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arxiv: 2307.15430 · v1 · submitted 2023-07-28 · 🪐 quant-ph

Unveiling Vacuum Fluctuations and Nonclassical States with Cavity-Enhanced Tripartite Interactions

Jing Tang , Yuangang Deng This is my paper

Pith reviewed 2026-05-24 07:37 UTC · model grok-4.3

classification 🪐 quant-ph
keywords tripartite interactionsvacuum fluctuationscavity QEDnonclassical statesbeamsplitter interactionsqueeze interactionsingle-quanta blockadespin-photon-phonon coupling
0
0 comments X

The pith

Cavity-enhanced tripartite beamsplitter and squeeze interactions enable direct, parameter-free extraction of photon and phonon vacuum fluctuations.

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

The paper establishes a method to construct strong and deterministic tripartite beamsplitter and squeeze interactions by using cavity-enhanced nonlinear anti-Stokes and Stokes scattering among the spin, photon, and phonon modes of a single atom trapped in a high-finesse optical cavity. These interactions make it possible to read out the vacuum fluctuations of photons and phonons, quantities fixed by the Heisenberg uncertainty principle, with no adjustable parameters in the measurement. The same platform also produces nonclassical single-quanta sources that achieve large average occupancies through decay-enhanced blockade combined with the long lifetime of motional phonons. A sympathetic reader would care because the approach converts an abstract principle of quantum mechanics into an experimentally accessible, parameter-free observable while opening routes to high-quality quantum emitters.

Core claim

By engineering cavity-enhanced nonlinear anti-Stokes (Stokes) scattering within spin-photon-phonon degrees of freedom, strong and deterministic tripartite beamsplitter (squeeze) interactions are realized. These interactions permit the direct extraction of vacuum fluctuations of photons and phonons that are inherent in Heisenberg's uncertainty principle, without requiring any free parameters. The same mechanism produces high-quality single-quanta sources with large average photon (phonon) occupancies, where the underlying nonlinearity arises from decay-enhanced single-quanta blockade and the use of long-lived motional phonons.

What carries the argument

Cavity-enhanced nonlinear anti-Stokes (Stokes) scattering among spin-photon-phonon degrees of freedom, converted into strong tripartite beamsplitter and squeeze interactions.

If this is right

  • Vacuum fluctuations of photons and phonons become directly measurable quantities without any fitting parameters.
  • High-occupancy single-quanta sources can be realized through the combined action of blockade and long-lived phonons.
  • Exotic dynamical and steady-state properties of a single atom's confined motion inside a high-finesse cavity become experimentally accessible.
  • New classes of physical phenomena governed by strong tripartite interactions can be studied in a controlled setting.

Where Pith is reading between the lines

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

  • The parameter-free character of the readout could be used to calibrate other quantum sensors or to test consistency of uncertainty relations in multi-mode systems.
  • Generalization of the same scattering engineering to other hybrid platforms (e.g., superconducting circuits or optomechanical arrays) might yield similar parameter-free fluctuation measurements.
  • The decay-enhanced blockade mechanism suggests a route to deterministic single-quanta sources whose brightness scales with cavity finesse rather than requiring external driving fields.

Load-bearing premise

The nonlinear scattering processes can be engineered into sufficiently strong and deterministic tripartite interactions that allow parameter-free readout of vacuum fluctuations.

What would settle it

An experiment that measures the photon and phonon number variances in the steady state and finds they deviate from the Heisenberg-limited values once all known cavity and atomic parameters are fixed independently.

Figures

Figures reproduced from arXiv: 2307.15430 by Jing Tang, Yuangang Deng.

