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REVIEW 2 major objections 6 minor 34 references

Nanomechanical test of quantum linearity

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper proposes a phonon-counting optomechanical protocol that could test spontaneous-collapse models down to a collapse rate of $\lambda_c = 10^{-12}\,\mathrm{s}^{-1}$, enough to cover the proposed lower bounds on continuous…

desk verdict A careful, well-scoped design study for a CSL test, but the headline reach into Bassi/Adler territory hinges on two unmeasured optomechanical improvements that the paper itself flags as challenging. read the letter →

arxiv 1909.01608 v2 pith:PKA36JF3 submitted 2019-09-04 quant-ph

Stefan Forstner , Magdalena Zych , Sahar Basiri-Esfahani , Kiran E. Khosla , Warwick P. Bowen This is my paper · ORCID
classification quant-ph
keywords spontaneouswavefunctioncollapsecontinuouslocalizationoptomechanicsphononcountingnanomechanicalresonatorrateboundscoincidencedetectionquantummeasurementproblem
topics The Measurement Problem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Spontaneous collapse theories modify quantum mechanics with a stochastic nonlinear term, predicting that isolated mechanical oscillators should heat up at a rate set by a collapse parameter $\lambda_c$. The best existing tests cannot resolve the tiny predicted heating because thermal noise overwhelms the signal and the oscillators are too large and slow. This paper proposes a gigahertz nanomechanical resonator, cooled near its ground state in a dilution refrigerator, whose collapse-induced phonons are read out one at a time through an optomechanical Raman transition. With noise from heat, probe light, measurement backaction, and detector dark counts suppressed, the protocol reaches a minimum testable collapse rate of $\lambda_c = 1.0\times10^{-12}\,\mathrm{s}^{-1}$, which would cover both proposed lower bounds on $\lambda_c$ from latent-image formation and human-eye collapse. If realised, this would be the first experiment able to decisively test whether continuous spontaneous localization resolves the measurement problem.

What carries the argument

The central mechanism is a three-mode optomechanical phonon counter: a probe mode at $\omega_p$, a signal mode at $\omega_s=\omega_p+\Omega$, coupled by a gigahertz mechanical resonator. A collapse-induced phonon converts a probe photon to a signal photon via anti-Stokes Raman scattering, and the signal photon is filtered, downconverted to a pair, and counted in coincidence. The argument is carried by the master equation for the three modes, which yields the conversion efficiency $\eta_{\mathrm{om}}=0.32$, and by the estimate that measurement-induced phonons are suppressed by $(\Omega/\kappa_p)^2$ while dark counts are suppressed as $R_{d,1}R_{d,2}\tau_c$. This combination reduces every noise channel below the predicted collapse phonon flux for $\lambda_c\ge10^{-12}\,\mathrm{s}^{-1}$.

What would settle it

Build the proposed photonic-phononic crystal and measure its optical linewidth and single-photon coupling at 10 mK. If $\kappa_{p,0}=\kappa_{s,0}$ is not near $2\pi\times9.2\,\mathrm{MHz}$ or $g_0/2\pi$ is not near $11.5\,\mathrm{MHz}$, the predicted $\lambda_c=1.0\times10^{-12}\,\mathrm{s}^{-1}$ is not reachable. If the parameters are met, run the array of $10^4$ resonators for two days: a coincidence rate significantly above the predicted total background of $5.6\times10^{-10}\,\mathrm{s}^{-1}$ would indicate collapse-induced phonons, while a null result at that background would confirm the projected bound.

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Extended reading notes

Core claim

At the level of a single phonon, continuous spontaneous localization (CSL) predicts that a mechanical resonator is heated by a collapse noise field at rate $\dot n_c = \lambda_c D$, where $D$ is a geometry factor; for the proposed 136 fg photonic-phononic crystal $D = 5.1\times10^5$. The scheme counts these phonons by driving a probe optical mode and detecting anti-Stokes photons emitted into a signal mode at frequency $\omega_s=\omega_p+\Omega$, with $\Omega/2\pi=5.3\,\mathrm{GHz}$. After filtering, each signal photon is nonlinearly downconverted to a pair and registered only upon coincidence, suppressing dark counts to $3.7\times10^{-10}\,\mathrm{s}^{-1}$. The authors show, by solving the master equation, that thermal phonons, measurement-induced phonons, absorption heating, and leaked probe photons each contribute less than one coincidence per month, giving a total background of $5.6\times10^{-10}\,\mathrm{s}^{-1}$ and hence a minimum testable collapse rate $\lambda_c = 1.0\times10^{-12}\,\mathrm{s}^{-1}$. That rate is sufficient to test both the latent-image bound and the human-eye bound, and, because the resonator frequency lies near the conjectured cutoff $\Omega_{\mathrm{csl}}/2\pi\sim10^{10}$–$10^{11}\,\mathrm{Hz}$, the same apparatus could distinguish a physical origin of collapse from white-noise models.

