Temperature-insensitive tunable and stable Fabry-Perot cavity for atomic physics

Francisco S. Ponciano-Ojeda; Joshua Ruelle; Marion Delehaye; Martin Hauden

REVIEW 2 major objections 5 minor 23 references

Temperature-insensitive tunable and stable Fabry-Perot cavity for atomic physics

T0 review · 2 major / 5 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read A piezo-tunable Fabry-Perot cavity can cancel thermal expansion near 5 °C and hold fractional frequency stability of 4×10^{-13} at one second, without external length locks.

desk verdict Solid experimental demo of a piezo-tunable Zerodur cavity that hits mid-10^{-13} free-running stability at a measured CTE zero near 5 °C, with multi-condition data that actually support the claim for SR-laser use. read the letter →

arxiv 2603.11817 v2 pith:JBWZHVC2 submitted 2026-03-12 physics.optics physics.atom-phphysics.ins-det

Joshua Ruelle , Martin Hauden , Francisco S. Ponciano-Ojeda , Marion Delehaye This is my paper · ORCID

classification physics.opticsphysics.atom-phphysics.ins-det

keywords Fabry-PerotcavitycoefficientofthermalexpansionpiezoelectrictuningfrequencystabilitysuperradiantlaserQEDZerodurPound-Drever-Hall

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

Metrology cavities are built for extreme length stability; atom-cavity experiments need the resonance frequency to be tunable onto a narrow atomic line. Those two requirements usually fight each other, so most precision atom-cavity setups add external length-feedback systems. This paper shows that a carefully chosen stack of materials (Zerodur spacer, PZT rings, Kovar washers) produces a composite cavity whose overall thermal-expansion coefficient crosses zero near 5 °C. Operated at that temperature, with heavy electrical filtering of the piezos, the free-running cavity reaches 4×10^{-13} fractional frequency stability at one second and stays in the mid-10^{-13} range even when an atomic oven is running. That level is already low enough that a future ytterbium superradiant laser would not be limited by cavity noise, and it removes the need for continuous external length stabilization in many cavity-QED experiments.

What carries the argument

The composite thermal-expansion coefficient α_tot(T) formed by the length-weighted sum of Zerodur, PZT and Kovar contributions; its measured zero-crossing near 5 °C is the operating point that suppresses thermal length noise while the piezos still provide multi-FSR tunability.

What would settle it

Measure the Allan deviation of the same cavity while deliberately detuning the set-point by a few kelvin from the claimed zero-crossing; if the short-term floor rises by the amount predicted by the fitted CTE slope a_tot, the thermal-cancellation claim is confirmed; if it does not, the temperature-cancellation mechanism is not the dominant stabilizer.

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Extended reading notes

Core claim

A piezoelectrically tunable composite Fabry-Perot cavity whose coefficient of thermal expansion vanishes at (4.9 ± 0.5) °C achieves a free-running fractional frequency instability of 4 × 10^{-13} at 1 s integration time (and remains in the 10^{-13} range under realistic oven conditions), eliminating the need for external length stabilization in many atom-cavity experiments.

Load-bearing premise

Once the set-point sits at the zero-crossing temperature, residual temperature fluctuations of a few millikelvin are assumed small enough that the residual thermal-expansion noise stays below the observed 4 × 10^{-13} floor.

Editorial extensions

If this is right

Superradiant lasers targeting 10^{-18} fractional instability can run free of continuous cavity-length locks.
Other cavity-QED platforms that need both high finesse and atomic resonance can adopt the same passive temperature set-point instead of active feedback.
Frequency-dependent squeezing cavities or space-borne interferometers that require occasional tuning can use the same material stack for long-term passive stability.
Feed-forward or PID correction of residual temperature drifts can be added later without redesigning the spacer.