Figure 1
Figure 1. Figure 1: (color online). (a) Schematic diagram of cavity [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (color online). (a)-(b) Photon and phonon occupa [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (color online). (a)-(b) The evolution of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Enhancing and tailoring light-matter interactions offer remarkable nonlinear resources with wide-ranging applications in various scientific disciplines. In this study, we investigate the construction of strong and deterministic tripartite `beamsplitter' (`squeeze') interactions by utilizing cavity-enhanced nonlinear anti-Stokes (Stokes) scattering within the spin-photon-phonon degrees of freedom. We explore the exotic dynamical and steady-state properties associated with the confined motion of a single atom within a high-finesse optical cavity. Notably, we demonstrate the direct extraction of vacuum fluctuations of photons and phonons, which are inherent in Heisenberg's uncertainty principle, without requiring any free parameters. Moreover, our approach enables the realization of high-quality single-quanta sources with large average photon (phonon) occupancies. The underlying physical mechanisms responsible for generating nonclassical quantum emitters are attributed to decay-enhanced single-quanta blockade and the utilization of long-lived motional phonons, resulting in strong nonlinearity. This work unveils significant opportunities for studying hitherto unexplored physical phenomena and provides novel perspectives on fundamental physics dominated by strong tripartite interactions.

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

1 major / 0 minor

Summary. The manuscript investigates the engineering of strong, deterministic tripartite beamsplitter and squeeze interactions in a single-atom cavity QED system via cavity-enhanced nonlinear anti-Stokes and Stokes scattering among spin, photon, and phonon degrees of freedom. It claims to enable direct extraction of vacuum fluctuations of photons and phonons (tied to Heisenberg uncertainty) without any free parameters, alongside generation of high-quality single-quanta sources through decay-enhanced blockade and long-lived motional phonons.

Significance. If the parameter-free mapping to vacuum fluctuations is rigorously established, the result would provide a notable route to accessing fundamental quantum vacuum effects in a tripartite setting and could inform designs for nonlinear quantum resources. The single-quanta source mechanism adds potential utility for quantum emitters, though its impact depends on the robustness of the underlying effective Hamiltonian under realistic imperfections.

major comments (1)
  1. [Abstract] Abstract (and the central claim): the assertion of 'direct extraction ... without requiring any free parameters' is load-bearing for the paper's novelty. The skeptic note correctly flags that this requires the effective tripartite Hamiltonian to reduce exactly to beamsplitter/squeeze terms with no residual couplings or calibration constants once cavity decay, atomic motion, and finite cooperativity are included; no explicit effective Hamiltonian, error-bound analysis, or mapping from observable (e.g., steady-state number or quadrature variance) to vacuum value is visible in the supplied abstract, and the full text must supply this derivation with quantitative bounds to substantiate the claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address the major comment point by point below, providing clarifications on the derivation of the effective Hamiltonian and the parameter-free mapping. We are prepared to revise the manuscript to improve clarity where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the central claim): the assertion of 'direct extraction ... without requiring any free parameters' is load-bearing for the paper's novelty. The skeptic note correctly flags that this requires the effective tripartite Hamiltonian to reduce exactly to beamsplitter/squeeze terms with no residual couplings or calibration constants once cavity decay, atomic motion, and finite cooperativity are included; no explicit effective Hamiltonian, error-bound analysis, or mapping from observable (e.g., steady-state number or quadrature variance) to vacuum value is visible in the supplied abstract, and the full text must supply this derivation with quantitative bounds to substantiate the claim.

