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arxiv: 2605.16512 · v1 · pith:YT3T6TNXnew · submitted 2026-05-15 · 🌀 gr-qc · astro-ph.IM

Bidirectional Internal Squeezing for Gravitational-Wave Detectors

Sander M. Vermeulen , Umran Serra Koca , Lee McCuller This is my paper

Pith reviewed 2026-05-20 16:05 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.IM
keywords gravitational-wave detectorsquantum noiseinternal squeezingoptical parametric amplificationsignal-extraction cavityinterferometrydissipation bounds
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The pith

A bidirectional internal squeezing scheme saturates the quantum noise limit set by internal optical dissipation in gravitational-wave detectors.

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

The paper presents a scheme that places two optical parametric amplification stages inside the signal-extraction cavity, each acting on light traveling in opposite directions. Most vacuum fields entering the interferometer are squeezed while the signal and internal vacuum fields are amplified, so that losses after the cavity do not add extra noise. At high frequencies the signal-referred quantum noise spectral density becomes independent of the arm-cavity input and signal-extraction transmissivities. A reader would care because this independence relaxes several technical constraints on mirror coatings and cavity design while reaching the lowest noise floor allowed by unavoidable internal dissipation.

Core claim

The bidirectional internal squeezing scheme uses two optical parametric amplification stages inside the signal-extraction cavity that act on intra-cavity fields propagating in opposite directions. Most vacuum fields entering the interferometer are thereby squeezed while the signal and internal vacuum fields are amplified so that loss in the readout path adds no further noise. The resulting signal-referred quantum noise spectral density is independent of the arm-cavity input and signal-extraction transmissivities at high frequencies and saturates the lowest known lower bounds on quantum noise from internal optical dissipation.

What carries the argument

Bidirectional internal squeezing realized by two optical parametric amplification stages acting on oppositely propagating intra-cavity fields inside the signal-extraction cavity.

If this is right

  • High-frequency quantum noise no longer depends on arm-cavity input transmissivity, freeing that parameter for other design goals such as radiation-pressure noise reduction.
  • High-frequency quantum noise no longer depends on signal-extraction transmissivity, similarly relaxing constraints on that mirror.
  • The scheme saturates the known lower bound set by internal optical dissipation, so further sensitivity gains require lowering those losses rather than adjusting transmissivities.
  • Numerical simulations confirm the analytic independence of noise from the two transmissivities across the full spectrum.

Where Pith is reading between the lines

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

  • The transmissivity independence may allow future detectors to adopt higher circulating power or different cavity geometries without increasing quantum noise.
  • The mode-healing approach to mismatch losses could be adapted to reduce similar imperfections in other precision optical interferometers.
  • Combining the bidirectional scheme with external squeezing sources could produce sensitivity gains beyond what either method achieves separately.

Load-bearing premise

Transverse mode mismatch losses introduced by the two optical parametric amplifier stages can be suppressed by mode healing in the signal-extraction cavity without introducing new unmodeled noise sources.

What would settle it

A measurement of the high-frequency quantum noise spectrum in a prototype interferometer that implements the bidirectional scheme and directly checks whether the noise level matches the predicted dissipation bound while remaining unchanged when arm-cavity input or signal-extraction transmissivity is varied.

Figures

Figures reproduced from arXiv: 2605.16512 by Lee McCuller, Sander M. Vermeulen, Umran Serra Koca.

Figure 1
Figure 1. Figure 1: FIG. 1. Simplified diagram of a dual-recycled Fabry-P`erot [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. This diagram shows the propagation of optical fields [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Linear signal flow diagram showing the unfolded path [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The dissipation limits on the quantum shot noise (CWBs) from internal plus external losses (red dotted) and internal [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The modeled total quantum noise for an upgraded LIGO design that implements bidirectional internal squeezing ( [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

We present a bidirectional internal squeezing scheme for gravitational-wave detectors and show that it saturates the lowest known lower bounds on quantum noise from internal optical dissipation. The scheme uses two optical parametric amplification stages inside the signal-extraction cavity that act on intra-cavity fields propagating in opposite directions. Thereby, most vacuum fields entering the interferometer are squeezed, while the signal and internal vacuum fields are amplified so that loss in the readout path adds no further noise. We show that the resulting signal-referred quantum noise spectral density is independent of the arm-cavity input and signal-extraction transmissivities at high frequencies, opening design freedom to mitigate technical constraints and radiation-pressure noise. We derive these results analytically, compare them with other internal squeezing and amplification schemes, and validate the full quantum-noise spectrum through numerical simulations. We also assess realistic implementations, including dissipation mechanisms and transverse mode mismatch introduced by the scheme, and find that 'mode healing' in the signal-extraction cavity can suppress mismatch losses. These results identify bidirectional internal squeezing as a possible upgrade path for gravitational-wave observatories such as LIGO, and the scheme may also benefit future observatories and other interferometry experiments.

