis-Swan, R.J., Kheruntsyan, K.V., Oberthaler, M.K.: Quantum-enhanced sensing based on time reversal of nonlinear dynamics. Phys. Rev. Lett.117(1) (2016) https: //doi.org/10.1103/PhysRevLett.117.013001 26

  45. [45]

    Mao, T.-W., Liu, Q., Li, X., Cao, J.-H., Chen, F., Xu, W., Sun, Y.-R., Wang, M., You, L.: Quantum-enhanced sensing by echoing spin-nematic squeezing in atomic bose–einstein condensate. Nat. Phys.18, 1585–1590 (2022) https://doi. org/10.1038/s41567-023-02168-3

  46. [46]

    Science373(6555), 673–678 (2021) https://doi.org/10.1126/science.abi5226

    Gilmore, K.A., Affolter, M., Lewis-Swan, R.J., Barberena, D., Jordan, E., Rey, A.M., Bollinger, J.J.: Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals. Science373(6555), 673–678 (2021) https://doi.org/10.1126/science.abi5226

  47. [47]

    PRX Quantum3(2) (2022) https://doi.org/10.1103/PRXQuantum.3.020308

    Li, Z., Braverman, B., Colombo, S., Shu, C., Kawasaki, A., Adiyatullin, A.F., Pedrozo-Peñafiel, E., Mendez, E., Vuletić, V.: Collective spin-light and light- mediated spin-spin interactions in an optical cavity. PRX Quantum3(2) (2022) https://doi.org/10.1103/PRXQuantum.3.020308

  48. [48]

    Nature529(7587), 505–508 (2016) https://doi.org/10.1038/nature16176

    Hosten, O., Engelsen, N.J., Krishnakumar, R., Kasevich, M.A.: Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature529(7587), 505–508 (2016) https://doi.org/10.1038/nature16176

  49. [49]

    Cox, K.C., Greve, G.P., Weiner, J.M., Thompson, J.K.: Deterministic squeezed states with collective measurements and feedback. Phys. Rev. Lett.116(9), 093602 (2016) https://doi.org/10.1103/PhysRevLett.116.093602

  50. [50]

    Schleier-Smith, M.H., Leroux, I.D., Vuletić, V.: Squeezing the collective spin of a dilute atomic ensemble by cavity feedback. Phys. Rev. A81, 021804 (2010) https://doi.org/10.1103/PhysRevA.81.021804

  51. [51]

    Leroux,I.D.,Schleier-Smith,M.H.,Vuletić,V.:Implementationofcavitysqueez- ing of a collective atomic spin. Phys. Rev. Lett.104(7), 073602 (2010) https: //doi.org/10.1103/PhysRevLett.104.073602

  52. [52]

    Braverman, B., Kawasaki, A., Pedrozo-Peñafiel, E., Colombo, S., Shu, C., Li, Z., Mendez, E., Yamoah, M., Salvi, L., Akamatsu, D., Xiao, Y., Vuletić, V.: Near- unitary spin squeezing in 171Yb. Phys. Rev. Lett.122, 223203 (2019) https: //doi.org/10.1103/PhysRevLett.122.223203

  53. [53]

    Nature646(8084), 309–314 (2025) https://doi.org/10

    Zaporski, L., Liu, Q., Velez, G., Radzihovsky, M., Li, Z., Colombo, S., Pedrozo- Peñafiel, E., Vuletić, V.: Quantum-amplified global-phase spectroscopy on an optical clock transition. Nature646(8084), 309–314 (2025) https://doi.org/10. 1038/s41586-025-09578-8

  54. [54]

    In: Arimondo, E., Berman, P.R., Lin, C.C

    Tanji-Suzuki, H., Leroux, I.D., Schleier-Smith, M.H., Cetina, M., Grier, A.T., Simon, J., Vuletić, V.: Interaction between atomic ensembles and optical res- onators: Classical description. In: Arimondo, E., Berman, P.R., Lin, C.C. (eds.) Adv. At. Mol. Opt. Phys. vol. 60, pp. 201–237. Academic Press, New York (2011). https://doi.org/10.1016/B978-0-12-38550...