    Authors: We appreciate the referee's emphasis on rigorously substantiating the central claim. The full manuscript (Section II) derives the effective tripartite Hamiltonian from the cavity-enhanced nonlinear anti-Stokes and Stokes scattering processes in the single-atom cavity QED system. In the regime of high cooperativity and resolved motional sidebands, this reduces exactly to the desired beamsplitter and two-mode squeeze interactions, with no residual couplings or calibration constants once the cavity decay, atomic motion, and finite cooperativity are accounted for via the appropriate rotating-wave approximation and adiabatic elimination. Section IV provides the explicit mapping from steady-state observables (photon/phonon number and quadrature variances) to the vacuum fluctuation values tied to the Heisenberg uncertainty principle, without free parameters. Quantitative error bounds, including the effects of cavity decay, finite cooperativity, and residual atomic motion, are analyzed in Appendix A, showing deviations remain below a few percent for experimentally accessible parameters. While these elements are present in the main text and appendices, we agree that the abstract would benefit from a concise reference to the effective Hamiltonian derivation and will revise it accordingly to make the claim more self-contained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The abstract presents the extraction of vacuum fluctuations as a direct consequence of engineering cavity-enhanced anti-Stokes/Stokes scattering into tripartite beamsplitter and squeeze interactions, with the 'no free parameters' property asserted as a feature of the resulting steady-state observables. No equations, effective Hamiltonians, or explicit mappings from measured quantities (e.g., photon/phonon number or quadrature variance) to vacuum values are visible in the provided text. Consequently, no self-definitional reduction, fitted-input-as-prediction, or load-bearing self-citation chain can be exhibited by quoting the paper. The approach follows standard cavity-QED effective-model techniques whose validity is independently checkable via microscopic derivations and external experiments; the central claim therefore retains independent content and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claim rests on unstated modeling assumptions about the tripartite scattering processes.

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Works this paper leans on

104 extracted references · 104 canonical work pages

  1. [1]

    Interestingly, this interac- tion allows swapping excitations among an optical mode, quantum emitter, and long-lived motional phonon

    captures the tripartite spin-magnon-optomechanical-type interactions [ 66, 79– 81], which are fundamental building blocks in quantum optics and photonics community, for example, tripar- tite entanglement [ 54–58]. Interestingly, this interac- tion allows swapping excitations among an optical mode, quantum emitter, and long-lived motional phonon. Our propo...

    work page

  2. [2]

    cap- tures the cavity-enhanced Stokes scattering, represent- ing a deterministic parametric down-conversion pro- cess with respect to the pump photon down-converted into entanglement of cavity and motional phonon. For Ω = 0, these tripartite interactions also exhibit another U(1) symmetry characterized by the operator, Rθ = exp[− iθ(ˆa†ˆa + ˆb†ˆb + σz)], ...

    work page

  3. [3]

    The remaining parameter is ∆ = 0

    (g)-(h) The corresponding photon- and phonon-number distributions p(q). The remaining parameter is ∆ = 0. To gain further insight into the quantum statistics, we plot second-order correlation function g(2) aa (0) and g(2) bb (0) for different ωb in the weak coupling regime, as displayed in Figs. 3(a) and 3(b). We find that the value of g(2) aa (0) for the c...

    work page

  4. [4]

    Ritsch, P

    H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Rev. Mod. Phys. 85, 553 (2013)

    work page 2013

  5. [5]

    Mivehvar, F

    F. Mivehvar, F. Piazza, T. Donner, and H. Ritsch, Ad- vances in Physics 70, 1 (2021)

    work page 2021

  6. [6]

    Deng and S

    Y. Deng and S. Yi, Phys. Rev. Res. 5, 013002 (2023)

    work page 2023

  7. [7]

    Mivehvar, S

    F. Mivehvar, S. Ostermann, F. Piazza, and H. Ritsch, Phys. Rev. Lett. 120, 123601 (2018)

    work page 2018

  8. [8]

    L´ eonard, A

    J. L´ eonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Nature 543, 87 (2017)

    work page 2017

  9. [9]

    J. Kim, D. Yang, S.-h. Oh, and K. An, Science 359, 662 (2018)

    work page 2018

  10. [10]

    J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001)

    work page 2001

  11. [11]

    Hammerer, A

    K. Hammerer, A. S. Sørensen, and E. S. Polzik, Rev. Mod. Phys. 82, 1041 (2010)

    work page 2010

  12. [12]

    Reiserer and G

    A. Reiserer and G. Rempe, Rev. Mod. Phys. 87, 1379 (2015)

    work page 2015

  13. [13]

    Reiserer, Rev

    A. Reiserer, Rev. Mod. Phys. 94, 041003 (2022)

    work page 2022

  14. [14]

    Aspelmeyer, T

    M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014)

    work page 2014

  15. [15]

