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REVIEW 3 major objections 5 minor 45 references

A phase-sensitive optomechanical amplifier for quantum noise reduction in laser interferometers

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A phase-sensitive optomechanical amplifier at an interferometer's output port can suppress readout-loss noise by its gain squared, improving squeezed-light gravitational-wave sensitivity.

desk verdict A careful, well-caveated design study showing how a Mach-Zehnder optomechanical amplifier could relax readout-loss requirements for squeezed-vacuum GW detectors, but the headline Voyager gain rests on an unvalidated package of optimistic parameter values. read the letter →

arxiv 1909.02264 v2 pith:W4C2HQIH submitted 2019-09-05 quant-ph physics.ins-det

Yuntao Bai , Gautam Venugopalan , Kevin Kuns , Christopher Wipf , Aaron Markowitz , Andrew R Wade , Yanbei Chen , Rana X Adhikari This is my paper · ORCID
classification quant-phphysics.ins-det
keywords squeezedvacuuminjectionoptomechanicalamplificationphase-sensitiveamplifiergravitational-waveinterferometersreadoutlossmitigationMach-Zehnderinterferometerquantumnoisecryogenicsilicondetector
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

The paper proposes placing a phase-sensitive optomechanical amplifier between a gravitational-wave interferometer's dark port and its photodetectors, and argues that this lets the detector exploit squeezed-vacuum injection despite a lossy readout chain. The central mechanism is that amplifying the signal quadrature by a factor $G$ before the lossy stage reduces the noise power added by readout loss from $\epsilon$ to $\epsilon/G^2$, so stronger squeezing survives without proportionally better photodetectors. Using the planned Voyager cryogenic upgrade as a case study, the authors simulate a Mach-Zehnder amplifier built from two triangular ring cavities with 30 g suspended mirrors and find a modest broadband sensitivity gain, largest in the 50–500 Hz band, when 15 dB of frequency-dependent squeezing is injected. They state explicitly that the benefit is contingent on internal interferometer losses and coating thermal noise being at or below the assumed values, while readout loss stays at the assumed 10%.

What carries the argument

The central object is a Mach-Zehnder optomechanical amplifier: two triangular ring cavities, each holding a low-mass suspended mirror, placed between two 50/50 beamsplitters so that the interferometer's dark-port field enters one port and a strong pump enters the other. In each ring the pump and signal beat to produce radiation-pressure forces that displace the mirror, phase-modulating the reflected light and anti-squeezing one quadrature while deamplifying the orthogonal one. This is what makes the amplifier phase-sensitive and therefore able to evade the added-noise limit that applies to phase-insensitive amplifiers. The gain is set by the parameter $K_A$ in Eqs. (6)–(9), which grows as the inverse square of signal frequency; an output filter cavity then provides a frequency-dependent homodyne angle so the amplified quadrature is read out where $K_A$ is large and the unamplified quadrature where it is small. The Mach-Zehnder topology also routes the strong pump out a separate port and gives common-mode rejection of pump intensity noise between the two rings.

What would settle it

A table-top version of the two-ring amplifier with a deliberately lossy readout should show the loss-induced noise falling as $G^{-2}$ as gain increases; if the loss penalty stays roughly constant, or if the noise floor follows the phase-insensitive amplifier limit, the central claim is wrong.

