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REVIEW 2 major objections 5 minor 47 references

300 {\mu}s optical cavity storage time and $\mathbf{10^{-7}}$ active RAM cancellation for $\mathbf{10^{-19}}$ laser frequency stabilisation

T0 review · 2 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A 68 cm cavity with 300 µs storage time plus active RAM cancellation pushes RAM-induced laser frequency noise to $3\times 10^{-19}$, below the thermal noise floor.

desk verdict Record 300 µs cavity storage and 10^-7 RAM cancellation are real, but the 10^-19 frequency-stability headline is an overreach: it is a derived estimate, not a measured lock. read the letter →

arxiv 2504.16731 v1 pith:MLK23DYR submitted 2025-04-23 physics.optics physics.atom-ph

Adam L. Parke , Marco Schioppo This is my paper · ORCID
classification physics.opticsphysics.atom-ph
keywords residualamplitudemodulationRAMcancellationPound-Drever-Halllockingopticalreferencecavitystoragetimelaserfrequencystabilizationelectro-opticmodulatorfractionalinstability
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 claims that residual amplitude modulation (RAM) from the electro-optic modulator — the main technical noise that corrupts Pound-Drever-Hall locking signals — can be pushed so low that it no longer limits the stability of cavity-stabilized lasers. It does this by pairing a 68 cm optical cavity with a storage time of $\tau_{\mathrm{cav}}=(295\pm 2)\,\mu$s, the longest reported for a cavity with state-of-the-art thermal noise, with an active RAM-cancellation servo on a waveguide modulator that holds the RAM-induced voltage fluctuation at the $10^{-7}$ level. The measured RAM-induced fractional frequency instability is $1.3\times 10^{-18}$ at 1 s and $3\times 10^{-19}$ at 10–100 s, almost two orders of magnitude below the cavity's thermal noise limit of $2\times 10^{-17}$. If correct, RAM is no longer a barrier to $10^{-19}$ fractional frequency stabilization.

What carries the argument

The load-bearing object is the relation in Eq. (1): $\Delta f_{\mathrm{RAM}}/f_L = (\Delta V_{\mathrm{PDH\,RAM}}/V_{\mathrm{PDH\,PP}})(1/D)$, with $D\propto \tau_{\mathrm{cav}}$; it converts the RAM-induced voltage noise of the PDH error signal into a laser frequency instability. The second object is the active RAM-cancellation loop, which extracts a RAM error signal from a photodetector before the cavity and feeds a ~1 V bias voltage back to the EOM to cancel the amplitude modulation at its source. The third is the cavity itself: 68 cm length, $\tau_{\mathrm{cav}}=(295\pm 2)\,\mu$s ringdown, finesse $\simeq 410{,}000$, linewidth $\simeq 540$ Hz, from which $D=(4.7\pm 0.5)\times 10^{11}$ was measured directly by adding a 10\% DC offset to the PDH error signal and observing the resulting frequency shift.

What would settle it

Inject a known oscillating offset into the PDH error signal at frequencies between 0.1 and 100 Hz, with amplitude set so that the predicted fractional frequency shift via $D$ is around $10^{-18}$, and measure the actual laser frequency shift against an independent reference laser; if the measured response deviates from the DC-calibrated prediction by more than the quoted $3\times 10^{-19}$ level, the central claim fails.

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Extended reading notes

Core claim

The central claim is that the RAM-induced fractional frequency shift of a locked laser is governed by Eq. (1), $\Delta f_{\mathrm{RAM}}/f_L = (\Delta V_{\mathrm{PDH\,RAM}}/V_{\mathrm{PDH\,PP}})(1/D)$, with the normalized discriminator coefficient $D$ proportional to the cavity storage time $\tau_{\mathrm{cav}}$. The paper demonstrates this relation in a 68 cm cavity with $\tau_{\mathrm{cav}}=(295\pm 2)\,\mu$s and an active bias-field servo on a fibre-coupled annealed-proton-exchanged lithium-niobate waveguide EOM, reducing the normalized RAM voltage fluctuation to $6\times 10^{-7}$ at 1 s, $2.5\times 10^{-7}$ at 10 s, and $1.5\times 10^{-7}$ at 10–100 s. Using the directly measured $D=(4.7\pm 0.5)\times 10^{11}$, these correspond to RAM-induced laser fractional frequency instabilities of $1.3\times 10^{-18}$, $5\times 10^{-19}$, and $3\times 10^{-19}$ at the same integration times. The claim is that RAM has therefore ceased to be the limiting noise source for this design.

