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Measurement and feed-forward correction of the fast phase noise of lasers

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Pith's one-line read This paper reports a fully fiberized phase noise eater that measures fast laser phase noise with a delayed Mach-Zehnder interferometer and feedforward-corrects it with a fiber electro-optic modulator, cutting frequency-noise PSD by more…

desk verdict Solid instrument paper: the fully fiberized phase noise eater achieves the claimed >20 dB suppression at 1–10 MHz and the central result survives scrutiny; only reporting gaps need fixing. read the letter →

arxiv 2411.10021 v2 pith:PTOGB6U2 submitted 2024-11-15 physics.atom-ph physics.opticsquant-ph

Tom Denecker , Yukii Torii Chew , Oscar Guillemant , Genki Watanabe , Takufumi Tomita , Kenji Ohmori , Sylvain de Léséleuc This is my paper · ORCID
classification physics.atom-phphysics.opticsquant-ph
keywords laserphasenoisefrequencyPSDfeedforwardcorrectionMach-Zehnderinterferometerelectro-opticmodulatorRydbergquantumgatesRamanRamseyinterferometryfiberizedoptics
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

Lasers used to drive quantum gates in neutral atoms and trapped ions carry fast phase noise that standard feedback loops cannot remove, because loop latency limits correction to roughly a few MHz. This paper builds a fully fiberized 'phase noise eater' that measures the laser's frequency noise with a short-delay Mach-Zehnder interferometer and then applies an inverted copy of the noise to a fiber electro-optic modulator placed after a matching fiber delay. The result is a measured frequency-noise floor below 0.1 Hz²/Hz and a suppression of more than 20 dB in the 1 to 10 MHz Fourier range, with a peak of about 30 dB near 3 MHz where the noise is pushed to roughly 0.5 Hz²/Hz. The authors also show that the correction visibly improves a Ramsey interference signal on cold rubidium atoms driven by two such stabilized lasers. If the method holds up, it lets ordinary extended-cavity diode lasers serve in high-fidelity Rydberg and Raman gates without switching to far more expensive laser architectures.

What carries the argument

The load-bearing object is the delayed Mach-Zehnder interferometer used as a frequency discriminator, whose output voltage is proportional to the phase difference $\phi(t)-\phi(t-\tau)$ and, in the Fourier domain, has sensitivity $s(f)=s_0 \sin(\pi f \tau)/(\pi f \tau) e^{-i\pi f \tau}$. A low-pass filter with cut-off $f_c$ converts the frequency-proportional signal into a phase-proportional signal, and the feedforward path applies it to a fiber electro-optic modulator after a roughly 10 m fiber delay that matches the electronics delay. The correction transfer function $C(f)$ is the product of the interferometer response, the filter, the modulator $V_\pi$, the adjustable gain, and the adjustable delay; the noise PSD is reduced by $|1-C|^2$, so the whole scheme works by setting gain within about 3% and electrical delay within about 0.5 ns while keeping the Fourier frequency inside the band $30 f_c < f < 0.15/\tau$, here roughly a 60 kHz low-pass cutoff and a 20-22 ns interferometer delay.

What would settle it

Feed a laser whose own noise is far below the claimed floor (for instance a TiSapph laser) into the phase noise eater, or block the main beam while leaving the interferometer lit, and measure the output PSD with a second independent interferometer; if the delay line or the first interferometer adds noise at 1-10 MHz, the output PSD will rise above the 0.1 Hz²/Hz floor instead of staying at the detection limit.

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Extended reading notes

Core claim

The central claim is that a delayed Mach-Zehnder interferometer can act as both a sensitive fast frequency discriminator and the front end of a feedforward correction loop, and that the loop can cancel sub-microsecond laser phase noise at levels relevant to Rydberg and Raman gates. Operated at quadrature and calibrated through the interference fringe peak-to-peak voltage and the delay extracted from sensitivity nulls, the interferometer converts frequency fluctuations into a voltage with a known frequency-dependent response; a low-pass filter integrates that signal to recover phase fluctuations, and a fiber electro-optic modulator under a precisely matched gain and delay applies the correction. The paper reports the frequency-noise PSD of the corrected laser dropping from about 700 Hz²/Hz to as low as 0.5 Hz²/Hz at 3-4 MHz, a 31.5 dB reduction, with more than 20 dB suppression across 1-10 MHz, and it confirms the measured noise reduction matches the model built from the interferometer roll-off, filter dispersion, delay mismatch, and detection noise floor. On a Raman Ramsey sequence on 87Rb, activating the phase noise eater removes the periodic contrast collapse caused by a strong servo-bump in one laser.