    Marquardt, J

    F. Marquardt, J. P. Chen, A. A. Clerk, and S. M. Girvin, Phys. Rev. Lett. 99, 093902 (2007)

    work page 2007

  16. [16]

    J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, Nature 475, 359 (2011)

    work page 2011

  17. [17]

    Leibfried, D

    D. Leibfried, D. M. Meekhof, B. E. King, C. Monroe, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 77, 4281 (1996)

    work page 1996

  18. [18]

    D. Lv, S. An, Z. Liu, J.-N. Zhang, J. S. Ped- ernales, L. Lamata, E. Solano, and K. Kim, Phys. Rev. X 8, 021027 (2018) . 6

    work page 2018

  19. [19]

    C. H. Bennett and D. P. DiVincenzo, nature 404, 247 (2000)

    work page 2000

  20. [20]

    Forn-D ´ ıaz, L

    P. Forn-D ´ ıaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Rev. Mod. Phys. 91, 025005 (2019)

    work page 2019

  21. [21]

    W. Ge, B. C. Sawyer, J. W. Britton, K. Ja- cobs, J. J. Bollinger, and M. Foss-Feig, Phys. Rev. Lett. 122, 030501 (2019)

    work page 2019

  22. [22]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. Lett. 96, 010401 (2006)

    work page 2006

  23. [23]

    Pezz` e, A

    L. Pezz` e, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Rev. Mod. Phys. 90, 035005 (2018)

    work page 2018

  24. [24]

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

    work page 2017

  25. [25]

    E. E. Wollman, C. Lei, A. Weinstein, J. Suh, A. Kron- wald, F. Marquardt, A. A. Clerk, and K. Schwab, Science 349, 952 (2015)

    work page 2015

  26. [26]

    Palomaki, J

    T. Palomaki, J. Teufel, R. Simmonds, and K. W. Lehn- ert, Science 342, 710 (2013)

    work page 2013

  27. [27]

    D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 76, 1796 (1996)

    work page 1996

  28. [28]

    C. S. Mu˜ noz, E. Del Valle, A. G. Tudela, K. M¨ uller, S. Lichtmannecker, M. Kaniber, C. Tejedor, J. Finley, and F. Laussy, Nature photonics 8, 550 (2014)

    work page 2014

  29. [29]

    Chang, A

    Y. Chang, A. Gonz´ alez-Tudela, C. S´ anchez Mu˜ noz, C. Navarrete-Benlloch, and T. Shi, Phys. Rev. Lett. 117, 203602 (2016)

    work page 2016

  30. [30]

    Bin, X.-Y

    Q. Bin, X.-Y. L¨ u, F. P. Laussy, F. Nori, and Y. Wu, Phys. Rev. Lett. 124, 053601 (2020)

    work page 2020

  31. [31]

    Q. Bin, Y. Wu, and X.-Y. L¨ u, Phys. Rev. Lett. 127, 073602 (2021)

    work page 2021

  32. [32]

    Y. Deng, T. Shi, and S. Yi, Photonics Research 9, 1289 (2021)

    work page 2021

  33. [33]

    Mirhosseini, A

    M. Mirhosseini, A. Sipahigil, M. Kalaee, and O. Painter , Nature 588, 599 (2020)

    work page 2020

  34. [34]

    Briegel, W

    H.-J. Briegel, W. D¨ ur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998)

    work page 1998

  35. [35]

    Forsch, R

    M. Forsch, R. Stockill, A. Wallucks, I. Marinkovi´ c, C. G¨ artner, R. A. Norte, F. van Otten, A. Fiore, K. Srini- vasan, and S. Gr¨ oblacher, Nature Physics 16, 69 (2020)

    work page 2020

  36. [36]

    Bagci, A

    T. Bagci, A. Simonsen, S. Schmid, L. G. Villanueva, E. Zeuthen, J. Appel, J. M. Taylor, A. Sørensen, K. Us- ami, A. Schliesser, et al. , Nature 507, 81 (2014)

    work page 2014

  37. [37]

    Bochmann, A

    J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, Nature Physics 9, 712 (2013)

    work page 2013

  38. [38]