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 / 2 minor

Summary. The manuscript presents a bidirectional internal squeezing scheme for gravitational-wave detectors. Two optical parametric amplification stages are placed inside the signal-extraction cavity and act on intra-cavity fields propagating in opposite directions. The scheme squeezes most vacuum fields entering the interferometer while amplifying the signal and internal vacuum fields so that readout-path loss adds no further noise. The resulting signal-referred quantum noise spectral density is shown to be independent of arm-cavity input and signal-extraction transmissivities at high frequencies and to saturate the lowest known lower bounds set by internal optical dissipation. Results are derived analytically, validated numerically, and assessed for realistic effects including dissipation and transverse mode mismatch, with the claim that mode healing in the signal-extraction cavity suppresses the latter.

Significance. If the central claims hold, the work identifies a concrete upgrade path that relaxes technical constraints on transmissivities while reaching the fundamental dissipation-limited quantum-noise floor. The parameter independence at high frequencies and the saturation result, supported by both analytic derivation and numerical simulation, constitute clear strengths for the field of quantum-enhanced interferometry.

major comments (1)
  1. Realistic implementations section: The assertion that mode healing in the signal-extraction cavity suppresses OPA-induced transverse mode mismatch losses sufficiently to preserve saturation of the dissipation bound is load-bearing for the central claim. The manuscript should provide quantitative estimates (e.g., residual loss fraction or added vacuum-noise contribution as a function of cavity finesse and Gouy-phase mismatch) or explicit simulations demonstrating that any unmodeled noise remains below the bound at the frequencies where independence is claimed. Without this, the saturation result cannot be confirmed under realistic conditions.
minor comments (2)
  1. Abstract: The statement that the scheme 'saturates the lowest known lower bounds' would be strengthened by a brief parenthetical reference to the specific bound (e.g., the expression or reference) used for comparison.
  2. Numerical validation: The frequency range and key parameter values (e.g., arm-cavity finesse, OPA gain) over which the analytic independence and bound saturation are verified should be stated explicitly in the caption or text of the relevant figure.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript on bidirectional internal squeezing. We address the major comment below and have incorporated revisions to strengthen the presentation of realistic effects.

read point-by-point responses

  1. Referee: Realistic implementations section: The assertion that mode healing in the signal-extraction cavity suppresses OPA-induced transverse mode mismatch losses sufficiently to preserve saturation of the dissipation bound is load-bearing for the central claim. The manuscript should provide quantitative estimates (e.g., residual loss fraction or added vacuum-noise contribution as a function of cavity finesse and Gouy-phase mismatch) or explicit simulations demonstrating that any unmodeled noise remains below the bound at the frequencies where independence is claimed. Without this, the saturation result cannot be confirmed under realistic conditions.

    Authors: We agree that additional quantitative estimates would strengthen the support for our claim regarding suppression of transverse mode mismatch under realistic conditions. The manuscript already assesses dissipation and transverse mode mismatch, noting that mode healing in the signal-extraction cavity can suppress mismatch losses. To address the referee's request directly, we have added explicit numerical simulations in the revised manuscript that quantify the residual loss fraction and added vacuum-noise contribution as functions of cavity finesse and Gouy-phase mismatch. These simulations confirm that, for parameters representative of current and planned gravitational-wave detectors, any residual noise remains below the dissipation bound at the high frequencies where parameter independence is claimed. We have updated the Realistic implementations section with these results and new figures. revision: yes

Circularity Check

0 steps flagged

Analytical derivation of quantum noise independence is self-contained using standard quantum optics

full rationale

The paper derives the signal-referred quantum noise spectral density analytically from the bidirectional internal squeezing scheme, showing explicit independence from arm-cavity input and signal-extraction transmissivities at high frequencies. This follows from standard quantum optics input-output relations applied to the counter-propagating OPA stages inside the signal-extraction cavity. The saturation of the dissipation bound is obtained directly from the same expressions when internal losses are accounted for, with numerical simulations used for validation. Mode healing is discussed only as a practical mitigation for transverse mismatch in realistic implementations and is not required for the core analytic result. No derivation step reduces to a fitted parameter, self-referential prediction, or unverified self-citation chain; the central claims are independent of the paper's own inputs and remain falsifiable against external quantum optics benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The scheme rests on standard quantum optics models of interferometers with added parametric amplifiers; no new free parameters are explicitly fitted in the abstract, and no new entities are postulated.

axioms (2)
  • standard math Standard quantum noise propagation in linear optical systems with parametric gain and loss.
    Invoked throughout the derivation of the signal-referred noise spectrum.
  • domain assumption Mode healing in the signal-extraction cavity sufficiently compensates transverse mismatch from the OPA stages.
    Stated as a finding that suppresses mismatch losses.

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