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Extended reading notes

Core claim

The paper's central claim is that a phase-sensitive pre-amplifier with gain $G$ converts the loss-limited noise spectrum $e^{-2r}+\epsilon$ of a squeezed readout into $e^{-2r}+\epsilon/G^2$, so the penalty for imperfect photodetection is divided by the amplifier gain squared rather than suffered in full. Its concrete discovery is an optomechanical implementation of that amplifier: a Mach-Zehnder layout in which the dark-port signal and a strong pump are combined on a 50/50 beamsplitter, sent through two triangular ring cavities whose low-mass mirrors amplify one quadrature via radiation pressure, and recombined so the strong pump exits a separate port. In the two-photon formalism the input-output relation is $b_1 = e^{2i\eta} b_{\mathrm{IFO},1}$ and $b_2 = e^{2i\eta}(-K_A b_{\mathrm{IFO},1} + b_{\mathrm{IFO},2})$, plus an added-noise term; the gain parameter obeys $K_A \simeq (0.01/T_A)(30\,\mathrm{g}/m_A)(P_{\mathrm{circ}}/40\,\mathrm{kW})(1.5\,\mathrm{kHz}/f)^2$, so low-frequency signals see the largest amplification. Combining this amplifier with an output filter cavity that rotates the readout quadrature with frequency, the paper computes total strain noise for the Voyager design and reports that the amplifier improves sensitivity across much of the band, with the largest gains at low frequencies where the optomechanical gain is highest.

Load-bearing premise

The scheme only helps if the interferometer's internal losses and coating thermal noise meet the paper's aggressive targets, such as 20 ppm arm loss, 300 ppm signal-recycling-cavity loss, and a factor-of-4–5 coating Brownian-noise reduction, while the readout loss stays at the assumed 10%.

Editorial extensions

If this is right

  • If the amplifier is installed and its gain is large, the effective readout loss seen by the squeezed field is $\epsilon/G^2$, so a detector with 10% readout loss behaves as though the loss were far smaller, letting injected squeezing do more of the noise suppression.
  • The benefit is concentrated where the optomechanical gain is highest; because $G \propto 1/f^2$, the amplifier most helps the 50–500 Hz band and needs the output filter cavity to avoid attenuating high-frequency signals.
  • Lighter amplifier mirrors increase the useful gain band; the paper finds a 3 g mirror gives more sensitivity improvement than a 300 g mirror, with 30 g chosen as a compromise for suspension thermal noise and power handling.
  • For the stronger 20 dB squeezing case the amplifier's payoff is larger, but it requires two input filter cavities, 10 g mirrors, and even lower internal losses.

Reading between the lines

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

  • If the $1/G^2$ scaling of readout-loss noise is generic for phase-sensitive pre-amplification, the same two-ring architecture could be adapted to other squeezed-light sensors, such as table-top metrology or quantum imaging, wherever photodetector efficiency is the limiting loss.
  • The least experimentally demonstrated component is the 40 m output filter cavity; a small-scale test that measures the frequency-dependent readout rotation and its added loss would directly probe whether the scheme's high-frequency behavior survives.
  • Because the amplifier's benefit depends on readout loss being the dominant loss, the design's real-world value will be set by the race between improvements in photodetector efficiency and improvements in interferometer internal loss; if internal losses improve faster, the amplifier becomes unnecessary.
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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

3 major / 5 minor

Summary. The paper proposes placing a Mach-Zehnder optomechanical amplifier between the antisymmetric port of a gravitational-wave interferometer and the readout chain, with the goal of suppressing the effect of readout loss on injected squeezed vacuum. Using the two-photon formalism, the authors derive the amplifier input-output relation (Appendix A), show that a phase-sensitive pre-amplifier suppresses the readout-loss term by the gain squared (Eq. 5), and present a full noise budget for the amplifier (ring-cavity loss, pump RIN, backscatter, coating Brownian, suspension thermal) and for the interferometer (arm loss, SRC loss, IFC/injection losses, coating Brownian). They simulate the sensitivity of LIGO Voyager with 15 dB (and in Appendix D, 20 dB) frequency-dependent squeezing, obtaining a modest improvement in the 50–500 Hz band (Figures 3 and 8). The authors are explicit that the improvement requires a package of optimistic parameters, including 30 ppm ring loss, 10^-9/√Hz pump RIN with 60 dB common-mode rejection, and a factor 4–5 reduction of test-mass coating Brownian noise.