Load-bearing premise

The conversion of the measured RAM voltage noise into a frequency instability assumes that the discriminator coefficient $D$, calibrated by adding a 10% DC offset to the PDH error signal, applies unchanged to the oscillating RAM-induced noise; if RAM enters the loop through a different transfer function, the reported $10^{-19}$ values would not hold.

Editorial extensions

If this is right

  • At 10–100 s averaging, the RAM-induced instability of $3\times 10^{-19}$ sits almost two orders below the cavity thermal noise limit of $2\times 10^{-17}$, so RAM no longer sets the frequency-stability floor for this design.
  • A 68 cm cavity with 300 µs storage time and a directly measured discriminator coefficient is a practical route to $10^{-19}$ fractional frequency stabilization; the next limits are thermal noise and other technical noises, not RAM.
  • The active RAM cancellation works with a simple low-voltage bias servo and no temperature stabilisation, so it can be adopted in existing ultrastable laser systems without major redesign.
  • Maintaining the cancellation requires stable RF phases: a 10 mrad phase drift at 20 MHz degrades the RAM level from $2.5\times 10^{-7}$ to $5\times 10^{-7}$ at 10 s, so the RF path lengths must be controlled.

Reading between the lines

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

  • Because $D$ grows with $\tau_{\mathrm{cav}}$, pushing storage times beyond 300 µs or increasing finesse would push the RAM-induced instability below $10^{-19}$, provided the thermal noise limit is lowered in parallel; combining this RAM servo with cryogenic crystalline cavities could make RAM irrelevant at the $10^{-18}$ total-instability scale.
  • The same bias-port cancellation on an annealed-proton-exchanged waveguide EOM should transfer to other modulation-based locking schemes (FM spectroscopy, other wavelengths), wherever RAM sets a noise floor.
  • The RAM values were measured with an open test cavity and a beam stop, which the paper argues is an upper limit; a locked-cavity measurement would likely give even lower in-loop RAM, a testable consequence.
  • Fully digitising the error-signal extraction after photodetection could remove the RF pick-up and ground noise that currently limit 10 s to 100 s averaging, leaving the RAM term even more dominant as the residual.
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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 / 5 minor

Summary. The paper reports two technical advances for cavity-stabilized lasers: a 68 cm optical reference cavity with a measured ringdown storage time of (295 ± 2) µs (finesse ≈ 410,000) and an active residual amplitude modulation (RAM) cancellation scheme using an annealed-proton-exchanged lithium-niobate waveguide EOM with bias-field feedback. The authors measure the RAM-induced PDH error-signal voltage fluctuations with the cavity in an open (beam-blocked) configuration, normalize to the PDH error-signal peak-to-peak voltage, and convert to fractional laser frequency instability using a directly measured discriminator coefficient D = (4.7 ± 0.5) × 10^11. With active cancellation they report RAM-induced fractional frequency instability of 1.3 × 10^-18 at 1 s and 3 × 10^-19 at 10–100 s, about two orders of magnitude below the cavity thermal noise floor of 2 × 10^-17. The paper concludes that RAM no longer limits the stability of such cavity-stabilized lasers.

Significance. If the conversion from open-cavity voltage noise to locked-laser frequency instability is valid, the result is significant: it demonstrates that the RAM contribution can be pushed far below the thermal noise floor, and it provides a state-of-the-art storage time for an optical reference cavity. The direct measurement of the discriminator coefficient D, the explicit noise-floor characterization (DVM, mixer, PD noise), and the careful ringdown measurement are strengths; the reported numbers are conservative if the open-cavity measurement is indeed an upper bound. The claim of 10^-19 laser frequency stabilisation, however, is not demonstrated in total, since the cavity thermal noise floor of 2 × 10^-17 caps the overall locked-laser instability.