Load-bearing premise

The whole correction rests on the assumption that the phase noise measured by the first interferometer is the same as the noise carried by the main beam after the 10 m fiber delay, so that the correction signal does not inject extra noise from the interferometer paths or the delay line itself; the authors rely on literature estimates rather than an in-situ measurement of the delay-line noise.

Editorial extensions

If this is right

  • An extended-cavity diode laser equipped with the phase noise eater can deliver frequency noise below about 1 Hz²/Hz in the 1-10 MHz band, replacing more costly VECSEL or self-injection-locked lasers in demanding gate applications.
  • Combined with a standard Pound-Drever-Hall feedback loop, the phase noise eater covers a noise spectrum from a few Hz to 10 MHz, offering a single low-noise source for Rydberg and molecular-state manipulation.
  • The 0.1 Hz²/Hz measurement floor lets the same fiberized interferometer serve as a fast laser-noise diagnostic, ranking lasers whose white-noise floors span eight orders of magnitude.
  • The demonstrated Raman Ramsey improvement indicates that phase-noise-driven contrast loss in two-photon atomic transitions can be inverted by feedforward correction.

Reading between the lines

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

  • A direct extension would be to use the same balanced interferometer output to cancel intensity noise at megahertz rates, since the paper already quantifies the residual amplitude modulation the electro-optic modulator adds.
  • With an automatic gain-control loop on the variable optical attenuator, the device could hold its optimum cancellation as laser power drifts, moving it from a laboratory setup toward a turnkey instrument.
  • The published acoustic-noise estimates for fibers leave open how far the approach can be pushed at lower Fourier frequencies; an in-situ measurement of the 10 m delay-line noise would settle the practical floor for metrology-style applications.
  • If the delay line is as quiet as the estimates suggest, cascading two feedforward stages could push cancellation beyond 30 dB or extend the corrected band above 10 MHz, where Rydberg-gate sensitivity falls but other fast processes may matter.
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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 / 7 minor

Summary. The paper reports a fully fiberized instrument that measures and corrects fast (sub-microsecond) laser phase noise. A fraction of the light is sent to a delayed Mach-Zehnder interferometer (MZI) used as a frequency discriminator; the resulting electronic signal is low-pass filtered, amplified, and fed forward to a fiber electro-optic modulator acting on the main beam, which is delayed in fiber to match the electronic latency. The authors report a reduction of the frequency-noise PSD of a DBR laser from about 700 Hz^2/Hz to about 0.5 Hz^2/Hz at 3-4 MHz (31.5 dB), more than 20 dB suppression over 1-10 MHz, and a detection noise floor below 0.1 Hz^2/Hz in some configurations. They also characterize the fast frequency noise of five laser types and show that the phase noise eater improves the contrast of a Ramsey sequence on cold 87Rb atoms driven on a Raman transition.

Significance. If the quantitative claims are reliable, the instrument provides a practical, waveguide-based solution to a recognized bottleneck for Rydberg and Raman quantum gates, with a simple calibration procedure and a component-level model (Eq. (7), Fig. 4) that reproduces the observed cancellation. The independent confirmation of the correction by a second MZI and by an atomic Ramsey signal is a notable strength, as is the direct comparison with a commercial phase-noise analyzer in Fig. 3(e). The paper should be useful to experimental groups seeking MHz-bandwidth phase-noise reduction without high-finesse cavity filtering.