Significance. The analytic machinery is sound: Appendix A gives a careful derivation of the Mach-Zehnder input-output relation, and Eq. (5) correctly captures the standard Caves idea that a phase-sensitive amplifier placed before loss reduces the effective loss by G^2. The noise decomposition in Figures 4 and 5 is useful and makes the assumptions transparent. The paper's main value is as an exploratory design study: it identifies a concrete optomechanical topology and enumerates the technical noise sources that would limit it, rather than claiming a ready-to-build device. If the assumed parameter package were met, the scheme would allow future detectors to benefit from stronger squeezing without proportionally better photodetectors; however, none of the key parameters (especially the coating Brownian reduction and the 30 ppm/60 dB amplifier package) is demonstrated, so the significance is conditional rather than established.

major comments (3)
  1. [Section V B and Figure 3] The claimed sensitivity gain relies on an assumed factor of 4–5 reduction in Voyager test-mass coating Brownian noise, with no concrete proposal or measurement. This is load-bearing because Eq. (9) shows the amplifier gain grows as f^-2, so the amplifier is most effective at 40–100 Hz, exactly where the nominal coating Brownian noise dominates (Section V B). If the coating noise is not reduced, the dominant noise is unaffected while the readout-loss term the amplifier suppresses is subdominant, so the Figure 3 improvement largely disappears. The authors should provide a sensitivity curve as a function of the coating-noise reduction factor (e.g., factors 1, 2, 4, 5) or otherwise identify the threshold at which the amplifier ceases to help.
  2. [Section IV A and Figure 4] At the assumed 30 ppm ring-cavity round-trip loss, amplifier optical loss is already the largest amplifier noise contribution. The 30 ppm figure is an estimate based on 5 ppm scatter per optic from an empirical scaling law plus absorption assumptions, and the proposed SiN/aSi coatings at 2 µm and 123 K are not demonstrated. Because the amplifier is only beneficial when its noise is below the readout-loss term it removes, a factor-of-two degradation in ring loss could remove the benefit; the manuscript should quantify this with a loss-sensitivity study (e.g., 15, 30, 60 ppm) and a discussion of the realism of 30 ppm for the proposed coating.
  3. [Section IV B] The pump RIN requirement of 10^-9/√Hz with 60 dB common-mode rejection is acknowledged by the authors as challenging, and Figure 4 shows that pump RIN is not far below the other amplifier noise terms. The design has no demonstrated operating point for either quantity; if common-mode rejection is 40 dB or RIN is a few times 10^-9/√Hz, the pump-noise term can become dominant. The authors should include a sensitivity analysis or at least an explicit margin statement showing how much degradation in RIN or common-mode rejection is tolerable before the Figure 3 improvement vanishes.
minor comments (5)
  1. [Abstract] The word 'through-out' in the abstract should be 'throughout'.
  2. [Table I] The entry 'Reflactive index' should be 'Refractive index'.
  3. [Section III B] The informal footnote 'E-mail me at: gautam@caltech.edu' could be replaced by standard corresponding-author formatting.
  4. [Section III C and Eq. (16)] The loss notation is inconsistent: Eq. (16) uses Ldet, while the following paragraph and Table I use LPD; please unify.
  5. [Appendix C] The text refers to Figure 6 in the ring-cavity analysis, but the figure appears only near the end of the paper; consider moving the schematic earlier for readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No constructional circularity: Eq. 5 is an analytic identity for a noiseless phase-sensitive amplifier, and the optomechanical gain is derived independently. Only minor non-load-bearing self-citations prevent a clean zero.