Reading between the lines

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

The same zero-crossing strategy could be retuned for other wavelengths simply by changing the relative thicknesses of the PZT and Kovar layers.
If the residual oven-induced gradients can be reduced further, the free-running floor may reach the thermal-noise limit of a few times 10^{-15} already estimated in the paper.
The design suggests that many existing piezo-tunable cavities could be re-operated at a carefully chosen temperature rather than rebuilt.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a clean experimental paper that does what it says: a composite Zerodur + PZT + Kovar cavity with optical access for atoms, voltage-tunable over FSRs, and free-running fractional frequency stability of 4×10^{-13} at 1 s when held at its measured CTE zero-crossing of (4.9±0.5) °C. Under realistic oven-on conditions it stays mid-10^{-13}. That combination is the actual new result; pure ultra-stable cavities and pure piezo-tunable cavities already exist, but this engineered stack places the zero near a convenient temperature while keeping the optical and mechanical features needed for cQED/SR work.

What they do well is the measurement campaign. Allan and Hadamard deviations are shown with PZTs disconnected, filtered, and unfiltered, at T0 versus room temperature, and with the atomic oven on/off. The reference chain (PDH lock → OFC → H-maser) is quantified, the low-pass filter that kills PZT voltage noise is described, and the temperature-step data that locate the zero-crossing are shown with a simple parabolic fit. The thermal-noise floor estimate (~3×10^{-15}) and acceleration-sensitivity simulation are secondary but consistent. Citations to NPL, Möhle, Numata/Kessler, etc., are appropriate; no circularity.

Soft spots are real but secondary. Finesse dropped from ~21 k to ~7 k after bake-out (possible NEG contamination); that is a practical nuisance for atom-cavity coupling but does not undercut the stability claim. Residual temperature stability (<2 mK out-of-loop) plus the fitted a_tot is assumed to keep thermal expansion below the observed floor once the set-point is fixed at T0; the multi-condition data make that assumption plausible rather than load-bearing. No active length feedback is used, which is the point of the paper.

This is for people building SR lasers, cQED systems, or frequency-dependent squeezing who need both tunability and mid-10^{-13} free-running performance without an external lock. The math and data are solid enough that a serious editor should send it to referees. I would cite it if I were designing a similar cavity, and I would bring it to reading group for the practical engineering details.

Referee Report

2 major / 5 minor

Summary. The manuscript reports a piezoelectrically tunable Fabry–Perot cavity built around a 50 mm Zerodur spacer, ring PZTs and Kovar washers, designed for an ytterbium superradiant-laser experiment. By operating at the measured CTE zero-crossing temperature T0 = (4.9 ± 0.5) °C of the composite stack, the free-running cavity reaches a fractional frequency instability of 4 × 10^{-13} at 1 s (Allan deviation) when the PZTs are either disconnected or low-pass filtered, and remains in the mid-10^{-13} range under realistic atomic-oven conditions. Optical, thermal and electrical characterizations (finesse, PZT voltage noise, temperature regulation, CTE mapping) are presented, together with multi-condition Allan and Hadamard deviations referenced to an H-maser via an optical frequency comb.

Significance. The work addresses a genuine practical bottleneck: the simultaneous need for cavity tunability and passive length stability at the 10^{-13} level required by active optical clocks and related cQED experiments. The multi-condition stability data (PZTs on/off/filtered, oven on/off, T0 versus room temperature) provide a clear experimental demonstration that external length feedback can be dispensed with for many atom-cavity applications. The design is transferable to other precision experiments that require both tunability and thermal-noise-limited performance (e.g., frequency-dependent squeezing, cavity-enhanced spectroscopy). Strengths include the transparent separation of noise sources and the direct comparison against an independent H-maser reference.

major comments (2)

The finesse after bake-out is only 6920 ± 40 (decay time 411 ns), attributed to possible NEG contamination. For the intended Yb SR laser the cavity must support high atom-cavity cooperativity; the manuscript should quantify whether this finesse still meets the design requirements or whether a re-coating / re-bake path is planned. Without that assessment the claim that the cavity is “ideal for ultra-stable superradiant lasers” rests on an incomplete optical characterization.
The residual thermal contribution is asserted to lie below the observed 4 × 10^{-13} floor once the set-point is fixed at T0. While the out-of-loop temperature stability (< 2 mK) and the fitted a_tot = (4.8 ± 0.9) imes 10^{-8} K^{-2} are consistent with this statement, an explicit calculation of the expected frequency noise from the measured temperature spectrum (or a short-term temperature Allan deviation converted via a_tot) would make the argument quantitative rather than qualitative.