Load-bearing premise

The whole projected sensitivity rests on two device improvements that have not yet been shown in the lab: a tenfold stronger photon–phonon coupling and a fiftyfold narrower optical resonance; if real devices deliver less, the claimed coverage of the collapse bounds fails.

Editorial extensions

If this is right

  • If the protocol is built, it would close the gap between current experimental upper bounds on $\lambda_c$ and the proposed lower bounds, giving the first conclusive test of CSL as a resolution of the measurement problem.
  • The thermal background at 10 mK for a 5.3 GHz oscillator is exponentially suppressed, so collapse-induced heating would appear above background; existing lower-frequency experiments cannot reach this regime.
  • With an array of $N\sim10^4$ resonators, the time to probe either proposed bound drops from more than 57 years to about two days, and the dark-count limit becomes negligible.
  • At frequencies near the conjectured cutoff, the protocol could distinguish coloured-noise collapse from white-noise CSL, and could support or rule out a cosmological origin for the collapse field.
  • The same setup is predicted to bound classical-channel gravity models roughly an order of magnitude more strongly than previous experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The quadratic-coupling variant described in the paper suggests a nearer-term path: zero-point quadratic couplings near $2\pi\cdot245\,\mathrm{Hz}$ already exceed the $2\pi\cdot28\,\mathrm{Hz}$ needed for the human-eye bound, so the decisive milestone is demonstrating suppression of linear coupling to $g/2\pi\lesssim0.1\,\mathrm{Hz}$.
  • The coincidence-downconversion readout is a generic low-dark-count phonon detector; the same trick could be applied to searches for rare events such as dark-matter or axion interactions, where detector dark counts are the limiting background.
  • If the required linewidth and coupling improvements are not reached, the minimum testable rate degrades through the conversion efficiency and the measurement-induced phonon background; quantifying that trade-off as $\lambda_c \propto \kappa^2/(g_0^2)$ would show which device parameter to push first.
  • Because the signal rate scales linearly with the geometry factor $D$ while the background does not, resonators engineered for larger $D$ (denser, heavier, or shaped to maximise the CSL decoherence operator) would extend the same protocol to smaller $\lambda_c$, at the cost of higher thermal occupation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 6 minor

Summary. The manuscript proposes a phonon-counting optomechanical protocol to test spontaneous collapse models, in particular Continuous Spontaneous Localization (CSL), using a gigahertz nanomechanical resonator at millikelvin temperatures. In the proposed three-mode optomechanical system, a weak probe mode and a signal mode are coupled by the mechanical resonator; a collapse-induced phonon enables anti-Stokes scattering of a probe photon into the signal mode. Signal photons are spectrally filtered, nonlinearly downconverted into photon pairs, and detected in coincidence to suppress dark counts. The authors estimate the CSL-induced phonon flux via a geometrical factor D=5.1×10^5, compute the thermal phonon flux analytically, solve a Born-Markov master equation for measurement-induced phonon noise, estimate photoabsorptive heating, and evaluate coincidence dark counts. With the assumed device parameters (g0/2π=11.5 MHz, κp,0=κs,0=2π·9.2 MHz, Ω/2π=5.3 GHz, T=10 mK), they report a minimum testable collapse rate λc=1.0×10^−12 s^−1, which would cover both Bassi et al.'s and Adler's proposed lower bounds; with an array of N~10^4 devices they estimate a measurement time of about two days. An alternative quadratic-coupling readout is also analyzed.