full rationale

The paper's derivation chain is: (i) show analytically that a noiseless phase-sensitive amplifier before readout loss suppresses the loss term by G^2 (Eq. 5); (ii) derive the optomechanical gain G from the ring-cavity input-output relation (Eqs. 6-10, Appendix A); (iii) add separately modeled amplifier noise sources (Section IV) and interferometer losses/coating noise (Section V); and (iv) combine these into the total sensitivity plots (Figures 3-5). Equation (5) is not a fitted prediction; it is a direct consequence of placing a gain G before a loss element, and G itself is computed from physical parameters (TA, mA, Pcirc, f) via Eq. (9) rather than tuned to match the final sensitivity curve. The design parameters in Table I were obtained by optimizing the modeled total noise, which is engineering design optimization rather than fitting a parameter to data and then claiming a prediction. The paper also explicitly states that the improvement is conditional: 'our amplification strategy will be appropriate for application only if the interferometer's internal losses, test-mass coating thermal noise, achievable injected squeezed vacuum, and all other pre-amplification noises in Voyager turn out to be the same as or better than what we have chosen here, and if the readout photodetector inefficiency... turn out to be the same as or worse than what we have chosen here.' This is a stated limitation, not a circular move. The self-citations include prior work by Yanbei Chen (Refs. [15], [23]) used for standard two-photon and interferometer transfer functions, and an in-preparation coating optimizer by the present authors (Ref. [33]) used for a subdominant amplifier coating noise estimate. These citations are not load-bearing in the sense of importing the conclusion: the central readout-loss-suppression result follows from Eq. (5) with an independently derived G, and the main sensitivity improvement also relies on external, published loss and coating assumptions. Therefore there is no constructional circularity, only minor non-load-bearing self-citation.

Assumptions & free parameters 9 free parameters · 7 assumptions · 0 invented entities

The proposal is not circular, but it relies on a long list of assumed technical parameters. The free parameters are design choices, not fitted data; the axioms are standard quantum optics, empirical scattering models, and stated domain assumptions. No new natural entities, forces, or particles are introduced.

free parameters (9)
  • Ring cavity round-trip optical loss = 30 ppm (15 ppm for 20 dB design)
    Assumed rather than measured; the paper states amplifier noise is dominated by this loss in Section IV A, so the central sensitivity gain depends on it.
  • Pump relative intensity noise amplitude = 1e-9 per root hertz with f0 = 50 Hz (Eq. 18)
    Imposed requirement; the authors say meeting it is challenging. Failure would erase the amplifier advantage.
  • Common-mode rejection ratio = 60 dB
    Assumed to reject pump intensity noise in the Mach-Zehnder topology; the authors note real detectors have achieved similar levels but tuning may be needed.
  • Amplifier mirror mass = 30 g (10 g for 20 dB design)
    Chosen as a compromise between gain and suspension noise; lighter mirrors improve gain but are harder to suspend.
  • M1 mirror transmissivity = 0.89 percent (0.90 percent for 20 dB)
    Optimized together with the output filter cavity to minimize total noise in the 50 to 500 Hz band.
  • Pump source power = 220 W (230 W for 20 dB)
    Chosen input power with power recycling to achieve 40 kW circulating power in each ring; high circulating power drives the gain.
  • Test-mass coating Brownian noise reduction factor = 4 to 5 times
    Assumed to fully exploit the amplifier; the authors state this is speculative and needed for the claimed sensitivity.
  • Readout chain loss = 10 percent
    Motivating assumption for Voyager; if actual readout loss is lower, the amplifier's benefit is reduced.
  • Output filter cavity parameters = Length 40 m, detuning -80.4 Hz, input coupler transmission 43 ppm
    Chosen to implement frequency-dependent readout; small changes alter the frequency-dependent gain curve.
assumptions (7)
  • standard math Two-photon formalism of Caves and Schumaker
    Used throughout; the paper relies on this framework for input-output relations and quadrature noise.
  • domain assumption Linearized optomechanical radiation-pressure coupling with a strong classical pump
    The ring-cavity input-output relation in Eq. A1 follows the standard optomechanical model of Ref. [15] and assumes the signal is much weaker than the pump.
  • domain assumption Lossless ring-cavity derivation followed by perturbative insertion of optical loss as vacuum noise
    Eq. 6 is derived in the lossless limit; optical losses are then added by hand as in Eq. 12. The accuracy of this split is not demonstrated.
  • domain assumption Empirical scatter-loss scaling law with A = 8e-3 nm^2 mm and gamma = 1.2
    Used to justify 5 ppm scatter per optic; the parameters come from prior cavity measurements and are extrapolated to this design.
  • standard math Fluctuation-dissipation theorem for suspension thermal noise
    Applied in Eq. 20 with assumed loss angles and fiber dimensions.
  • domain assumption Interferometer transfer functions and squeezed-vacuum models from Refs. [9] and [23] are correct for Voyager parameters
    The overall sensitivity calculation combines the amplifier with existing interferometer noise models without re-deriving them.
  • domain assumption Ideal 50/50 beamsplitters, no mode mismatch, and no alignment fluctuations at the amplifier input
    The Mach-Zehnder cancellation and forward/backward isolation assume symmetric cavities; the authors list alignment and mode-matching as unaddressed future work.

