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arxiv: 1907.11399 · v1 · pith:5E4UJB2Tnew · submitted 2019-07-26 · 🪐 quant-ph · physics.ins-det· physics.optics

Studying fundamental limit of optical fiber links to 10⁻²¹ level

Dan Xu , Won-Kyu Lee , Fabio Stefani , Olivier Lopez , Anne Amy-Klein , Paul-Eric Pottie This is my paper

Pith reviewed 2026-05-24 16:04 UTC · model grok-4.3

classification 🪐 quant-ph physics.ins-detphysics.optics
keywords optical fiber linkfrequency transfertwo-way comparisonfrequency stabilitynoise reciprocityinterferometric noiseultra-stable oscillator
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The pith

A self-synchronized two-way fiber setup measures one-way and round-trip noises simultaneously, yielding 4×10^{-21} stability for optical frequency transfer over 43 km after 16 days.

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

The paper introduces a hybrid optical fiber link that combines frequency transfer with a self-synchronized two-way comparison method. This allows simultaneous detection of round-trip noise and separate forward and backward one-way noises along the same fiber. Using data from 160000 seconds of continuous operation, the authors verify that noise accumulated in the forward and backward directions is reciprocal to within 3.1(±3.9)×10^{-20}. They also report the first experimental observation of interferometric noise between adjacent fibers at very low Fourier frequencies. Redundant estimates from the various signals converge on a transferred frequency stability and accuracy of 4×10^{-21} after 16 days of integration over 43 km.

Core claim

By acquiring multiple signals from the hybrid setup, the authors isolate and quantify the individual noise contributions in a bidirectional fiber link. They demonstrate that the accumulated phase noise is reciprocal between the two propagation directions to the level of a few parts in 10^{-20}. The same data set yields consistent estimates of the one-way transferred frequency stability reaching 4×10^{-21} after 16 days, while also revealing correlated noise features between neighboring fibers that appear as interferometric signatures at the lowest Fourier frequencies.

What carries the argument

Self-synchronized two-way comparison that extracts forward, backward, and round-trip fiber noises from the same data stream without separate synchronization hardware.

If this is right

  • Reciprocity of accumulated noise holds to 3×10^{-20} over 160000 s of continuous data.
  • Adjacent fibers exhibit measurable interferometric noise at the lowest Fourier frequencies.
  • Uni-directional urban fiber links can reach frequency comparison instability of 8×10^{-18}.
  • Redundant extraction methods produce mutually consistent stability figures at the 4×10^{-21} level.

Where Pith is reading between the lines

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

  • The technique could be scaled to longer metropolitan or inter-city links to test whether the same reciprocity holds at greater distances.
  • The observed low-frequency interferometric noise between fibers suggests a possible diagnostic tool for fiber network health or for sensing environmental perturbations.
  • If the 10^{-21} floor is reproducible, it opens the possibility of comparing optical clocks across fiber networks at the level needed to search for temporal drifts in fundamental constants.

Load-bearing premise

The synchronization and local electronics in the two-way setup add no unaccounted systematic frequency offsets to the extracted one-way noise estimates.

What would settle it

An independent frequency comparison between the link output and a co-located reference clock that deviates by more than 4×10^{-21} after 16 days of averaging would contradict the reported stability and accuracy.

Figures

Figures reproduced from arXiv: 1907.11399 by Anne Amy-Klein, Dan Xu, Fabio Stefani, Olivier Lopez, Paul-Eric Pottie, Won-Kyu Lee.

Figure 1
Figure 1. Figure 1: Experimental scheme for the hybrid fiber links. AOM, acousto-optic modulator; PD, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Measurements of frequency data acquired only at SYRTE: half the round-trip noise [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Measurement of three sets of TWU and three sets of TWB by combining the four [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Phase evolution of the bi-directional LTW observables: TWBs and TWNF, (b) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Modified Allan deviation(MDEV) of 3 bi-directional LTW observables TWB1, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Fractional frequency stabilities of TWB1 in terms of overlapping Allan deviation [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Long-term fractional frequency instabilities and (b) phase evolution of a uni [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
read the original abstract