major comments (2)
  1. [Title and Abstract] The title states "for 10^-19 laser frequency stabilisation" and the abstract says "unlocking 10^-19 fractional frequency laser stabilisation," but the paper only measures the RAM-induced contribution to the frequency instability, not the total stabilised laser instability. The text explicitly states (after Fig. 2(b)) that the cavity has an estimated thermal noise limit of 2 × 10^-17, which caps the total fractional frequency instability of any laser locked to this cavity. The abstract and title should be reworded to refer to "RAM-induced fractional frequency instability at the 10^-19 level" or to "a step towards 10^-19 stabilisation," otherwise the central claim as presented is not supported by the measurements.
  2. [Eq. (1) and the paragraph beginning "Traditionally, the effects of RAM"] The conversion of the measured voltage noise into frequency instability uses ΔV_PDH_RAM measured with the beam stopper in the cavity (open test cavity) and V_PDH_PP measured from the cavity resonance sweep. The paper argues that this gives an upper limit because the reflection coefficient of a locked cavity near resonance is smaller than that of a mirror. However, Eq. (1) involves the ratio ΔV_PDH_RAM/V_PDH_PP, and if both quantities scale with the reflected carrier amplitude, the ratio would be approximately invariant rather than an upper bound. The authors should either provide a quantitative analysis of how the cavity reflection coefficient affects both numerator and denominator, or explicitly label the reported 1.3 × 10^-18 and 3 × 10^-19 values as conservative upper bounds. This is load-bearing because the headline numbers are obtained solely through this conversion.
minor comments (5)
  1. [Fig. 2(b) caption] The caption reports "τ_cav = (295 ± 2) ms" but the text gives (295 ± 2) µs; the caption unit should be corrected to µs.
  2. [Fig. 2(b) inset] The inset shows a ringdown in air with τ_cav = 14 µs, but the caption text mentions "Chamber pressure 6 × 10^-8 mbar"; clarify that this pressure applies to the vacuum measurement only.
  3. [Paragraph reporting numerical values] The RAM-induced frequency instability values (1.3 × 10^-18, 5 × 10^-19, 3 × 10^-19) are reported without uncertainties; given the 10% uncertainty on D, a propagation of this uncertainty would be useful for readers.
  4. [Fig. 3(c) and text] The power spectral density values are given as "~10^-30 Hz^-1" and "~10^-35 Hz^-1"; specify the frequency at which these are evaluated (the text says 10 s integration time, which corresponds to 0.1 Hz, but the axis should make this clear).
  5. [Conclusion] The phrase "the demonstrated simplicity, robustness and effectiveness of this technique has the potential for a wide application" is vague; consider specifying the intended applications (optical clocks, spectroscopy, gravitational-wave lasers) and any limitations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the reported 10^-19 RAM-induced instability is obtained by applying a directly measured discriminator coefficient to an out-of-loop voltage measurement, not by fitting or renaming an input.

full rationale

The derivation chain is self-contained and not circular. The headline RAM-induced fractional frequency instability is computed from Eq. (1), Δf_RAM/f_L = (ΔV_PDH_RAM/V_PDH_PP) × (1/D), where both factors are independently measured: the voltage ratio is an out-of-loop measurement with the RAM servo on and off (Fig. 3), and D is measured directly by adding a known 10% DC offset to the PDH error signal and observing the resulting frequency shift against a reference laser (Fig. 2(c)). D is not adjusted to reproduce the 10^-19 values; it is reported with its measurement uncertainty as (4.7 ± 0.5) × 10^11. The storage time τcav = (295 ± 2) µs is a direct ringdown exponential fit, not an input chosen to force the discriminator. The paper explicitly chooses direct measurement over literature-derived D because of inconsistencies in the literature, which avoids importing D from τcav. The only self-citations [4,24] are contextual examples of state-of-the-art instability, not load-bearing premises, and no uniqueness theorem or ansatz is imported from prior work. The paper even states that the open test cavity gives an upper limit for RAM, and it reports separate DVM, mixer, and mixer+PD noise floors, so the reported values are not obtained by construction. Any concern that the DC discriminator calibration may not fully characterize the transfer of time-varying RAM noise at 0.01–1 Hz is an experimental validity question, not circularity: the target frequency values are not used as inputs to the calibration or to any fit.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central numbers rest on measured calibration parameters, tau_cav and D, and on standard cavity and PDH models. The most important model assumption is that Eq. (1) is a faithful linear transfer relation between RAM-induced error-signal voltage and laser frequency shift. No new physical entities are introduced.