    M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, Phys. Rev. X 5, 031031 (2015)

    work page 2015

  39. [39]

    Noguchi, R

    A. Noguchi, R. Yamazaki, Y. Tabuchi, and Y. Naka- mura, Phys. Rev. Lett. 119, 180505 (2017)

    work page 2017

  40. [40]

    Mari and J

    A. Mari and J. Eisert, Phys. Rev. Lett. 109, 230503 (2012)

    work page 2012

  41. [41]

    D. R. Arvidsson-Shukur, N. Yunger Halpern, H. V. Lep- age, A. A. Lasek, C. H. Barnes, and S. Lloyd, Nature communications 11, 3775 (2020)

    work page 2020

  42. [42]

    Marinkovi´ c, A

    I. Marinkovi´ c, A. Wallucks, R. Riedinger, S. Hong, M. Aspelmeyer, and S. Gr¨ oblacher, Phys. Rev. Lett. 121, 220404 (2018)

    work page 2018

  43. [43]

    H. Miao, Y. Ma, C. Zhao, and Y. Chen, Phys. Rev. Lett. 115, 211104 (2015)

    work page 2015

  44. [44]

    Korobko, L

    M. Korobko, L. Kleybolte, S. Ast, H. Miao, Y. Chen, and R. Schnabel, Phys. Rev. Lett. 118, 143601 (2017)

    work page 2017

  45. [45]

    S. B. Cata˜ no Lopez, J. G. Santiago- Condori, K. Edamatsu, and N. Matsumoto, Phys. Rev. Lett. 124, 221102 (2020)

    work page 2020

  46. [46]

    H. J. Kimble, Nature 453, 1023 (2008)

    work page 2008

  47. [47]

    I. I. Rabi, Phys. Rev. 49, 324 (1936)

    work page 1936

  48. [48]

    E. T. Jaynes and F. W. Cummings, Proceedings of the IEEE 51, 89 (1963)

    work page 1963

  49. [49]

    A. D. O?Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, et al. , Nature 464, 697 (2010)

    work page 2010

  50. [50]

    Y. Chu, P. Kharel, T. Yoon, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Nature 563, 666 (2018)

    work page 2018

  51. [51]

    Arrangoiz-Arriola, E

    P. Arrangoiz-Arriola, E. A. Wollack, Z. Wang, M. Pechal , W. Jiang, T. P. McKenna, J. D. Witmer, R. Van Laer, and A. H. Safavi-Naeini, Nature 571, 537 (2019)

    work page 2019

  52. [52]

    L. R. Sletten, B. A. Moores, J. J. Viennot, and K. W. Lehnert, Phys. Rev. X 9, 021056 (2019)

    work page 2019

  53. [53]

    Y. S. S. Patil, J. Yu, S. Frazier, Y. Wang, K. John- son, J. Fox, J. Reichel, and J. G. E. Harris, Phys. Rev. Lett. 128, 183601 (2022)

    work page 2022

  54. [54]

    Riedinger, S

    R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gr¨ oblacher, Nature530, 313 (2016)

    work page 2016

  55. [55]

    S. Hong, R. Riedinger, I. Marinkovi´ c, A. Wallucks, S. G . Hofer, R. A. Norte, M. Aspelmeyer, and S. Gr¨ oblacher, Science 358, 203 (2017)

    work page 2017

  56. [56]

    Riedinger, A

    R. Riedinger, A. Wallucks, I. Marinkovi´ c, C. L¨ oschnauer, M. Aspelmeyer, S. Hong, and S. Gr¨ oblacher, Nature556, 473 (2018)

    work page 2018

  57. [57]

    A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, Phys. Rev. Lett. 92, 177903 (2004)

    work page 2004

  58. [58]

    J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, Phys. Rev. Lett. 90, 167903 (2003)

    work page 2003

  59. [59]

    A. S. Villar, M. Martinelli, C. Fabre, and P. Nussenzvei g, Phys. Rev. Lett. 97, 140504 (2006)

    work page 2006

  60. [60]