Significance. If the projected device parameters are realized, this is an important and timely proposal. It directly targets the main limitation of previous mechanical collapse tests—thermal noise—by combining a high-frequency resonator, cryogenic cooling, and quantum measurement techniques, and it would, for the first time, close the gap between measured upper bounds and proposed lower bounds for CSL. The noise budget is carefully constructed: the master-equation calculations of measurement-induced phonons, the explicit comparison of all noise sources in Table I, and the coincidence-counting scheme for dark-count suppression are genuine strengths. The protocol is also falsifiable in the sense that it specifies a concrete device, a concrete detection chain, and a concrete expected signal rate. However, the headline sensitivity is conditional on a joint extrapolation of optomechanical parameters that has not been demonstrated in a single device, so the contribution is best understood as a design study with a clear roadmap rather than a demonstrated experimental sensitivity.

major comments (2)
  1. [Table I; 'Feasibility and alternative parameter regimes'] The central claim that the protocol can test Bassi et al.'s and Adler's lower bounds rests on the simultaneous assumption of g0/2π=11.5 MHz and κp,0=κs,0=2π·9.2 MHz, a tenfold increase in single-photon coupling and a roughly fiftyfold reduction in optical linewidth relative to the demonstrated device of Ref. [38], with both values taken from theoretical predictions [39,40]. These parameters enter the conversion efficiency ηom and the measurement-induced phonon background, which scales as (Ω/κ)^2. With the demonstrated values (g0/2π≈1.15 MHz, κ/2π≈575 MHz), the resolved-sideband suppression is degraded by more than three orders of magnitude and ηom drops correspondingly, pushing the minimum testable collapse rate well above the Bassi et al. lower edge. The manuscript states that these improvements are 'challenging but plausible' but provides no sensitivity analysis or error budget. I request a quantitative analysis of λc,min as a function of g0 and κ (and, where relevant, detector dark counts), together with a discussion of whether the two predicted improvements are compatible in a single device.
  2. [Methods, 'Optical absorption heating'; Supplemental Note 2, 'Noise phonons due to photoabsorptive heating'] The absorption-heating estimate relies on an unproven model assumption: 'any discrete photon absorption event is expected to create a fixed amount of heat' once the interval between events exceeds the THz dissipation time. The numerical input n_abs,1=1.9×10^−9 is obtained by extrapolating from Refs. [17,34] with n_abs=10 at n_cav=1; no derivation or uncertainty is given. This term is small in the main protocol (Table I), so it does not by itself change the headline λc,min, but the paper's broader claim that optical absorption noise can be brought below the collapse lower bounds depends on this estimate. In the quadratic-coupling section the same model yields n_abs≈5 and a noise rate ≈3 s^−1, about seven orders of magnitude above the Bassi flux, and the proposed pulsed regime is only sketched. The authors should either derive this model or explicitly label it as an assumption, and quantify the impact of its uncertainty on both the main protocol and the quadratic-coupling alternative.
minor comments (6)
  1. [Reference list; main text Ref. [41]] Reference [41] is given as 'See Supplemental Material at []' with an empty URL; the placeholder should be completed with a DOI or a permanent link, since the Supplemental Material is an integral part of the noise budget.
  2. [Supplemental Note 2, Eq. (10)] The filter-transmission formula pf(Ω)=ηf[1+(4/κf)^2 sin^2(πΔ/ωfsr)]^−1 is dimensionally inconsistent as written if κf is a linewidth; the term (4/κf)^2 would carry units of time squared. Please clarify whether κf denotes a finesse or a normalized linewidth, and verify that the quoted pf=3.5×10^−10 follows from the stated cavity parameters.
  3. [References [80] and Supplemental Ref. [26]] Both references are listed as 'Calculations for other experiments to be published elsewhere', which is not a citable reference; these should be replaced by actual publications or removed.
  4. [Table I and surrounding text] The notation λc is used both for the CSL collapse rate and for the minimum testable collapse rate (e.g., 'λc=∑iλc,i' in the Table I caption). Please introduce an explicit symbol such as λc,min to avoid ambiguity.
  5. [Detector parameters, Ref. [47]] The dark-count parameters Rd=3.5 s^−1 and τc=30 ps are attributed to a private communication with PhotonSpot; since coincidence dark counts contribute a substantial share of the noise budget (λc,det=6.7×10^−13/N), a publicly available datasheet or published characterization would make the proposal more robust.
  6. [Throughout] There are several typographical and typesetting issues: 'The later approach' should read 'the latter approach' (Introduction); the Fig. 3 caption begins with the garbled 'Ea) b) c)'; and the symbol 'greaterorsimilar' appears in the Methods section where a typeset ≳ is intended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the minimum testable collapse rate is derived from stated device parameters and external benchmarks, with no fitted value or self-citation chain doing the work.