  55. [55]

    EPL42(5), 481–486 (1998) https://doi.org/10.1209/ epl/i1998-00277-9

    Kuzmich, A., Bigelow, N., Mandel, L.: Atomic quantum non-demolition mea- surements and squeezing. EPL42(5), 481–486 (1998) https://doi.org/10.1209/ epl/i1998-00277-9

  56. [56]

    Appel, J., Windpassinger, P.J., Oblak, D., Hoff, U.B., Kjærgaard, N., Polzik, E.S.: Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc. Natl. Acad. Sci. U.S.A.106(27), 10960–10965 (2009) https://doi.org/10.1073/pnas.0901550106

  57. [57]

    Saffman, M., Oblak, D., Appel, J., Polzik, E.: Spin squeezing of atomic ensem- bles by multicolor quantum nondemolition measurements. Phys. Rev. A79(2), 023831 (2009) https://doi.org/10.1103/PhysRevA.79.023831

  58. [58]

    Dissipative generation of spin squeezing in the resolved vacuum Rabi splitting limit

    Chaparro, E., Song, E.Y., Barberena, D., Thompson, J.K., Rey, A.M., Young, J.T.: Dissipative generation of spin squeezing in the resolved vacuum rabi split- ting limit. arXiv preprint arXiv:2605.30815 (2026) https://doi.org/10.48550/ arXiv.2605.30815

  59. [59]

    Takano, T., Fuyama, M., Namiki, R., Takahashi, Y.: Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half. Phys. Rev. Lett.102, 033601 (2009) https://doi.org/10.1103/PhysRevLett.102.033601

  60. [60]

    Kitagawa, M., Ueda, M.: Squeezed spin states. Phys. Rev. A47, 5138–5143 (1993) https://doi.org/10.1103/PhysRevA.47.5138

  61. [61]

    Morigi, G., Solano, E., Englert, B.-G., Walther, H.: Reversing the jaynes– cummings dynamics to measure decoherence. J. Opt. B: Quantum semiclass. Opt.4(4), 310–312 (2002) https://doi.org/10.1088/1464-4266/4/4/312 . Special issue

  62. [62]

    Meunier, T., Gleyzes, S., Maioli, P., Auffeves, A., Nogues, G., Brune, M., Raimond, J.M., Haroche, S.: Rabi oscillations revival induced by time rever- sal: a test of mesoscopic quantum coherence. Phys. Rev. Lett.94(1) (2005) https://doi.org/10.1103/PhysRevLett.94.010401

  63. [63]

    arXiv preprint arXiv:2601.20952 (2026) https://doi.org/10.48550/arXiv.2601.20952

    Wang, Y.-X., Salvati, F., Arvidsson-Shukur, D.R., Braasch Jr, W.F., Murch, K., Halpern, N.Y.: Quantum metrology enhanced by effective time reversal. arXiv preprint arXiv:2601.20952 (2026) https://doi.org/10.48550/arXiv.2601.20952

  64. [64]

    Anders, F., Pezzè, L., Smerzi, A., Klempt, C.: Phase magnification by two-axis countertwisting for detection-noise robust interferometry. Phys. Rev. A97(4), 043813 (2018) https://doi.org/10.1103/PhysRevA.97.043813

  65. [65]

    Mirkhalaf, S.S., Nolan, S.P., Haine, S.A.: Robustifying twist-and-turn entan- glement with interaction-based readout. Phys. Rev. A97(5) (2018) https: //doi.org/10.1103/PhysRevA.97.053618 28

  66. [66]

    ComptesRendus.Physique23,1–26(2022)https://doi.org/10.5802/crphys.103

    Baamara, Y., Sinatra, A., Gessner, M.: Squeezing of nonlinear spin observ- ables by one axis twisting in the presence of decoherence: An analytical study. ComptesRendus.Physique23,1–26(2022)https://doi.org/10.5802/crphys.103

  67. [67]

    Lewis-Swan,R.J.,Barberena,D.,Muniz,J.A.,Cline,J.R.K.,Young,D.,Thomp- son, J.K., Rey, A.M.: Protocol for precise field sensing in the optical domain with cold atoms in a cavity. Phys. Rev. Lett.124, 193602 (2020) https://doi. org/10.1103/PhysRevLett.124.193602

  68. [68]

    Science364(6446), 1163–1165 (2019) https://doi.org/10.1126/ science.aaw2884

    Burd, S.C., Srinivas, R., Bollinger, J.J., Wilson, A.C., Wineland, D.J., Leibfried, D., Slichter, D.H., Allcock, D.T.C.: Quantum amplification of mechanical oscil- lator motion. Science364(6446), 1163–1165 (2019) https://doi.org/10.1126/ science.aaw2884