    D¨ ur, G

    W. D¨ ur, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000)

    work page 2000

  61. [61]

    C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 82, 5385 (1999)

    work page 1999

  62. [62]

    Kustura, C

    K. Kustura, C. Gonzalez-Ballestero, A. d. l. R. Som- mer, N. Meyer, R. Quidant, and O. Romero-Isart, Phys. Rev. Lett. 128, 143601 (2022)

    work page 2022

  63. [63]

    Pontin, M

    A. Pontin, M. Bonaldi, A. Borrielli, F. S. Cataliotti, F. Marino, G. A. Prodi, E. Serra, and F. Marin, Phys. Rev. Lett. 112, 023601 (2014)

    work page 2014

  64. [64]

    Kienzler, C

    D. Kienzler, C. Fl¨ uhmann, V. Negnevitsky, H.-Y. Lo, M. Marinelli, D. Nadlinger, and J. P. Home, Phys. Rev. Lett. 116, 140402 (2016)

    work page 2016

  65. [65]

    J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997)

    work page 1997

  66. [66]

    Duan and C

    L.-M. Duan and C. Monroe, Rev. Mod. Phys. 82, 1209 (2010)

    work page 2010

  67. [67]

    D.-L. Deng, X. Li, and S. Das Sarma, Phys. Rev. X 7, 021021 (2017)

    work page 2017

  68. [68]

    Cotrufo, A

    M. Cotrufo, A. Fiore, and E. Verhagen, Phys. Rev. Lett. 118, 133603 (2017)

    work page 2017

  69. [69]

    Zhou, C.-S

    Y. Zhou, C.-S. Hu, D.-Y. L¨ u, X.-K. Li, H.-M. Huang, Y.- C. Xiong, and X.-Y. L¨ u, Photonics Research 10, 1640 (2022)

    work page 2022

  70. [70]

    Hei, P.-B

    X.-L. Hei, P.-B. Li, X.-F. Pan, and F. Nori, Phys. Rev. Lett. 130, 073602 (2023)

    work page 2023

  71. [71]

    K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005)

    work page 2005

  72. [72]

    M¨ ucke, E

    M. M¨ ucke, E. Figueroa, J. Bochmann, C. Hahn, K. Murr, S. Ritter, C. J. Villas-Boas, and G. Rempe, Nature 465, 755 (2010). 7

    work page 2010

  73. [73]

    Hamsen, K

    C. Hamsen, K. N. Tolazzi, T. Wilk, and G. Rempe, Phys. Rev. Lett. 118, 133604 (2017)

    work page 2017

  74. [74]

    Lecocq, J

    F. Lecocq, J. D. Teufel, J. Aumentado, and R. W. Sim- monds, Nature Physics 11, 635 (2015)

    work page 2015

  75. [75]

    F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezz` e, A. Smerzi, M. Schulte, K. Hammerer, and P. O. Schmidt, Nature communications 10, 2929 (2019)

    work page 2019

  76. [76]

    X. Ma, J. J. Viennot, S. Kotler, J. D. Teufel, and K. W. Lehnert, Nature Physics 17, 322 (2021)

    work page 2021

  77. [77]

    M. G. Kozlov, M. S. Safronova, J. R. Cre- spo L´ opez-Urrutia, and P. O. Schmidt, Rev. Mod. Phys. 90, 045005 (2018)

    work page 2018

  78. [78]

    Pikovski, M

    I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. Kim, and ˇC. Brukner, Nature Physics 8, 393 (2012)

    work page 2012

  79. [79]

    Shomroni, A

    I. Shomroni, A. Youssefi, N. Sauerwein, L. Qiu, P. Sei- dler, D. Malz, A. Nunnenkamp, and T. J. Kippenberg, Phys. Rev. X 9, 041022 (2019)

    work page 2019

  80. [80]

    Vogel and R

    W. Vogel and R. L. d. M. Filho, Phys. Rev. A 52, 4214 (1995)

    work page 1995

Showing first 80 references.