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Cite this review

Pith. "Pith review of A phase-sensitive optomechanical amplifier for quantum noise reduction in laser interferometers." pith.science (2026). https://pith.science/paper/W4C2HQIH

@misc{pith2026190902264,
  author       = {Pith},
  title        = {Pith review of: A phase-sensitive optomechanical amplifier for quantum noise reduction in laser interferometers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W4C2HQIH}},
  note         = {Machine review of arXiv:1909.02264}
}
read the original abstract

The sensitivity of future gravitational wave interferometers is expected to be limited through-out the detection band by quantum vacuum fluctuations, which can be reduced by quantum non-demolition methods such as squeezed vacuum injection. However, optical losses in the readout chainseverely limit the effectiveness of such schemes. We propose an optomechanical device to be installedat the output of the detector that mitigates the effect of readout loss, thus allowing the detector tobetter exploit quantum noise evasion schemes.

Figures

Figures reproduced from arXiv: 1909.02264 by the authors.

Figure 1
Figure 1. FIG. 1: Optical layout for the Mach-Zehnder ampli [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Optomechanical gain of the amplifier as a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Comparison of Voyager sensitivity with (solid [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Breakdown of the dominant noise sources in the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Breakdown of the dominant noise sources in the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: A three-mirror triangular ring cavity with pump [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Voyager sensitivity improvement as a function [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Sensitivity of LIGO Voyager for a more [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

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Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages

  1. [1]

    lighter masses in the amplifier (where the optome- chanical gain would extend to higher frequencies),

    work page

  2. [2]

    interferometers (with higher masses) which are lim- ited by shot noise rather than radiation pressure at lower frequencies (where there is already significant optomechanical gain),

    work page

  3. [3]

    ACKNOWLEDGMENTS We would like to acknowledge conversation with the Quantum Noise and Advanced Interferometer working groups of the LIGO Science Collaboration

    a hybrid diplexed crystal-optomechanical approach where a crystal amplifier is used to extend the op- tomechanical amplifier gain to higher frequencies. ACKNOWLEDGMENTS We would like to acknowledge conversation with the Quantum Noise and Advanced Interferometer working groups of the LIGO Science Collaboration. RXA thanks Carl Caves for several stimulating c...

    work page

  4. [4]

    Gw170814: a three-detector observation of gravitational waves from a binary black hole coales- cence

    Benjamin P Abbott, R Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, VB Adya, et al. Gw170814: a three-detector observation of gravitational waves from a binary black hole coales- cence. Physical review letters , 119(14):141101, 2017

    work page 2017

  5. [5]

    Observation of gravitational waves from a binary black hole merger

    Benjamin P Abbott, Richard Abbott, TD Abbott, MR Abernathy, Fausto Acernese, Kendall Ackley, Carl Adams, Thomas Adams, Paolo Addesso, RX Adhikari, et al. Observation of gravitational waves from a binary black hole merger. Physical review letters, 116(6):061102, 2016

    work page 2016

  6. [6]

    Gw151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence

    Benjamin P Abbott, R Abbott, TD Abbott, MR Aber- nathy, F Acernese, K Ackley, C Adams, T Adams, P Ad- desso, RX Adhikari, et al. Gw151226: Observation of gravitational waves from a 22-solar-mass binary black hole coalescence. Physical review letters , 116(24):241103, 2016

    work page 2016

  7. [7]

