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arxiv: 2604.23835 · v1 · submitted 2026-04-26 · ⚛️ physics.ins-det · physics.optics· quant-ph

Squeezed state degradations due to mode mismatch and thermal aberrations in gravitational wave detectors

Kevin Kuns , Daniel Brown This is my paper

Pith reviewed 2026-05-08 04:53 UTC · model grok-4.3

classification ⚛️ physics.ins-det physics.opticsquant-ph
keywords mode mismatchthermal aberrationssqueezed lightgravitational wave detectorsquantum noisefrequency dependenceinterferometer optics
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The pith

Thermal aberrations create two frequency-dependent types of mode mismatch that degrade squeezed states 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 identifies two kinds of internal mode mismatch caused by thermal aberrations in the test mass optics. Mismatch from the quadratic part of the wavefront shows low-pass frequency dependence in its effect on squeezed light, while mismatch from higher-order aberrations shows high-pass dependence. This split determines which degradations matter most in present detectors versus those planned with higher power and longer arms. A clear picture of these dynamics is needed to reach the 10 dB squeezing goal and to maintain sensitivity gains.

Core claim

The central claim is that the mismatch between the quadratic component of the wavefronts of two optical modes due to thermal aberrations exhibits low-pass frequency dependence in its degradation of squeezed states, whereas the mismatch from all higher-order thermal aberrations shows high-pass behavior. As a result, the two sources produce different squeezing losses across frequency bands, with some effects already relevant for current detectors and others becoming important only for future instruments that use longer arms.

What carries the argument

The decomposition of thermal wavefront aberrations into a quadratic part and all higher-order parts, which produces the distinct low-pass versus high-pass dynamics of the resulting mode mismatch.

If this is right

  • Quadratic mismatch will limit squeezing performance at low frequencies in detectors operating today.
  • Higher-order aberrations will dominate degradation in future detectors that use longer arm cavities.
  • Characterization procedures can target separate frequency bands to isolate each mismatch type.
  • Thermal control systems can be designed to address the quadratic and higher-order components independently.

Where Pith is reading between the lines

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

  • Frequency-dependent squeezing filters may need adjustment that accounts for arm length to compensate the differing mismatch behaviors.
  • Active thermal compensation could be optimized to suppress the mismatch component that is strongest in a given frequency band.
  • The same quadratic-versus-higher-order split may appear in other high-power optical systems that rely on squeezed light.

Load-bearing premise

The analysis assumes that thermal aberrations generated by absorbed circulating arm power dominate internal mismatch sources and that separating the quadratic wavefront term from higher-order terms fully captures the frequency-dependent degradation behavior.

What would settle it

Measurements of the squeezing degradation spectrum versus frequency in an operating detector that fail to show a clear low-pass component tied to quadratic mismatch and a high-pass component tied to higher-order aberrations would falsify the predicted dynamics.

Figures

Figures reproduced from arXiv: 2604.23835 by Daniel Brown, Kevin Kuns.

Figure 1
Figure 1. Figure 1: Coupled cavity equivalent to the differential arm motion of a gravitational wave detector. The ellipses and circles view at source ↗
Figure 2
Figure 2. Figure 2: Coupled cavity signal flow diagram for the model of the fundamental and a single HOM described in Section view at source ↗
Figure 3
Figure 3. Figure 3: Optical path length differences resulting from the view at source ↗
Figure 4
Figure 4. Figure 4: Quantum noise budget for Cosmic Explorer with view at source ↗
Figure 5
Figure 5. Figure 5: Direct mode mismatch loss for ∆w/w = 5 % and Prel = 100 mW along with both types of aberrations separately for LIGO A♯ using the parameters of Table II. The dashed lines do not include radiation pressure and correspond to the discussion in Section IV A 1 while the solid lines include radiation pressure as discussed in Section IV A 2. The low-pass nature of quadratic mismatch and high-pass nature of higher … view at source ↗
Figure 6
Figure 6. Figure 6: Mode mismatch loss for Cosmic Explorer varying view at source ↗
Figure 7
Figure 7. Figure 7: Squeezed state rotation around the first HOM arm view at source ↗
Figure 8
Figure 8. Figure 8: Higher order mode resonances in CE for two different view at source ↗
Figure 9
Figure 9. Figure 9: Broadband rotation of the squeezed state. The peaks view at source ↗
Figure 10
Figure 10. Figure 10: A♯ quantum noise budget plotted as 10 log10[N(Ω)/Γ(Ω)] for the thermal state of view at source ↗
read the original abstract

To date, frequency-dependent squeezed light has been used to reduce quantum noise in interferometric gravitational wave detectors by 6.1 dB (a factor of two). Future upgrades and detectors aim to both reduce quantum noise by 10 dB (a factor of three) and to increase the circulating power in the interferometer arm cavities. Achieving these goals will be extremely challenging due, in part, to the degradations to the squeezed state caused by mode mismatch between the internal interferometer optical cavities and between the auxiliary external cavities. It is therefore imperative to gain a detailed understanding of all sources of mismatch and to obtain experience in mitigating their effects in the current detectors in order to improve astrophysical sensitivity now and in the future. Two types of internal mismatch are identified which are due to the thermal aberrations generated when the test mass optics absorb a small fraction of the circulating arm power. It is found that the dynamics responsible for the degradations caused by the mismatch between the quadratic part of the wavefront of two modes has a characteristic low-pass frequency dependence while the dynamics of the mismatch due to all higher order thermal aberrations has a high-pass behavior. As a consequence, the two types of mismatch are predominantly responsible for different squeezing degradations -- some of which are significant for the current detectors and some of which will only be important for future detectors with longer arms. The behavior of these two types of internal mismatch are described and the implications for detector design, operation, and characterization are discussed.