minor comments (5)

Figure 3: the parabolic fit and the extraction of T0 and a_tot would be clearer if the raw frequency-versus-temperature data points were tabulated or if the fit residuals were shown.
Section 4.2: the mechanical resonances at 110 kHz and 10 MHz are mentioned; a short spectrum of the beat-note with and without the DC filter would strengthen the claim that the filter fully suppresses them.
Equation (1) and the subsequent discussion of α_PZT(T) rely on literature values whose temperature range (0–50 °C) is only partially overlapping with the operating point near 5 °C; a brief remark on the extrapolation uncertainty would be useful.
Typographical consistency: “5°C” versus “5 °C”, and occasional missing spaces around units (e.g., “50-mm”, “2mm-thick”).
The abstract states “around 5 °C” while the body reports (4.9 ± 0.5) °C; aligning the two statements would avoid minor confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: stability figures are direct counter measurements against an independent H-maser; the CTE zero-crossing is an operating point, not a definition of the result.

full rationale

The paper is an experimental demonstration of a composite Zerodur/PZT/Kovar cavity. Material CTEs are taken from literature or estimated, then the composite zero-crossing T0 is measured in situ by temperature steps and a parabolic fit (Fig. 3, §4.4); T0 is thereafter used only as the regulation set-point. Fractional frequency instabilities (Allan and Hadamard deviations in Fig. 4) are obtained by locking a 578 nm laser to the cavity via PDH and beating it against an optical frequency comb referenced to an independent hydrogen maser. Multi-condition data sets (PZTs disconnected/filtered/unfiltered, oven on/off, T0 vs room temperature) separate contributions without any quantity being predicted from a fit to a related subset of the same data. Thermal-noise estimates cite external calculations and are not load-bearing for the measured mid-10^{-13} floor. No self-definitional loop, fitted-input-as-prediction, uniqueness theorem imported from the authors, or renaming of a known result appears. The derivation chain is therefore self-contained against external metrological references.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard material properties, commercial component specifications, and a small number of fitted thermal coefficients extracted from the authors’ own temperature-step data. No new physical entities are postulated; the free parameters are ordinary experimental fit results used only to locate the operating point.

free parameters (3)

T0 (CTE zero-crossing temperature) = (4.9 ± 0.5) °C
Extracted from parabolic fit to frequency-vs-temperature step data; used as the regulation set-point for the best stability runs.
a_tot (linear CTE slope near T0) = (4.8 ± 0.9)×10^{-8} K^{-2}
Fitted coefficient that quantifies residual thermal sensitivity once the set-point is fixed at T0; enters the argument that temperature fluctuations remain tolerable.
a_PZT (PZT CTE temperature coefficient) = (-1.0 ± 0.2)×10^{-7} K^{-2}
Literature-based estimate used to choose Kovar washer thickness for cancellation; not re-measured in situ.

assumptions (4)

domain assumption Zerodur CTE is negligible (0 ± 5×10^{-8} K^{-1}) between 0–50 °C
Taken from manufacturer data and used in the composite CTE formula (Eq. 1).
domain assumption Kovar CTE is 5.86×10^{-6} K^{-1} (25–100 °C)
Literature value used to size the washers that cancel PZT expansion.
domain assumption Thermal-noise floor of the composite cavity is ~3×10^{-15}
Estimated from standard formulas (Numata, Kessler) and used only to argue that the observed 4×10^{-13} is not thermal-noise limited.
domain assumption H-maser + OFC transfer contributes σ_y = 10^{-13} (τ/s)^{-1/2}
Stated performance of the reference chain against which cavity stability is measured.