major comments (2)
  1. [Abstract and Sec. III.C.b] The measurement-noise-floor claim is internally inconsistent. The abstract asserts a noise floor below 0.1 Hz^2/Hz, while Sec. III.C.b quotes an electronic floor of about 0.1 Hz^2/Hz for the transimpedance-amplified detector and a photon-shot-noise floor of 0.2 Hz^2/Hz, which combine to roughly 0.22 Hz^2/Hz in quadrature. The paper must specify which detector configuration produced the dark-blue floor in Fig. 1(c) and reconcile these numbers; if the floor in the feedforward characterization is ~0.2 Hz^2/Hz, the '<0.1 Hz^2/Hz' statement in the abstract should be qualified to the configuration in which it was actually achieved.
  2. [Sec. II and Fig. 1(c)] The headline suppression values (31.5 dB at 3-4 MHz, 'more than 20 dB' over 1-10 MHz, 'up to 30 dB at 3 MHz') are quoted without error bars, confidence intervals, or repeatability information. These are the central quantitative claims of the paper. Please provide at least the shot-to-shot spread of the measured PSD ratio, or an uncertainty budget propagated from the calibration of Vpp, tau, and the spectrum-analyzer settings, so the reader can assess whether the 20 dB and 30 dB claims are statistically distinct.
minor comments (7)
  1. [Sec. II] The sentence 'The noise is remains below 10 Hz^2/Hz over the entire 1 to 10 MHz region, with the correction decreasing outside this range' is garbled; it should read 'The noise remains below 10 Hz^2/Hz ... with the correction degrading outside this range.'
  2. [Sec. III.D] The sentence 'For all lasers, expect the VECSEL' contains a typo: 'expect' should be 'except'.
  3. [Sec. III.C.b] The statement 'Together, the electronic and photon shot noise add up to a detection limit ... giving 32 dB of signal-to-noise ratio' should specify the reference signal level and Fourier frequency used for the 32 dB number; otherwise it is ambiguous.
  4. [Sec. IV.A, Eq. (7)] The text says 'correction C(f) phi applied by the phase modulator' but C(f) multiplies the Fourier component of phi; please use a tilde or state explicitly that the equation is in the Fourier domain.
  5. [Sec. IV.C and Fig. 4(b)] The 'sum of these' model curve should state whether the four independent imperfections are added in linear units, in quadrature, or in dB; the current wording does not specify the combination rule.
  6. [Sec. IV.C] The discussion of fiber delay-line noise would be clearer with an explicit statement of why the 10^2 Hz^2/Hz acoustic-fiber-noise levels from Refs. [42,43] do not apply at 1-10 MHz in the present setup.
  7. [Sec. V] The Ramsey revival is compelling but qualitative; given the paper's own admission that the atom interrogation 'was not very sensitive', the text should state explicitly that the atom result is an illustrative demonstration rather than a quantitative fidelity measurement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the suppression claim is an independent in-situ measurement with an external atomic check.

full rationale

The paper's claimed derivation chain is self-contained. The feedforward correction transfer function (Eq. 7) is assembled from independently characterized quantities: the MZI delay τ calibrated from sensitivity nulls, the peak-to-peak voltage Vpp, the low-pass cutoff fc, the EOM half-wave voltage Vπ, and the amplifier/delay settings; none of these inputs equals the target suppression ratio. The central suppression claim is an in-situ measurement, not a prediction from fitted values: the second MZI placed after the EOM measures the actual corrected beam, so any noise added by the delay line or first MZI would appear in the output PSD and would prevent the reported 0.5 Hz²/Hz residual; the literature estimates for acoustic fiber noise in Sec. IV.C are therefore not load-bearing. The atomic Ramsey result in Sec. V provides an independent external check. Self-citations (Refs. [12], [45]) are descriptive (PDH signal extraction, apparatus description) and carry no load-bearing argument. The abstract's 0.1 Hz²/Hz noise-floor statement versus Sec. III.C.b's 0.2 Hz²/Hz shot-noise floor is a reporting inconsistency, not a circular step. No equation is equivalent to its inputs by construction, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The central instrument uses standard components, and the listed free parameters are measured calibrations or manually tuned control settings rather than hidden theoretical fudge factors. The most fragile unmeasured premise is the passivity of the fiber delay line at MHz Fourier frequencies, which the authors support only through literature estimates.