full rationale

The derivation chain is self-contained. The CSL phonon flux is n_dot_c = lambda_c D with D = 5.1e5 computed from the cuboid geometry via the standard CSL decoherence formula; the signal rate is R_c = lambda_c D eta with eta = eta_p eta_om eta_chi eta_d eta_f = 1.1e-3, and the minimum testable rate is lambda_c = sum_i lambda_c,i = 1.0e-12 s^-1 from the Table I noise rates. Each noise rate is computed with stated parameters and external benchmarks: thermal phonons from Gamma and T, optomechanical phonons from a Born-Markov master-equation solution with g0/2pi = 11.5 MHz and kappa_p0 = kappa_s0 = 2pi*9.2 MHz, dark counts from R_d = 3.5 s^-1 and tau_c = 30 ps, and filter leakage from a standard reference cavity. The g0 and kappa0 values are theory predictions [39,40], not measurements; the paper itself labels these improvements 'challenging but plausible'. That is a feasibility and correctness risk, not circularity, because eta_om = 0.32 and the noise rates are outputs of the model, not quantities fitted to the claimed lambda_c. The only self-referential item is the side claim about classical-channel gravity, where the Supplemental Material defers to '[26] Calculations for other experiments to be published elsewhere'; this is not load-bearing for the central CSL test, and the cited gravity papers are independent peer-reviewed work. The claimed lambda_c therefore does not reduce to its inputs by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The calculation rests on established CSL formulas, standard optomechanical master equations, and a set of assumed device parameters. The most load-bearing are the projected g0 and linewidth improvements, which are theoretical predictions rather than measured values. The absorption-heating model is an ad hoc extrapolation, though it contributes negligibly to the total noise. No new physical entities are introduced.

free parameters (6)
  • g0/2π = 11.5 MHz = 11.5 MHz (assumed)
    Tenfold enhancement over the demonstrated 1.15 MHz in MacCabe et al. [38], based on optimized designs [40]. Directly sets ηom = 0.32 and the optomechanical phonon background; the central λc_min scales with it.
  • κp,0 = κs,0 = 2π·9.2 MHz = 2π·9.2 MHz (theoretical)
    Scattering-limited intrinsic optical decay rates from Ren et al. [39], about 50 times narrower than the currently demonstrated linewidth. Needed for resolved-sideband operation and probe leakage suppression.
  • Absorption phonon number per probe photon, ¯nabs,1 = 1.9×10^-9
    Extrapolated from Meenehan et al. and Ren et al. under an assumed breakdown of the ¯nabs ∝ ¯ncav^{1/3} scaling. Enters Rabs; too crude to affect dominant noise, but an unverified model.
  • CSL geometrical factor D = 5.1×10^5
    Computed from the cuboid formula with dimensions 1.21, 0.22, 0.22 µm chosen to reproduce effective mass 136 fg. Converts λc into phonon flux; the cuboid approximation follows Vinante et al. [9].
  • Probe photon probability ηp = 0.01
    Chosen operating point balancing signal (∝ηp) against measurement-induced noise (∝ηp^2); it is a tunable experimental setting, not a fitted constant.
  • Detector dark count rate Rd and timing jitter τc = Rd = 3.5 s^-1, τc = 30 ps
    From private communication with PhotonSpot [47], not a public datasheet; sets the coincidence dark count floor 3.7×10^-10 s^-1, a dominant noise term.
assumptions (6)
  • domain assumption CSL collapse heating is correctly described by the phonon injection term ˙nc = λcD added to the master equation (Eq. 2).
    The whole test targets this predicted heating; the sensitivity calculation adopts the CSL model as the signal hypothesis, which is the standard approach for a model-testing experiment.
  • standard math Born-Markov master equation is valid in the regime g0 << Ω and Γ << κp, κs, g0.
    Stated in Methods; justifies the Lindblad treatment and the numerical conversion efficiencies.
  • domain assumption Cuboid approximation for the mechanical mode shape gives the correct D factor.
    Follows the method of Vinante et al. [9] for photonic-crystal beams; any error in D shifts the inferred λc proportionally.
  • domain assumption The filter cavity transmission and nonlinear downconversion to photon pairs perform as specified.
    Relies on standard laser stabilization cavities (Kessler et al.) and near-unit conversion (Langford et al.); small deviations affect ηf and ηχ but not order-of-magnitude conclusions.
  • ad hoc to paper Discrete photon absorption events create a fixed amount of heat once the interval between events exceeds the THz dissipation time.
    This breakdown of the ¯nabs ∝ ¯ncav^{1/3} relationship is introduced in Methods to estimate ¯nabs,1; it is not directly measured.
  • domain assumption The colored-noise collapse spectrum has a high-frequency cutoff Ωcsl/2π ≈ 10^10-10^11 Hz.
    Used only for identifying the physical origin of collapse; not needed for the white-noise CSL test.