We present an hybrid fiber link combining effective optical frequency transfer and evaluation of performances with a self-synchronized two-way comparison. It enables us to detect the round-trip fiber noise and each of the forward and backward one-way fiber noises simultaneously. The various signals acquired with this setup allow us to study quantitatively several properties of optical fiber links. We check the reciprocity of the accumulated noise forth and back over a bi-directional fiber to the level of $3.1(\pm 3.9)\times 10^{-20}$ based on a 160000s continuous data. We also analyze the noise correlation between two adjacent fibers and show the first experimental evidence of interferometric noise at very low Fourier frequency. We estimate redundantly and consistently the stability and accuracy of the transferred optical frequency over 43~km at $4\times 10^{-21}$ level after 16 days of integration and demonstrate that frequency comparison with instability as low as $8\times 10^{-18}$ would be achievable with uni-directional fibers in urban area.

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 / 1 minor

Summary. The manuscript presents an experimental hybrid optical fiber link over 43 km that uses a self-synchronized two-way comparison to simultaneously measure round-trip fiber noise and forward/backward one-way noises. It reports a reciprocity check of accumulated noise to 3.1(±3.9)×10^{-20} over 160000 s of continuous data, first experimental evidence of low-frequency interferometric noise between adjacent fibers, and redundantly consistent estimates of transferred frequency stability and accuracy at the 4×10^{-21} level after 16 days of integration. The work also projects that uni-directional fiber comparisons could reach 8×10^{-18} instability in urban environments.

Significance. If the accuracy claim is substantiated, the long continuous datasets (160000 s and 16 days), explicit uncertainty on the reciprocity test, and redundant consistency checks provide strong experimental support for characterizing fiber-link performance at the 10^{-21} level. These elements are genuine strengths for precision metrology applications in frequency transfer and optical clock comparisons.

major comments (2)
  1. [Setup description and accuracy estimation (abstract and corresponding methods section)] The central accuracy claim of 4×10^{-21} after 16 days (abstract) rests on the self-synchronized two-way comparison cleanly isolating forward/backward fiber noises from local electronics and synchronization hardware offsets. The reported reciprocity bound of 3.1(±3.9)×10^{-20} constrains only differential fiber noise and does not independently bound common-mode local contributions at the target level; explicit calibration or additional bounds on these offsets are required to support the accuracy estimate.
  2. [Accuracy and stability estimation section] The manuscript states that stability and accuracy are estimated 'redundantly and consistently,' but the full error budget, data exclusion criteria, and how local hardware systematics are quantified at 10^{-21} are not detailed in the provided summary. This information is load-bearing for the accuracy claim.
minor comments (1)
  1. [Abstract] Clarify in the abstract and main text the precise distinction between the reported stability (Allan deviation) and the accuracy (systematic offset) claims, including how each is extracted from the redundant signals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback on our manuscript. We respond to each major comment below and will revise the manuscript accordingly to address the points raised.

read point-by-point responses

  1. Referee: [Setup description and accuracy estimation (abstract and corresponding methods section)] The central accuracy claim of 4×10^{-21} after 16 days (abstract) rests on the self-synchronized two-way comparison cleanly isolating forward/backward fiber noises from local electronics and synchronization hardware offsets. The reported reciprocity bound of 3.1(±3.9)×10^{-20} constrains only differential fiber noise and does not independently bound common-mode local contributions at the target level; explicit calibration or additional bounds on these offsets are required to support the accuracy estimate.

    Authors: We agree that the reciprocity test constrains differential fiber noise between the forward and backward paths. The self-synchronized two-way architecture is intended to render local electronics and synchronization offsets common-mode, which are then suppressed in the differential signals. However, to strengthen the accuracy claim at the 4×10^{-21} level, we will add an explicit error budget and calibration details in the methods section of the revised manuscript, including quantitative bounds on residual common-mode local contributions. revision: yes

  2. Referee: [Accuracy and stability estimation section] The manuscript states that stability and accuracy are estimated 'redundantly and consistently,' but the full error budget, data exclusion criteria, and how local hardware systematics are quantified at 10^{-21} are not detailed in the provided summary. This information is load-bearing for the accuracy claim.