    Gw170104: observation of a 50-solar- mass binary black hole coalescence at redshift 0.2

    LIGO Scientific, BP Abbott, R Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, et al. Gw170104: observation of a 50-solar- mass binary black hole coalescence at redshift 0.2. Phys- ical Review Letters , 118(22):221101, 2017

    work page 2017

  8. [8]

    Carlton M. Caves. Quantum-mechanical noise in an in- terferometer. Phys. Rev. D , 23:1693–1708, Apr 1981

    work page 1981

Show all 45 references
  1. [9]

    Gw170817: observation of gravitational waves from a binary neutron star inspiral

    Benjamin P Abbott, Rich Abbott, TD Abbott, Fausto Acernese, Kendall Ackley, Carl Adams, Thomas Adams, Paolo Addesso, RX Adhikari, VB Adya, et al. Gw170817: observation of gravitational waves from a binary neutron star inspiral. Physical Review Letters , 119(16):161101, 2017

    2017

  2. [10]

    Gw170608: Observation of a 19 solar- mass binary black hole coalescence

    Benjamin P Abbott, R Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, VB Adya, et al. Gw170608: Observation of a 19 solar- mass binary black hole coalescence. The Astrophysical Journal Letters, 851(2):L35, 2017

    2017

  3. [11]

    Gwtc-1: a gravitational-wave transient catalog of compact binary mergers observed by ligo and virgo dur- ing the first and second observing runs

    LIGO Scientific Collaboration, Virgo Collaboration, et al. Gwtc-1: a gravitational-wave transient catalog of compact binary mergers observed by ligo and virgo dur- ing the first and second observing runs. arXiv preprint arXiv:1811.12907, 2018

    2018 arXiv

  4. [12]

    Enhanced sensitivity of the ligo gravitational wave detector by us- ing squeezed states of light

    Junaid Aasi, J Abadie, BP Abbott, Richard Abbott, TD Abbott, MR Abernathy, Carl Adams, Thomas Adams, Paolo Addesso, RX Adhikari, et al. Enhanced sensitivity of the ligo gravitational wave detector by us- ing squeezed states of light. Nature Photonics, 7(8):613, 2013

    2013

  5. [13]

    H. J. Kimble, Yuri Levin, Andrey B. Matsko, Kip S. Thorne, and Sergey P. Vyatchanin. Conversion of con- ventional gravitational-wave interferometers into quan- tum nondemolition interferometers by modifying their input and/or output optics. Phys. Rev. D , 65:022002, Dec 2001

    2001

  6. [14]

    The geo 600 squeezed light source

    Henning Vahlbruch, Alexander Khalaidovski, Nico Lastzka, Christian Gr¨ af, Karsten Danzmann, and Roman Schnabel. The geo 600 squeezed light source. Classical and Quantum Gravity , 27(8):084027, 2010

    2010

  7. [15]

    Abadie, B

    J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. Abernathy, C. Adams, R. Adhikari, et al. A gravita- tional wave observatory operating beyond the quantum shot-noise limit. Nature Physics, 7(12):962–965, 2011

    2011

  8. [16]

    Measurement of quantum back action in the audio band at room temperature

    Jonathan Cripe, Nancy Aggarwal, Robert Lanza, Adam Libson, Robinjeet Singh, Paula Heu, David Follman, Garrett D Cole, Nergis Mavalvala, and Thomas Corbitt. Measurement of quantum back action in the audio band at room temperature. Nature, 568(7752):364–367, 2019

    2019

  9. [17]

    Quantum tomography enhanced through parametric amplification

    E Knyazev, K Yu Spasibko, Maria V Chekhova, and F Ya Khalili. Quantum tomography enhanced through parametric amplification. New Journal of Physics , 20(1):013005, 2018

    2018

  10. [18]

    Overcoming inefficient detection in sub-shot- noise absorption measurement and imaging

    Eugene Knyazev, Farid Ya Khalili, and Maria V Chekhova. Overcoming inefficient detection in sub-shot- noise absorption measurement and imaging. Optics ex- press, 27(6):7868–7885, 2019

