Effect of helium surface fluctuations on the Rydberg transition of trapped electrons

Denis Konstantinov; Mikhail Belianchikov; Natalia Morais

REVIEW 3 major objections 6 minor 27 references

Effect of helium surface fluctuations on the Rydberg transition of trapped electrons

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Sub-hertz oscillations of the superfluid helium surface—read out through the Rydberg transition of trapped electrons—are traced to the inertia of superfluid film flow inside the microchannel cell.

desk verdict The paper reports a real, under-studied sub-hertz helium-level oscillation in a microchannel electron trap, but the amplitude and frequency arithmetic both need fixing before the quantitative story should be taken at face value. read the letter →

arxiv 2501.07971 v1 pith:74UYPY3M submitted 2025-01-14 cond-mat.mes-hall cond-mat.quant-gasphysics.app-ph

Mikhail Belianchikov , Natalia Morais , Denis Konstantinov This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.quant-gasphysics.app-ph

keywords electronsonheliumRydbergtransitionsuperfluidfilmmicrochanneldevicesub-hertzoscillationsStarkshiftimage-chargedetectiontransport-currentmeasurement

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

This paper reports that the Rydberg transition of electrons trapped on liquid helium in a microchannel device oscillates in time with a period of about 7 seconds when the cell is given a small thermal pulse. The oscillations correspond to slow, weakly damped changes in the depth of the helium filling the channel, which shift the electron transition frequency through the Stark effect by about 10 mV in equivalent bias. The authors attribute the motion to the inertia of superfluid film flow connecting the microchannels to the bulk helium reservoir, and a simple oscillator estimate gives 0.4 Hz, in reasonable order-of-magnitude agreement with the observed 0.14 Hz. If the attribution is right, this sub-hertz surface motion is a distinct, potentially controllable mechanical noise source for electrons-on-helium qubits, separate from the cryostat vibrations studied before.

What carries the argument

Two models carry the argument. First, the parallel-plate capacitor description of the charged helium surface in the channel, Eqs. (2)–(3), relates the perpendicular electric field on the electrons to the helium depth $z$ and gives the linear conversion $\delta V_B = \delta z (V_B - V_T)/z$ between a depth change and the equivalent bias shift of the Rydberg resonance; this turns the measured Stark shifts into physical depth amplitudes of 180–250 nm. Second, the superfluid film-inertia oscillator, $\omega = \sqrt{gS/(LA)}$, with $S$ the film cross-section, $A$ the total channel area, and $L$ the connector length, supplies the predicted sub-hertz frequency that the authors compare with the observed 7 s period.

What would settle it

Shorten the film flow path by replacing the five cylindrical connectors with a single connector of half the total length, keeping the fill level fixed, and re-measure the oscillation period: the proposed model predicts $f \propto 1/\sqrt{L}$, so the 7 s period should shrink to about 5 s, and an unchanged period would rule out the film-inertia origin.

Watch

Extended reading notes

Core claim

The central claim is that the temporal dynamics of the Rydberg transition of electrons in a microchannel device reveal a weakly damped oscillation of the liquid helium depth with a period of about 7 s (frequency about 0.14 Hz), and that this oscillation originates from the inertia of superfluid film flow inside the experimental cell. At the onset of the oscillations the helium depth varies by roughly 180–250 nm, shifting the Rydberg resonance by about 10 mV in equivalent bias voltage. The image-charge signal and the transport-current signal oscillate together with the expected $\pi$ phase difference, showing that both readouts see the same helium-depth motion. The proposed mechanism, modeled as an inertia-dominated oscillator $\omega = \sqrt{gS/(LA)}$ with a 30 nm superfluid film covering five cylindrical connectors, yields about 0.4 Hz, which the authors call satisfactory agreement with the measured 0.14 Hz for such a simplified estimate.