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Pith. "Pith review of Temperature-insensitive tunable and stable Fabry-Perot cavity for atomic physics." pith.science (2026). https://pith.science/paper/JBWZHVC2

@misc{pith2026260311817,
  author       = {Pith},
  title        = {Pith review of: Temperature-insensitive tunable and stable Fabry-Perot cavity for atomic physics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JBWZHVC2}},
  note         = {Machine review of arXiv:2603.11817}
}

abstract

Optical Fabry-Perot cavities are crucial tools for metrology experiments, where they achieve extreme length stability, and for some atomic physics experiments, where tunability to atomic transitions enables atom-light interactions. However, achieving both frequency stability and tunability in a single cavity has remained a challenge, forcing metrology experiments exploiting atom-cavity interactions to rely on external active feedback systems to stabilize the length of the cavity. Here, we describe a piezoelectrically-tunable cavity with a cancellation of the coefficient of thermal expansion at around $5^\circ\mathrm{C}$, achieving fractional frequency instabilities at the $4\times 10^{-13}$ level for 1~s integration time. This advance eliminates the need for external stabilization in many atom-cavity experiments, making this design ideal for applications such as ultra-stable superradiant lasers and other cavity quantum electrodynamics experiments.

Figures

Figures reproduced from arXiv: 2603.11817 by the authors.

**Figure 1.** 3D representation of the tunable Fabry-Perot cavity consisting of a 50-mm long Zerodur spacer and mirrors stacked on a PZT ring and a Kovar washer [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 3.** Cavity coefficient of thermal expansion measured by applying temperature steps [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Fractional frequency stability of the tunable cavity measured against the H [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

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Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.

[1] [1]

D. Lee, Z. Z. Hu, B. Lewis, A. Aeppli, K. Kim, Z. Yao, T. Legero, D. Nicolodi, F. Riehle, U. Sterr and J. Ye,Frequency stability of2.5×10 −17 in a Si cavity with AlGaAs crystalline mirrors, Phys. Rev. Lett.136(3), 033801 (2026), doi:10.1103/ zgrm-cjbb

2026

[2] [2]

D.G.Matei, T.Legero, S.Häfner, C.Grebing, R.Weyrich, W.Zhang, L.Sonderhouse, J.M.Robinson, J.Ye, F.RiehleandU.Sterr,1.5µm lasers with sub 10 mHz linewidth, Phys. Rev. Lett.118(263202) (2017), doi:10.1103/PhysRevLett.118.263202. 7

doi:10.1103/physrevlett.118.263202 2017

[3] [3]

Meiser, J

D. Meiser, J. Ye, D. R. Carlson and M. J. Holland,Prospects for a millihertz-linewidth laser, Phys. Rev. Lett.102(163601) (2009), doi:10.1103/PhysRevLett.102.163601

work page doi:10.1103/physrevlett.102.163601 2009

[4] [4]

M. A. Norcia, J. R. K. Cline, J. A. Muniz, J. M. Robinson, R. B. Hutson, A. Goban, G. E. Marti, J. Ye and J. K. Thompson,Frequency measurements of superradiance from the strontium clock transition, Phys. Rev. X8(021036) (2018), doi:10.1103/ PhysRevX.8.021036

2018

[5] [5]

G. A. Kazakov, S. Dubey, A. Bychek, U. Sterr, M. Bober and M. Zawada,Ultimate stability of active optical frequency standards, Phys. Rev. A106(5), 053114 (2022), doi:10.1103/PhysRevA.106.053114

work page doi:10.1103/physreva.106.053114 2022

[6] [6]

S. J. M. Kuppens, M. P. van Exter and J. P. Woerdman,Quantum-limited linewidth of a bad-cavity laser, Phys. Rev. Lett.72(24), 3815 (1994), doi:10.1103/PhysRevLett. 72.3815

doi:10.1103/physrevlett 1994

[7] [7]

M. A. Norcia and J. K. Thompson,Cold-strontium laser in the superradiant crossover regime, Phys. Rev. X6(011025) (2016), doi:10.1103/PhysRevX.6.011025

doi:10.1103/physrevx.6.011025 2016

[8] [8]

Axner, P

O. Axner, P. Ehlers, A. Foltynowicz, I. Silander and J. Wang,NICE- OHMS—Frequency Modulation Cavity-Enhanced Spectroscopy—Principles and Per- formance, pp. 211–251, Springer Berlin Heidelberg, ISBN 9783642400032, doi: 10.1007/978-3-642-40003-2_6 (2014)

work page doi:10.1007/978-3-642-40003-2_6 2014