free parameters (3)
  • MZI delay tau = 22.4 ns (calibrated from sensitivity nulls)
    Used in the MZI frequency response and in the feedforward model Eq. (7). It is a measured calibration parameter extracted from the nulls of the interference sensitivity, not a free constant fitted to the suppression result.
  • Feedforward gain G = tuned to unity, within about 3%
    Manually adjusted with fixed attenuators and an optical attenuator to maximize cancellation (Sec. IV.B). This is a control setting rather than a hidden fit, but the central claim depends on it being set correctly.
  • Residual delay mismatch tau_d = approximately 0.5 ns (cable-length resolution limit)
    Included in the model's delay-error contribution shown in Fig. 4(b). The authors state it is the smallest delay resolution they had, not a number fitted to the measured curve.
assumptions (5)
  • domain assumption The laser field is described by E(t) = E0 cos(2*pi*nu0*t + phi(t)) with stochastic phase phi(t), and the one-sided PSD S_nu captures the noise relevant to gate errors.
    Standard laser phase-noise model used throughout Sec. III.A and in the gate-error motivation.
  • standard math The delayed MZI output at quadrature is a linear response to phase fluctuations, with exact Fourier relation V_tilde = s(f) nu_tilde given in Eq. (4).
    The entire measurement calibration and feedforward model rest on this linear-response relation; the detector and amplifier chain are assumed flat over the 1-10 MHz band.
  • domain assumption The RC low-pass filter acts as an ideal integrator for f >> fc, and the fiber EOM phase shift is linear with applied voltage.
    Used in Eqs. (6)-(7) and Sec. IV.B. The authors state the measured gain flatness was better than 3% over 1-10 MHz.
  • domain assumption The 10 m fiber delay line and the MZI paths add negligible phase noise at 1-10 MHz compared with the laser noise.
    Invoked in Sec. IV.C using literature estimates from Refs. [42,43] rather than an in-situ measurement. This is the weakest load-bearing premise and is mirrored in the weakest_assumption field.
  • domain assumption The Ramsey fringe contrast loss in Sec. V is dominated by laser phase noise, with Doppler and electric-field noise suppressed by using ground-state Raman transitions.
    Motivates the atom demonstration; the authors acknowledge the test was deliberately made sensitive by worsening the servo bump.

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Cite this review

Pith. "Pith review of Measurement and feed-forward correction of the fast phase noise of lasers." pith.science (2026). https://pith.science/paper/PTOGB6U2

@misc{pith2026241110021,
  author       = {Pith},
  title        = {Pith review of: Measurement and feed-forward correction of the fast phase noise of lasers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PTOGB6U2}},
  note         = {Machine review of arXiv:2411.10021}
}
abstract

Lasers are the workhorse of quantum engineering in the atomic-molecular-optic community. However, phase noise of the laser, which can be especially large in popular semiconductor-based lasers, can limit fidelity of operation. Here, we present a fully-fiberized instrument detecting and correcting the fast, sub-microsecond, phase fluctuations of lasers. We demonstrate a measurement noise floor of less than 0.1 Hz$^{2}$/Hz, and a noise suppression of more than 20 dB for Fourier frequencies in the 1 to 10 MHz region (reaching up to 30 dB at 3 MHz), where noise is critical for Rydberg-based quantum gates. Finally, we observe the improvement offered by this fast phase noise eater on a Raman transition driven by two such stabilized lasers. These measurement and correction techniques are important tools for high-fidelity manipulation of the excited electronic states of atoms and molecules.

Figures

Figures reproduced from arXiv: 2411.10021 by the authors.

Figure 1
Figure 1. FIG. 1. Measurement and correction of fast phase noise. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. A delayed MZI as a fast phase/frequency noise dis [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Gallery of laser frequency noise PSD. (a) Five lasers of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Feedforward correction results. (a) Elements in the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Atom interrogation. (a) Ramsey interferometry [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Reviewed August 12, 2026 · model on record in the stance chip above.