    Authors: The redundant estimates arise from cross-consistency among the simultaneously acquired round-trip, forward one-way, and backward one-way signals. We will expand the accuracy and stability estimation section in the revised manuscript to include the complete error budget, explicit data exclusion criteria, and the methods used to quantify local hardware systematics below the 10^{-21} level. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental measurements from acquired signals

full rationale

The paper describes an experimental fiber-link setup and reports stability/accuracy estimates extracted directly from 160000 s of continuous data and 16-day integrations. No derivation chain exists that reduces a 'prediction' or 'first-principles result' to its own inputs by construction. Reciprocity checks, noise correlations, and redundant estimates are computed from measured signals rather than fitted parameters renamed as outputs. No self-citation load-bearing steps, ansatz smuggling, or uniqueness theorems appear in the provided text. The work is self-contained against external benchmarks (acquired optical signals) and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental work; no free parameters, new axioms, or invented entities are introduced. Relies on standard domain assumptions of optical metrology (reciprocity in ideal bidirectional fibers, stationarity of noise statistics over long averages).

axioms (1)
  • domain assumption Standard assumptions of optical frequency transfer and fiber noise modeling hold (reciprocity, stationarity).
    Invoked to interpret the measured noise correlations and stability figures.

pith-pipeline@v0.9.0 · 5727 in / 1264 out tokens · 30388 ms · 2026-05-24T16:04:23.292750+00:00 · methodology

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    Introduction Optical fiber links have been developed rapidly for time dissemination and frequency transfer over the last decade [1,2]. They are the most efficient technique for the distant comparison of the rapidly progressing optical atomic clocks [3–8]. These impressive progresses in optical frequency metrology pave the way for a future redefinition of the ...

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    The two fibers, denoted by F1 and F2, are a pair of urban fibers of 43 km connecting two laboratories, SYRTE and LPL

    Experimental scheme The hybrid experimental scheme we implement for optical frequency transfer and comparison is shown in Fig.1. The two fibers, denoted by F1 and F2, are a pair of urban fibers of 43 km connecting two laboratories, SYRTE and LPL. An ANC setup is built on F1; an LTW setup is built on F2 as introduced in [18]. The fibers are fed with one ultra...

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    On PD1, one records the beat note between the laser beam reflected by FM labeled A and by p-FM labeled D, shown in Fig.1 as green filled circles

    Experimental results At SYRTE, we obtain four beat notes: one on PD1 and three on PD2. On PD1, one records the beat note between the laser beam reflected by FM labeled A and by p-FM labeled D, shown in Fig.1 as green filled circles. This signal exhibits the round-trip propagation noise on F1. It is detected, tracked and divided to apply an active noise comp...

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    the beat note between the local light and the virtual ultra-stable laser (the point D on p-FM), which is transferred backward on F2. We denote it the one-way backward term (OWB); 3) the beat note between the local light transferred forward on F2, reflected by p-FM, then transferred backward on F2, and the virtual ultra-stable laser transferred backward on ...

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    TWNF reaches2.6× 10−22 at 10000 s, which further indicates that TWNF is insensitive to diurnal noise bump due to Fig. 5. Modified Allan deviation(MDEV) of 3 bi-directional LTW observables TWB1, TWB2, TWB3, as well as TWNF (Λ-counting). Fig. 6. Fractional frequency stabilities of TWB1 in terms of overlapping Allan deviation (ADEV) and modified Allan deviatio...

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    Accuracy and reciprocity We evaluate the accuracy of the frequency comparison of the hybrid setup

    Uni-directional and bi-directional data over days 5.1. Accuracy and reciprocity We evaluate the accuracy of the frequency comparison of the hybrid setup. We calculate the arithmetic mean of the difference between the expected and the measured beat frequency of the relevant observables TWUs and TWBs introduced above. The statistical uncertainty is estimated...

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    optical fiber links chain

    Conclusion We present fully new data and data analysis for the2× 43 km hybrid fiber link. We demonstrate an hybrid setup suitable for the study of fundamental limits of fiber links, while being a very effective link for optical frequency dissemination and optical frequency comparison. We show that the hybrid setup evaluates uni-directional LTW abilities to r...

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