Load-bearing premise

The frequency comparison assumes that the superfluid film connecting the microchannels to the bulk helium is a uniform roughly 30 nm thick layer coating all five cylindrical connectors, so that the oscillator formula $\omega = \sqrt{gS/(LA)}$ correctly describes the restoring flow; if the real film thickness, wetted area, or flow path differs substantially, the predicted 0.4 Hz would not match the observed 0.14 Hz even though the oscillation itself is well documented.

Editorial extensions

If this is right

Electrons-on-helium qubits operated in microchannel devices will be subject to slow helium-depth motion in the sub-hertz range, so Rydberg transition frequencies can drift by tens of millivolts in equivalent bias on a timescale of seconds.
Because the oscillations are triggered by small thermal pulses and persist for minutes to thousands of seconds, heat from filament charging or millimetre-wave excitation can leave a long-lived mechanical memory in the helium surface.
The $\pi$ phase difference between the image-charge and transport-current oscillations indicates that the effect is a genuine change in helium depth rather than an electronic artifact of the detection circuit.
The frequency estimate depends on the geometry of the film path, so changing the connector length, the channel area, or the bulk helium level should shift the period in a predictable way and can serve as a direct test of the proposed origin.
Reducing thermal excitation of the cell or decoupling the microchannel liquid from the film-connected reservoir should suppress or eliminate this particular surface-fluctuation source.

Reading between the lines

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

A testable extension of the paper's mechanism is that the oscillation frequency should scale as the square root of the film cross-section divided by the connector length, so a cell with a shorter or wider film path should show a measurably different period while retaining the same qualitative damped response.
In our reading, the Rydberg-transition readout may be a more sensitive sub-hertz helium-surface monitor than resonator-frequency jitter, since it resolves depth changes of order 200 nm at frequencies below 1 Hz that earlier vibration studies did not probe.
The observed onset behavior—oscillations appearing immediately or half a period earlier depending on whether the excitation pulse heats or cools the cell—suggests the sign of the initial helium-depth displacement matters; a quantitative model of the thermal pulse's effect on film thickness could predict the phase and amplitude of the first oscillation cycle.
If the film is indeed the conduit, the damping rate should depend on the normal-fluid viscosity, so measuring the quality factor as a function of temperature could separate inertial film flow from thermal counterflow as the restoring mechanism.

Share X Bluesky LinkedIn Reddit HN

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

Worth a look: the experiment clearly sees weakly damped, ~7 s oscillations in both image-charge and Sommer-Tanner signals, correlated in phase and amplitude, and triggered by a thermal pulse. Prior noise spectra in this field stopped above 1 Hz, so the sub-hertz regime is genuinely new. The interpretation that the helium depth in the microchannel is oscillating is plausible, and the simultaneous uim/ST correlation is decent supporting evidence.

What is weaker is the quantitative packaging. The relation δVB = δz(VB − VT)/z gives about 26 nm if you use the stated operating point (VB = 168 mV, VT = −0.4 V), not the 180–250 nm quoted. The paper never tells you which VB values go into the three numbers, and if the right-most resonance in Fig. 2(a) is the one measured at 168 mV in Fig. 3, then the 180–250 nm amplitudes and the "about 20%" depth variation are off by a factor of about seven. That matters because the claimed order-of-magnitude agreement with the Sommer-Tanner signal amplitude depends on δz/z ≈ 17%; with ~26 nm the expected ST modulation is only ~1.7%, and the correlated signal could conceivably be driven by density or potential shifts from the excitation pulse rather than by helium depth. The observation itself still stands; the amplitude claim needs re-examination or clarification.

Another slip: the oscillator estimate ω = sqrt(gS/(LA)) with the stated 30 nm film and five 3.6 mm adapters gives about 0.13 Hz, not the paper's 0.4 Hz. That corrected number actually agrees much better with the observed 0.14 Hz, so this is a numerical mistake that helps the proposed mechanism rather than hurting it.