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Pith. "Pith review of Nanomechanical test of quantum linearity." pith.science (2026). https://pith.science/paper/PKA36JF3

@misc{pith2026190901608,
  author       = {Pith},
  title        = {Pith review of: Nanomechanical test of quantum linearity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKA36JF3}},
  note         = {Machine review of arXiv:1909.01608}
}
read the original abstract

Spontaneous wavefunction collapse theories provide the possibility to resolve the measurement problem of quantum mechanics. However, the best experimental tests have been limited by thermal fluctuations and have operated at frequencies far below those conjectured to allow the physical origins of collapse to be identified. Here we propose to use high-frequency nanomechanical resonators to surpass these limitations. We consider a specific implementation that uses a quantum optomechanical system cooled to near its motional ground state. The scheme combines phonon counting with efficient mitigation of technical noise, including non-linear photon conversion and photon coincidence counting. It is capable of resolving the exquisitely small phonon fluxes required for a conclusive test of collapse models as well as potentially identifying their physical origin.

Figures

Figures reproduced from arXiv: 1909.01608 by the authors.

Figure 1
Figure 1. Illustration of protocol. Top left: array of optomechanical cavities. Top right: nonlinear pair production from a signal and pump photon (frequency ωpump). Bottom: Energy level diagram for scattering of a probe photon with a phonon. nb: phonon number. In this work we propose to test collapse theories with high frequency nanomechanical resonators. This offers the advantages of miniaturisation to match the expected co… view at source ↗
Figure 2
Figure 2. Heating rates of a Q = Ω/Γ = 107 silica sphere resonator vs. mechanical frequency and sphere diameter. Red traces: heating due to coupling to the thermal environment at temperatures 300,1 and 0.01 K. Gray shaded: Lower bounds on CSL heating rates for a sphere, according to Adler [21], Bassi et al. [20] and GRW [22], assuming the fundamental mechanical breathing mode frequency Ω = c/R, with sphere radius R and speed … view at source ↗
Figure 3
Figure 3. Signal pathways due to measurement-induced phonons. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Numerical calculations of noise magnitude. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Parameter diagram for CSL-model. Excluded upper bounds: gravitational wave detectors (yellow shaded); cold atoms (gray shaded); microcantilevers (dashed blue line); KDTL-interferometry (dashed black); Excluded for simple CSL only: neutron stars (dashed black) and X-ray…

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Reference graph

Works this paper leans on

34 extracted references · 30 canonical work pages

  1. [1]

    Bassi, K

    A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Reviews of Modern Physics 85, 471 (2012)

    work page 2012

  2. [2]

    Bassi, A

    A. Bassi, A. Großardt, and H. Ulbricht, Classical and Quantum Gravity 34, 193002 (2017)

    2017

  3. [3]

    Ferialdi and A

    L. Ferialdi and A. Bassi, Phys. Rev. A 86, 022108 (2012)

    work page 2012

  4. [4]

    L Adler and T

    S. L Adler and T. Brun, Journal of Physics A: Mathematical and General 34, 4797 (2001). 12

    work page 2001

  5. [5]

    Ghirardi, A

    G. Ghirardi, A. Rimini, and T. Weber, Physical Review D: Particles and Fields 34, 470 (1986)

    work page 1986

  6. [6]

    Pearle, Phys

    P. Pearle, Phys. Rev. A 39, 2277 (1989)

    work page 1989

  7. [7]

    G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990)

    work page 1990

  8. [8]

    Nimmrichter, K

    S. Nimmrichter, K. Hornberger, and K. Hammerer, Phys. Rev. Lett. 113, 020405 (2014)

    work page 2014

Show all 34 references
  1. [9]