free parameters (5)
  • EOM bias voltage V_bias = ~1 V
    Manually set to minimize RAM; load-bearing for the active cancellation but not fitted to the headline frequency values.
  • Modulation depth = 15%
    Chosen as a trade-off between PDH error-signal size and sideband harmonics; affects the calibration and conversion of the error signal.
  • Cavity ringdown decay time tau_cav = 295 +/- 2 microseconds
    Exponential fit to ringdown transmission data; used to compute finesse and linewidth and to support the claimed record storage time.
  • Discriminator coefficient D = 4.7 +/- 0.5 x 10^11
    Measured by applying a 10% offset modulation to the PDH error signal and observing the resulting laser frequency shift; used to convert all RAM voltage noise into fractional frequency instability.
  • RF phase offset phi_RAM = optimum, not specified
    Passive delay line phase tuned to maximize RAM cancellation; the paper shows a 10 mrad deviation degrades cancellation from 2.5e-7 to 5e-7.
assumptions (6)
  • domain assumption Equation (1): delta_f_RAM / f_L = (delta_V_RAM / V_PP) * (1 / D), with D proportional to tau_cav
    Stated as the transfer relation between RAM voltage noise and frequency deviation; used to convert all measured RAM levels into frequency instability. It is not derived in the paper. Appears after Eq. (1) in Letter 3.
  • domain assumption D = f_L / Gamma from Ref. [18]
    Used as a cross-check for the directly measured discriminator coefficient; if this relation were wrong, the conversion scale would shift, though the authors favor the direct measurement.
  • standard math tau_cav = L_cav / (c A) for a symmetric cavity and F = pi * tau * c / L_cav
    Standard cavity relations used to compute finesse and linewidth from the ringdown decay time.
  • domain assumption The cavity thermal noise limit is 2e-17 fractional frequency
    Stated without derivation or citation; used to argue that the RAM-induced instability is almost two orders of magnitude below the cavity floor.
  • domain assumption APE waveguide transmits a single polarization and the angled cut suppresses etalons
    Taken from cited device literature, Ref. [23]; motivates the EOM choice and the claim of homogeneous, low RAM.
  • domain assumption The 10% offset used for D calibration stays in the linear regime of the PDH error signal
    The paper says this explicitly; if the response is nonlinear, the D calibration and the subsequent RAM-to-frequency conversion would be distorted.

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Cite this review

Pith. "Pith review of 300 {\mu}s optical cavity storage time and $\mathbf{10^{-7}}$ active RAM cancellation for $\mathbf{10^{-19}}$ laser frequency stabilisation." pith.science (2026). https://pith.science/paper/MLK23DYR

@misc{pith2026250416731,
  author       = {Pith},
  title        = {Pith review of: 300 \mus optical cavity storage time and $\mathbf10^-7$ active RAM cancellation for $\mathbf10^-19$ laser frequency stabilisation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MLK23DYR}},
  note         = {Machine review of arXiv:2504.16731}
}
abstract

Frequency stabilisation of lasers to optical reference cavities is an established method to achieve state-of-the-art stability. The strengths of this method are the high discriminator coefficient of optical cavities, and the low-noise extraction of the stabilisation signal using modulation techniques. In this Letter we report beyond state-of-the-art performance on both of these fundamentals, unlocking $10^{-19}$ fractional frequency laser stabilisation. We employ a 68 cm long cavity to realise an optical storage time of 300 microseconds, achieving ultrahigh frequency discrimination. We develop a simple and robust scheme to actively cancel residual amplitude modulation (RAM) at the $10^{-7}$ level in an annealed-proton-exchanged lithium-niobate waveguide electro-optic-modulator (EOM).

Figures

Figures reproduced from arXiv: 2504.16731 by the authors.

Figure 1
Figure 1. Experimental scheme for active RAM cancellation and characterisation. The red (grey) lines represent the free-space optical path (electronic connections) and fibre connections are labeled "fibre". VRF (Vbias) is the RF modulation signal (bias voltage for RAM stabilisation) applied to the EOM. M are mirrors, ISO are free-space optical isolators, L are lenses, PBS is a polarising beam splitter, BS is a beam splitter, … view at source ↗
Figure 2
Figure 2. (a) Photograph of the 68 cm long cavity used in this Letter. (b) Black points are ringdown measurements in vacuum and in air (in inset plot). The green (red) line is an exponential fit to the ringdown measurement in vacuum (air). (c) Diagram representing the measurement method of the discriminator coefficient D. The blue part of the diagram shows a modulation of the PDH error signal offset at 10 percent of the PDH e… view at source ↗
Figure 3
Figure 3. (a) Time traces of the PDH error signal, with RAM cancellation off (red line) and on (blue line). (b) and (c) are respectively, the corresponding modified Allan deviations (MDEV) and power spectral densities of the PDH error signal measured in different conditions: with RAM cancellation off; with RAM cancellation on; with no light on the PDH PD (Mixer + PD noise); with the PDH mixer terminated at 50 Ω (Mixer noise) … view at source ↗

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