Also missing: error bars on the oscillation frequency and amplitude, a sensitivity analysis of the assumed film thickness and flow path, and raw data. The model is intentionally order-of-magnitude, and the authors explicitly ask for a proper theoretical framework, so I would not punish the paper for not having one.

Who benefits: people building electrons-on-helium qubits or microchannel devices, and anyone doing low-frequency noise spectroscopy of superfluid films. It deserves a serious referee—the experiment is unusual and the sub-hertz channel is under-studied—but that referee should insist on resolving the amplitude arithmetic and adding the sensitivity analysis. I would not desk-reject it.

Referee Report

3 major / 6 minor

Summary. The paper reports time-domain measurements of the Rydberg transition of electrons trapped on superfluid helium in a microchannel device. After a pulsed heating excitation, the image-charge signal oscillates with a period of about 7 s, and the Sommer-Tanner current shows correlated oscillations with a phase difference consistent with a common origin in variations of the helium depth. The authors attribute these oscillations to inertia of superfluid film flow connecting the microchannels to the bulk helium reservoir, and they estimate peak-to-peak depth variations of 180–250 nm from the voltage-equivalent shift of the Stark spectrum. A simple oscillator model is used to estimate the oscillation frequency, with a stated value of 0.4 Hz compared to the observed 0.14 Hz.

Significance. If the interpretation is correct, the paper identifies a new sub-hertz mechanism of helium surface fluctuations that could affect the coherence of electrons-on-helium qubits in microchannel devices. The simultaneous measurement of two independent signals (image-charge and Sommer-Tanner) with a clear correlation is a notable strength, and the proposed superfluid-film-inertia mechanism is falsifiable and testable by varying device geometry. The paper also extends the study of helium surface noise into the sub-hertz range, which was largely unexplored in prior work. However, the quantitative amplitude extraction contains a serious arithmetical inconsistency, and the frequency estimate contains a numerical error that, once corrected, actually improves the agreement with observation. These issues must be resolved before the quantitative conclusions can be accepted.

major comments (3)

[Section 3, paragraph after Eq. (3)] The relation δVB = δz(VB − VT)/z is stated, followed by 'With δVB ≈ 10 mV and z ≈ h, we obtain an estimate δz ≈ 250, 226 and 180 nm'. Using the authors' own operating values for the right-most resonance, VB = 168 mV and VT = −0.4 V, with z = h = 1.5 μm, this relation gives δz ≈ 26 nm, not 180–250 nm. This inconsistency is load-bearing because the 'about 20%' depth variation and the order-of-magnitude agreement with the Sommer-Tanner amplitude both rely on the 180–250 nm values. The authors should either recalculate δz with the correct voltages for each trace or explain what values of VB and δVB were used; if the correct amplitude is about 26 nm, the predicted ST modulation is only about 1.7%, and the stated agreement must be revised accordingly.
[Section 3, last paragraph] The oscillator frequency estimate contains a numerical error. Using ω = sqrt(gS/(LA)) with the stated film thickness of 30 nm covering five adapters of diameter 3.6 mm, L = 20.3 mm, and A = 1.2 mm^2, one obtains f ≈ 0.13 Hz, not 0.4 Hz. Correcting this arithmetic gives excellent agreement with the observed 0.14 Hz, and the 'satisfactory' agreement statement should be updated to reflect this.
[Section 3, paragraph following Eq. (3)] The caveat that the parallel-plate capacitor model is 'not adequate' for the low electron density of the right-most plot in Fig. 2(b) directly undermines the reliability of the δz values extracted for that trace, which is exactly the trace used for the quantitative comparisons in Figs. 3 and 4. The authors should quantify how this inadequacy affects the extracted δz and the subsequent ST amplitude comparison.

minor comments (6)