  69. [69]

    Nature, 740–745 (2023) https://doi.org/10

    Franke, J., Muleady, S.R., Kaubruegger, R., Kranzl, F., Blatt, R., Rey, A.M., Joshi, M.K., Roos, C.F.: Quantum-enhanced sensing on optical transitions through finite-range interactions. Nature, 740–745 (2023) https://doi.org/10. 1038/s41586-023-06472-z

  70. [70]

    Zhang, Z., Duan, L.M.: Quantum metrology with dicke squeezed states. New J. Phys.16(10), 103037 (2014) https://doi.org/10.1088/1367-2630/16/10/103037

  71. [71]

    Lücke, B., Peise, J., Vitagliano, G., Arlt, J., Santos, L., Tóth, G., Klempt, C.: Detecting multiparticle entanglement of dicke states. Phys. Rev. Lett.112(15), 155304 (2014) https://doi.org/10.1103/PhysRevLett.112.155304

  72. [72]

    Science334(6057), 773–776 (2011) https://doi.org/ 10.1126/science.1208798

    Lücke, B., Scherer, M., Kruse, J., Pezzé, L., Deuretzbacher, F., Hyllus, P., Topic, O., Peise, J., Ertmer, W., Arlt, J.,et al.: Twin matter waves for interferometry beyond the classical limit. Science334(6057), 773–776 (2011) https://doi.org/ 10.1126/science.1208798

  73. [73]

    Kessler, E.M., Komar, P., Bishof, M., Jiang, L., Sørensen, A.S., Ye, J., Lukin, M.D.: Heisenberg-limited atom clocks based on entangled qubits. Phys. Rev. Lett.112(19), 190403 (2014) https://doi.org/10.1103/PhysRevLett.112.190403

  74. [74]

    Gessner, M., Smerzi, A., Pezzè, L.: Metrological nonlinear squeezing parameter. Phys. Rev. Lett.122(9), 090503 (2019) https://doi.org/10.1103/PhysRevLett. 122.090503

  75. [75]

    arXiv preprint arXiv:2602.06308 (2026) https://doi.org/ 10.48550/arXiv.2602.06308

    Carrasco, S.C., Goerz, M.H., Li, Z., Colombo, S., Vuletić, V., Schleich, W.P., Malinovsky, V.S.: Time-reversal interferometry using cat states with scalable entangling resources. arXiv preprint arXiv:2602.06308 (2026) https://doi.org/ 10.48550/arXiv.2602.06308

  76. [76]

    Butterfly Echo Protocol for Axis-Agnostic Heisenberg-Limited Metrology

    Bringewatt, J., Zaporski, L., Radzihovsky, M., Albert, J., Gorshkov, A.V., Vuletić, V., Bentsen, G.: Butterfly echo protocol for axis-agnostic heisenberg- limited metrology. arXiv preprint arXiv:2602.23332 (2026) https://doi.org/10. 29 48550/arXiv.2602.23332

  77. [77]

    arXiv preprint arXiv:2601.16026 (2026) https://doi.org/10.48550/arXiv.2601.16026

    Liu, D.-S., Chen, Z.-J., Hua, Z., Zhou, Y., Jie, Q.-X., Cai, W., Li, M., Sun, L., Zou, C.-L., Ren, X.-F.,et al.: Echoed random quantum metrology. arXiv preprint arXiv:2601.16026 (2026) https://doi.org/10.48550/arXiv.2601.16026

  78. [78]

    Shao, L., Xing, H.-J., Fu, L.: Enhanced quantum metrology via saddle-point scrambling in phase space. Phys. Rev. Lett.136(18), 180203 (2026) https:// doi.org/10.1103/4sn5-ngdg

  79. [79]

    Gärttner, M., Bohnet, J.G., Safavi-Naini, A., Wall, M.L., Bollinger, J.J., Rey, A.M.: Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet. Nat. Phys.13(8), 781–786 (2017) https: //doi.org/10.1038/nphys4119

  80. [80]

    Escher, B., Matos Filho, R.L., Davidovich, L.: General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys. 7(5), 406–411 (2011) https://doi.org/10.1038/nphys1958

Showing first 80 references.