    2019

  11. [19]

    Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formal- ism

    Thomas Corbitt, Yanbei Chen, and Nergis Mavalvala. Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formal- ism. Phys. Rev. A , 72:013818, Jul 2005

    2005

  12. [20]

    Caves and Bonny L

    Carlton M. Caves and Bonny L. Schumaker. New formal- ism for two-photon quantum optics. i. quadrature phases and squeezed states. Phys. Rev. A , 31:3068–3092, May 1985

    1985

  13. [21]

    A cryogenic silicon interferometer for gravitational-wave detection

    Rana X Adhikari, Odylio Aguiar, Koji Arai, Bryan Barr, Riccardo Bassiri, Garilynn Billingsley, Ross Bir- ney, David Blair, Joseph Briggs, Aidan F Brooks, et al. A cryogenic silicon interferometer for gravitational-wave detection. arXiv preprint arXiv:2001.11173 , 2020

    2001 arXiv

  14. [22]

    R. X. Adhikari, P. Ajith, Y. Chen, J. A. Clark, V. Der- gachev, N. V. Fotopoulos, S. E. Gossan, I. Mand el, M. Okounkova, V. Raymond, and J. S. Read. Astrophys- ical science metrics for next-generation gravitational- wave detectors. Classical and Quantum Gravity , 36(24):24501...

    2019

  15. [23]

    negative inertia

    to get (in absence of optical losses) ( bIFO, 1 bIFO, 2 ) =e2iΦIFO ( 1 −KIFO 0 1 )( aIFO, 1 aIFO, 2 ) + √ 2KIFOeiΦIFO ( 1 0 ) h hSQL (11) Losses in the interferometer were treated in detail in [23], and will be further discussed in Section V. Here, up to leading order in power...

  16. [24]

    Carlton M. Caves. Quantum limits on noise in linear amplifiers. Phys. Rev. D , 26:1817–1839, Oct 1982

    1982

  17. [25]

    Schumaker and Carlton M

    Bonny L. Schumaker and Carlton M. Caves. New for- malism for two-photon quantum optics. ii. mathemat- ical foundation and compact notation. Phys. Rev. A , 31:3093–3111, May 1985

    1985

  18. [26]

    Thierry Botter, Daniel W. C. Brooks, Nathan Brahms, Sydney Schreppler, and Dan M. Stamper-Kurn. Linear amplifier model for optomechanical systems. Phys. Rev. A, 85:013812, Jan 2012

    2012

  19. [27]

    Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors

    Alessandra Buonanno and Yanbei Chen. Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors. Phys. Rev. D , 64:042006, Jul 2001

    2001

  20. [28]

    Isogai, J

    T. Isogai, J. Miller, P. Kwee, L. Barsotti, and M. Evans. Loss in long-storage-time optical cavities. Opt. Express , 21(24):30114–30125, Dec 2013

    2013

  21. [29]

    Applications of long storage time optical cavities

    Tomoki Isogai. Applications of long storage time optical cavities. PhD thesis, Massachusetts Institute of Tech- nology, Massachusetts Institute of Technology, February

  22. [30]

    Calculation method for light scattering caused by multilayer coated mirrors in gravitational wave detectors

    Simon Zeidler, Tomotada Akutsu, Yasuo Torii, Eiichi Hirose, Yoichi Aso, and Raffaele Flaminio. Calculation method for light scattering caused by multilayer coated mirrors in gravitational wave detectors. Opt. Express , 25(5):4741–4760, Mar 2017

    2017

  23. [31]

    Laser power stabilization beyond the shot noise limit using squeezed light

    Henning Vahlbruch, Dennis Wilken, Moritz Mehmet, and Benno Willke. Laser power stabilization beyond the shot noise limit using squeezed light. Phys. Rev. Lett. , 14 121:173601, Oct 2018

    2018

  24. [32]

    Laser power stabilization using optical ac coupling and its quantum and technical limits