[Figure 4 caption] The caption contains a long run of corrupted symbols ('/s48 /s50 ...'); the original source should be checked and the caption restored to readable text.
[Reference 15] The journal name 'L. Low Temp. Phys.' should be 'J. Low Temp. Phys.'
[Section 3, first paragraph] The word 'dependance' should be 'dependence'.
[Section 3, last paragraph] The word 'suprfluid' should be 'superfluid'.
[Conclusion] The word 'microchanel' should be 'microchannel'.
[Section 2, Eq. (1)] The statement that the liquid level is determined by 'the balance of gravitational force and the surface tension' would be clearer if the meniscus curvature assumption underlying Eq. (1) were explicitly mentioned in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the oscillation-frequency estimate is an independent model prediction, and the inferred helium-depth amplitude is a consistency check rather than a fitted input.

full rationale

The paper's derivation chain is not circular. The observed temporal oscillations of the Rydberg signal are converted to an equivalent bias shift δVB using the independently measured Stark slope (df21/dVB ≈ 0.4 GHz/mV), and then to a helium-depth variation δz via the capacitor model in Eqs. (2)-(3). This conversion is a calibration or consistency step, not a fit to the effect it explains. The proposed superfluid-film oscillator frequency is computed from assumed geometry (five SMP adapters, 30 nm film thickness, microchannel area 1.2 mm²) using the textbook formula ω = sqrt(gS/(LA)) and then compared with the observed 0.14 Hz; the observed period is not used as an input to the model. The ST-signal amplitude comparison is explicitly order-of-magnitude and does not feed back into the model parameters. Self-citations ([20], [22]) provide the amplifier and the standard electrostatics model, but those results are parameter-free with stated assumptions and do not presuppose the oscillation mechanism; they are not load-bearing uniqueness claims. Two numerical slips exist (δz from δVB=10 mV, z=1.5 μm, VB−VT=568 mV gives ≈26 nm, not 180-250 nm; and the stated 0.4 Hz from the given film parameters is closer to 0.13 Hz), but these are arithmetic or correctness issues, not circularity, and neither involves fitting the target quantity.

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

The paper introduces no new theoretical entities. Its quantitative claims rest on a small number of estimated geometric and film parameters plus standard models for electrostatics and superfluid flow. The key free parameter is the assumed film thickness; the key domain assumptions are the parallel-plate model and the oscillator model.

free parameters (4)

superfluid film thickness = 30 nm (assumed)
Used to compute the film cross-section S for the frequency estimate. Not fitted to data, but the predicted f_osc scales as sqrt(S), so this choice strongly affects the comparison.
total microchannel area A = 1.2 mm^2 (estimated)
Estimated from device geometry; enters the frequency formula in the denominator, affecting the predicted oscillation frequency.
bulk helium level distance H = 6.3 mm (estimated)
Inferred from the amount of helium condensed; sets the equilibrium depth z0 via Eq. (1) and affects the channel filling.
Stark calibration slope df21/dVB = 0.4 GHz/mV (measured)
Measured conversion coefficient used to translate bias-voltage shifts into frequency shifts and then into depth variations dz.

assumptions (4)

domain assumption Parallel-plate capacitor model (Eqs. 2 and 3 from Ref. 22) relating perpendicular electric field to bias voltages, electron density, and helium depth.
Used to convert observed voltage shifts dVB into helium depth variations dz. Assumes uniform charge and planar geometry, which the authors note is inadequate at low electron density.
domain assumption Superfluid film oscillator model omega = sqrt(gS/(LA)) from Refs. 25-27.
Adopted to estimate the frequency of helium level oscillations driven by inertia of flow through a capillary or film; its applicability to the microchannel/adapter geometry is asserted, not derived.
ad hoc to paper The helium in the channels is hydraulically connected to the bulk liquid via a film covering the SMP adapters.
Assumed to provide the flow path for the restoring oscillation; no direct measurement of the film thickness or coverage is given.
domain assumption The correlated oscillations in uim and iST both reflect changes in helium depth z, not independent effects.
The correlation and phase relation support a common origin, but the quantitative link from image-charge signal to z rests on the capacitor model.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Effect of helium surface fluctuations on the Rydberg transition of trapped electrons." pith.science (2026). https://pith.science/paper/74UYPY3M