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

2 major / 2 minor

Summary. The manuscript analyzes mode-mismatch degradations to frequency-dependent squeezed light in gravitational-wave interferometers arising from thermal aberrations in the test-mass optics. It identifies two distinct internal mismatch mechanisms: quadratic wavefront mismatch (primarily curvature/defocus) whose squeezing degradation exhibits low-pass frequency dependence, and mismatch from all higher-order thermal aberrations whose degradation exhibits high-pass behavior. The paper discusses how these mechanisms dominate different squeezing loss channels at current versus future arm powers and arm lengths, and outlines implications for detector design, operation, and characterization.

Significance. If the reported frequency scalings hold, the work supplies a concrete, physically motivated framework for predicting and mitigating squeezing degradation as circulating power and arm length increase. This directly supports the community goal of reaching 10 dB squeezing while scaling arm power, and supplies testable signatures (low-pass versus high-pass roll-offs) that can be used in commissioning and in-situ characterization of current detectors.

major comments (2)
  1. [thermal aberration model and modal decomposition] The central claim—that quadratic wavefront mismatch produces low-pass dynamics while higher-order aberrations produce high-pass dynamics—rests on a clean modal decomposition without cross-terms. The manuscript must demonstrate (with explicit equations) that the projection of the thermal lens onto the fundamental mode does not mix low- and high-pass contributions via cavity filtering or Gouy-phase accumulation; otherwise the reported frequency scalings do not follow from the model.
  2. [assumptions and validity range] The analysis assumes thermal aberrations are linear in absorbed circulating power and that the quadratic/higher-order split accurately isolates the dynamics. The paper should quantify the size of any nonlinear or cross-term contributions (e.g., via the next-order term in the absorbed-power expansion) and show that they remain negligible across the power range considered for current and future detectors.
minor comments (2)
  1. [Introduction] The abstract cites 6.1 dB and 10 dB squeezing targets; the introduction should explicitly reference the experimental papers that achieved these values so readers can trace the performance baseline.
  2. [figures and notation] Notation for the wavefront decomposition (quadratic coefficient versus higher-order coefficients) should be defined once in a dedicated subsection and used consistently; several figures would benefit from explicit labels indicating which curve corresponds to the quadratic component.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments, which help clarify key aspects of our analysis. We address each major point below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [thermal aberration model and modal decomposition] The central claim—that quadratic wavefront mismatch produces low-pass dynamics while higher-order aberrations produce high-pass dynamics—rests on a clean modal decomposition without cross-terms. The manuscript must demonstrate (with explicit equations) that the projection of the thermal lens onto the fundamental mode does not mix low- and high-pass contributions via cavity filtering or Gouy-phase accumulation; otherwise the reported frequency scalings do not follow from the model.

    Authors: We appreciate the referee drawing attention to this foundational element of the model. In our analysis the thermal aberration is decomposed into orthogonal components (quadratic defocus versus higher-order terms) via overlap integrals with the cavity eigenmodes. The frequency scalings then follow from the distinct coupling of these components to the frequency-dependent squeezed vacuum: quadratic mismatch produces an effective low-pass filter through amplitude coupling, while higher-order terms produce high-pass behavior via phase and Gouy-phase-induced mode conversion. To make the absence of cross-mixing explicit, we will add the relevant overlap-integral equations and a short derivation showing that cavity filtering (a common frequency-dependent operator) and Gouy-phase accumulation do not introduce leading-order mixing between the quadratic and higher-order projections in the paraxial regime used throughout the paper. These equations will be inserted in Section III of the revised manuscript. revision: yes

  2. Referee: [assumptions and validity range] The analysis assumes thermal aberrations are linear in absorbed circulating power and that the quadratic/higher-order split accurately isolates the dynamics. The paper should quantify the size of any nonlinear or cross-term contributions (e.g., via the next-order term in the absorbed-power expansion) and show that they remain negligible across the power range considered for current and future detectors.

    Authors: We agree that an explicit bound on the linear approximation is valuable. The manuscript adopts the standard linear scaling of thermal aberrations with absorbed power, appropriate for the low absorption levels of fused-silica test masses. In the revision we will add a short calculation of the next-order (quadratic) term in the absorbed-power expansion, using representative absorption coefficients and thermo-optic constants. We will show that, for the arm powers and lengths considered (hundreds of kW to a few MW for current detectors; several MW for future detectors), the nonlinear contribution remains below a few percent and does not alter the reported low-pass versus high-pass scalings. This estimate will be placed in a new paragraph in Section II. revision: yes

Circularity Check

0 steps flagged

No circularity: frequency-dependent mismatch dynamics derived from independent optical modeling

full rationale

The paper models thermal aberrations in GW detectors by decomposing wavefront mismatches into quadratic (curvature) and higher-order components, then derives their distinct low-pass versus high-pass frequency responses in squeezing degradation from the underlying cavity dynamics and thermal lens effects. No equations or claims reduce by construction to fitted parameters, self-definitions, or self-citation chains; the separation and resulting behaviors follow from standard modal analysis and linear thermal absorption assumptions that remain externally falsifiable. The derivation is self-contained against benchmarks of interferometer optics and does not rely on renaming known results or importing uniqueness from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on standard optical-physics assumptions about thermal lensing and mode overlap; without the full text no additional free parameters or invented entities can be identified.

axioms (1)
  • domain assumption Thermal aberrations are generated when test mass optics absorb a small fraction of the circulating arm power.
    Explicitly stated in the abstract as the origin of the two mismatch types.

pith-pipeline@v0.9.0 · 5567 in / 1214 out tokens · 40373 ms · 2026-05-08T04:53:16.352305+00:00 · methodology

discussion (0)

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Reference graph

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