    Patrick Kwee, Benno Willke, and Karsten Danzmann. Laser power stabilization using optical ac coupling and its quantum and technical limits. Appl. Opt. , 48(28):5423– 5431, Oct 2009

    2009

  25. [33]

    Lock Acquisition and Sensitivity Analy- sis of Advanced LIGO Interferometers

    Denis Martynov. Lock Acquisition and Sensitivity Analy- sis of Advanced LIGO Interferometers . PhD thesis, Cal- ifornia Institute of Technology, California Institute of Technology, May 2015. See section 8.3.4, in which the OMC reflectivity is measured

    2015

  26. [34]

    Gustafson, Rana X

    Ting Hong, Huan Yang, Eric K. Gustafson, Rana X. Ad- hikari, and Yanbei Chen. Brownian thermal noise in mul- tilayer coated mirrors. Phys. Rev. D , 87:082001, Apr 2013

    2013

  27. [35]

    Steinlechner, I

    J. Steinlechner, I. W. Martin, A. S. Bell, J. Hough, M. Fletcher, P. G. Murray, R. Robie, S. Rowan, and R. Schnabel. Silicon-based optical mirror coatings for ultrahigh precision metrology and sensing. Phys. Rev. Lett., 120:263602, Jun 2018

    2018

  28. [36]

    D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, and J. M. Parpia. Stress and silicon nitride: A crack in the universal dissi- pation of glasses. Phys. Rev. Lett., 102:225503, Jun 2009

    2009

  29. [37]

    Global optimization of multilayer dielectric coatings for precision measurements

    Gautam Venugopalan, Koji Arai, and Rana X Adhikari. Global optimization of multilayer dielectric coatings for precision measurements. In preparation

  30. [38]

    Silicon mir- ror suspensions for gravitational wave detectors.Classical and Quantum Gravity , 31(2):025017, Dec 2013

    A V Cumming, L Cunningham, G D Hammond, K Haughian, J Hough, S Kroker, I W Martin, R Nawrodt, S Rowan, C Schwarz, and A A van Veggel. Silicon mir- ror suspensions for gravitational wave detectors.Classical and Quantum Gravity , 31(2):025017, Dec 2013. See Eq. 1

    2013

  31. [39]

    Callen and Theodore A

    Herbert B. Callen and Theodore A. Welton. Irreversibil- ity and generalized noise. Phys. Rev., 83:34–40, Jul 1951

    1951

  32. [40]

    Development of mir- ror coatings for gravitational wave detectors

    Stuart Reid and Iain Martin. Development of mir- ror coatings for gravitational wave detectors. Coatings, 6(4):61, 2016

    2016

  33. [41]

    Engineering the optical spring via intra-cavity optical-parametric amplification

    Mikhail Korobko, F Ya Khalili, and Roman Schn- abel. Engineering the optical spring via intra-cavity optical-parametric amplification. Physics Letters A , 382(33):2238–2244, 2018

    2018

  34. [42]

    Overcoming the stan- dard quantum limit in gravitational wave detectors using spin systems with a negative effective mass

    F Ya Khalili and Eugene S Polzik. Overcoming the stan- dard quantum limit in gravitational wave detectors using spin systems with a negative effective mass. Physical re- view letters , 121(3):031101, 2018

    2018

  35. [43]

    J. D. Hunter. Matplotlib: A 2d graphics environment. Computing In Science & Engineering , 9(3):90–95, 2007

    2007

  36. [44]

    Evans, Lisa Barsotti, Jan Harms, Patrick Kwee, and H Miao

    Matthew J. Evans, Lisa Barsotti, Jan Harms, Patrick Kwee, and H Miao. Realistic filter cavities for advanced gravitational wave detectors. Physical Review D , 88, 05 2013

    2013

  37. [45]

    Practical speed meter designs for quantum nondemolition gravitational-wave interferometers

    Patricia Purdue and Yanbei Chen. Practical speed meter designs for quantum nondemolition gravitational-wave interferometers. Physical Review D, 66(12):122004, 2002

    2002

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