@misc{pith2026250107971,
  author       = {Pith},
  title        = {Pith review of: Effect of helium surface fluctuations on the Rydberg transition of trapped electrons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/74UYPY3M}},
  note         = {Machine review of arXiv:2501.07971}
}

read the original abstract

Electrons trapped on the surface of liquid helium is an extremely clean system which holds promise for a scalable qubit platform. However, the superfluid surface is not free from fluctuations which might cause the decay and dephasing of the electrons quantized states. Understanding and mitigating these fluctuations is essential for the advancement of electrons-on-helium (eHe) qubit technology. Some work has been recently done to investigate surface oscillations due to the mechanical vibration of the cryostat using a superconducting coplanar waveguide (CPW) resonator. In the present work, we focus on a sub-hertz frequency range and observe a strong effect of surface oscillations on the temporal dynamics of the Rydberg transition of electrons confined in a microchannel trapping device. We suggest possible origin of such oscillations and find a reasonable agreement between the corresponding estimation of the oscillation frequency and the observed result.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 26 canonical work pages

[1]

A. M. Tyryshkin1, J. J. L. Morton, S. C. Benjamin, A. Ardavan, G. A. D. Briggs, J. W. Ager, and S. A. Lyon, J. Phys.: Condens. Matter 18, S783 (2006)

work page 2006
[2]

Kawakami, P

E. Kawakami, P. Scarlino, D. R. Ward, F. R. Braakman, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, and L. M. K Vandersypen, Nat. Commun. 9, 660 (2014)

work page 2014
[3]

X. Zhou, G. Koolstra, X. Zhang, G.Yang, X. Han, B. Dizdar, X. Li, R. Divan, W. Guo, K. W. Murch, D. I. Schuster, and D. Jin, Nature 605, 46 (2022)

work page 2022
[4]

X. Zhou, X. Li, Q.Chen, G. Koolstra, G.Yang, B. Dizdar, Y. Huang, C. S. Wang, X. Han, X. Zhang, D. I. Schuster, and D. Jin, Nat. Phys. 20, 116 (2024)

work page 2024
[5]

E. Y. Andrei, Electrons on Helium and Other Cryogenic Substrates(Kluwer Academic, Dordrecht, 1997)

work page 1997
[6]

W. Guo, D. Konstantinov, and D. Jin, arXiv:2406.15870

arXiv
[7]

S. A. Lyon, Phys. Rev. A 74 052338 (2006)

work page 2006
[8]

F. R. Bradbury, M. Takita, T. M. Gurrieri, K. J. Wilkel, K. Eng, M. S. Carroll, and S. A. Lyon, Phys. Rev. Lett. 107 266803 (2011)

work page 2011

Show all 27 references

[9]

Kawakami, J

E. Kawakami, J. Chen, M. Benito, and D. Konstantinov, Phys. Rev. Appl. 20 054022 (2023)

2023
[10]

Schuster, A

D. Schuster, A. Fragner, M. Dykman, S. Lyon, and R. Schoelkopf, Phys. Rev. Lett. 105 040503 (2010)

2010
[11]

Jennings, X

A. Jennings, X. Zhou, I. Grytsenko, and E. Kawakami, Appl. Phys. Lett. 124 120501 (2024)

2024
[12]

Koolstra, G.Yang, and D

G. Koolstra, G.Yang, and D. I. Schuster, Nat. Commun. 10 5323 (2019)

2019
[13]

N. R. Beysengulov, C. A. Mikolas, J. M. Kitzman, J. R. Lane, D. Edmunds, D. G. Rees, E. A. Henriksen, S. A. Lyon, and J. Pollanen, J. Low Temp. Phys. 208 482–491 (2022)

2022
[14]