    Vinante, M

    A. Vinante, M. Bahrami, A. Bassi, O. Usenko, G. Wijts, and T. H. Oosterkamp, Physical Review Letters 116, 090402 (2015)

    2015

  2. [10]

    Bassi and G

    A. Bassi and G. Ghirardi, Physics Reports 379, 257 (2003)

    2003

  3. [11]

    Bassi, E

    A. Bassi, E. Ippoliti, and B. Vacchini, Journal of Physics A: Mathematical and General 38, 8017 (2005)

    2005

  4. [12]

    Smirne and A

    A. Smirne and A. Bassi, Scientific Reports 5, 12518 (2015)

    2015

  5. [13]

    S. L. Adler and A. Bassi, Journal of Physics A: Mathematical and Theoretical 40, 15083 (2007)

    2007

  6. [14]

    S. L. Adler and A. Bassi, Journal of Physics A: Mathematical and Theoretical 41, 395308 (2008)

    2008

  7. [15]

    Bassi, D

    A. Bassi, D. A. Deckert, and L. Ferialdi, EPL (Europhysics Letters) 92, 50006 (2010)

    2010

  8. [16]

    Pearle, Wavefunction collapse models with nonwhite noise, in Perspectives on Quantum Reality (Springer, Dodrecht, 1996) pp

    P. Pearle, Wavefunction collapse models with nonwhite noise, in Perspectives on Quantum Reality (Springer, Dodrecht, 1996) pp. 93–109

    1996

  9. [17]

    MacCabe, H

    G. MacCabe, H. Ren, R. Luo, J. D. Cohen, H. Zhou, A. Sipahigil, M. Mirhosseini, and O. Painter, arXiv:1901.04129 (2019)

    2019 arXiv

  10. [18]

    Disi, Physics Letters A 105, 199 (1984)

    L. Disi, Physics Letters A 105, 199 (1984)

    1984

  11. [19]

    Di´ osi, Phys

    L. Di´ osi, Phys. Rev. A40, 1165 (1989)

    1989

  12. [20]

    Penrose, General Relativity and Gravitation 28, 581 (1996)

    R. Penrose, General Relativity and Gravitation 28, 581 (1996)

    1996

  13. [21]

    Kafri, J

    D. Kafri, J. M. Taylor, and G. J. Milburn, New Journal of Physics 16, 065020 (2014)

    2014

  14. [22]

    K. E. Khosla and S. Nimmrichter, arXiv:1812.03118 (2018)

    2018 arXiv

  15. [23]

    Altamirano, P

    N. Altamirano, P. Corona-Ugalde, R. B. Mann, and M. Zych, Classical and Quantum Gravity 35, 145005 (2018)

    2018

  16. [24]

    Ghirardi, R

    G. Ghirardi, R. Grassi, and A. Rimini, Physical Review. A 42, 1057 (1990)

    1990

  17. [25]

    Di´ osi, New Journal of Physics16, 105006 (2014)

    L. Di´ osi, New Journal of Physics16, 105006 (2014)

    2014

  18. [26]

    Calculations for other experiments to be published elsewhere

  19. [27]

    Kessler, C

    T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. Martin, L. Chen, and J. Ye, Nature Photonics 6, 687692 (2012). 13

    2012

  20. [28]

    Aspelmeyer, T

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

    2014

  21. [29]

    Hecht, Optics, Pearson education (Addison-Wesley, 2002)

    E. Hecht, Optics, Pearson education (Addison-Wesley, 2002)

    2002

  22. [30]

    Langford, S

    N. Langford, S. Ramelow, R. Prevedel, W. Munro, G. J Milburn, and A. Zeilinger, Nature 478, 360 (2011)

    2011

  23. [31]

    private communication with PhotonSpot

  24. [32]

    J. Chan, T. Alegre, A. Safavi-Naeini, J. Hill, A. Krause, S. Gr¨ oblacher, M. Aspelmeyer, and O. Painter, Nature 478, 89 (2011)

    2011

  25. [33]

    S. M. Meenehan, J. D. Cohen, S. Gr¨ oblacher, J. T. Hill, A. H. Safavi-Naeini, M. Aspelmeyer, and O. Painter, Phys. Rev. A 90, 011803 (2014)

    2014

  26. [34]

    H. Ren, M. H. Matheny, G. S. MacCabe, J. Luo, H. Pfeifer, M. Mirhosseini, and O. Painter, arXiv:1910.02873 (2019). 14

    2019 arXiv

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