D. G. Rees, I. Kuroda, C. A. Marrache-Kikuchi, M. Hofer, P. Leiderer, and K. Kono, Phys. Rev. Lett 106, 026803 (2011)

2011
[15]

D. G. Rees, I. Kuroda, C. A. Marrache-Kikuchi, M. Hofer, P. Leiderer, and K. Kono, L. Low Temp. Phys. 166, 107 (2012)

2012
[16]

Ikegami, H

H. Ikegami, H. Akimoto, and K. Kono, Phys. Rev. B 82, 201104(R) (2010)

2010
[17]

Ikegami, H

H. Ikegami, H. Akimoto, D. G. Rees, and K. Kono, Phys. Rev. Lett. 109, 236802 (2012)

2012
[18]

D. G. Rees, N. R. Beysengulov, J. J. Lin, and K. Kono, Phys. Rev. Lett. 116, 206801 (2016)

2016
[19]

J.-Y. Lin, A. V. Smorodin, A. O. Badrutdinov, D. Konstantinov, J. Low Temp. Phys. 195, 289 (2019)

2019
[20]

Belianchikov, J

M. Belianchikov, J. A. Kraus, and D. Konstantinov, J. Low Temp. Phys. 215, 1–12 (2024)

2024
[21]

Kawakami, A

E. Kawakami, A. Elarabi, and D. Konstantinov, Phys. Rev. Lett. 100, 100 (2019)

2019
[22]

Zou and D

S. Zou and D. Konstantinov, New J. Phys. 24, 103026 (2022)

2022
[23]

W. T. Sommer and D. J. Tanner, Phys. Rev. Lett. 27, 1345 (1971)

1971
[24]

K. E. Castoria, H. Byeon, J. Theis, N. R. Beysengulov, E. O. Glen, G. Koolstra, M. Sammon, S. A. Lyon, J. Pollanen, and D. G. Rees, Rev. Sci. Instrum. 95, 043902 (2024)

2024
[25]

J. F. Allen and A. D. Misener, Proc. Roy. Soc. A172, 467 (1939)

1939
[26]

J. E. Robinson, Phys. Rev. 82, 440 (1951)

1951
[27]

K. R. Atkins, Proc. Roy. Soc. A203, 119 (1950)

1950

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

A. M. Tyryshkin1, J. J. L. Morton, S. C. Benjamin, A. Ardavan, G. A. D. Briggs, J. W. Ager, and S. A. Lyon, J. Phys.: Condens. Matter 18, S783 (2006)

work page 2006

[2] [2]

Kawakami, P

E. Kawakami, P. Scarlino, D. R. Ward, F. R. Braakman, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, M. A. Eriksson, and L. M. K Vandersypen, Nat. Commun. 9, 660 (2014)

work page 2014

[3] [3]

X. Zhou, G. Koolstra, X. Zhang, G.Yang, X. Han, B. Dizdar, X. Li, R. Divan, W. Guo, K. W. Murch, D. I. Schuster, and D. Jin, Nature 605, 46 (2022)

work page 2022

[4] [4]

X. Zhou, X. Li, Q.Chen, G. Koolstra, G.Yang, B. Dizdar, Y. Huang, C. S. Wang, X. Han, X. Zhang, D. I. Schuster, and D. Jin, Nat. Phys. 20, 116 (2024)

work page 2024

[5] [5]

E. Y. Andrei, Electrons on Helium and Other Cryogenic Substrates(Kluwer Academic, Dordrecht, 1997)

work page 1997

[6] [6]

W. Guo, D. Konstantinov, and D. Jin, arXiv:2406.15870

arXiv

[7] [7]

S. A. Lyon, Phys. Rev. A 74 052338 (2006)

work page 2006

[8] [8]

F. R. Bradbury, M. Takita, T. M. Gurrieri, K. J. Wilkel, K. Eng, M. S. Carroll, and S. A. Lyon, Phys. Rev. Lett. 107 266803 (2011)

work page 2011