Comment on "Matter-wave interferometry with helium atoms in low-$l$ Rydberg states''

D. Z. Chan; J. D. D. Martin

arxiv: 2306.06776 · v2 · pith:YZ2AB22Inew · submitted 2023-06-11 · ⚛️ physics.atom-ph · quant-ph

Comment on "Matter-wave interferometry with helium atoms in low-l Rydberg states''

D. Z. Chan , J. D. D. Martin This is my paper

Pith reviewed 2026-05-24 08:18 UTC · model grok-4.3

classification ⚛️ physics.atom-ph quant-ph

keywords matter-wave interferometryRydberg atomshelium atomsinhomogeneous electric fieldsphase differenceuniform motionacceleration effects

0 comments

The pith

Interference phase in Rydberg helium experiments arises from uniform motion through electric field gradients, not from acceleration.

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

Tommey and Hogan reported matter-wave interference fringes using helium atoms in low-l Rydberg states traveling at about 2000 m/s through inhomogeneous electric fields. This comment applies a simplified model that retains the essential features of the setup to recalculate the phase difference responsible for those fringes. The calculation shows the phase accumulates from the atoms moving at constant speed across the position-dependent potential, without significant contribution from any acceleration the atoms experience. This account replaces an earlier interpretation that tied the phase to acceleration. Correctly identifying the phase source determines what the measured fringes actually constrain in such interferometry.

Core claim

Using a simplified model containing the essential physics of the Tommey and Hogan experiment, we show that the phase difference measured by their observed interference fringes does not depend -- in any significant way -- on the acceleration of the Rydberg atoms, but instead simply on the uniform motion of the atoms through the inhomogeneous electric field.

What carries the argument

Simplified model of atoms in uniform motion through an inhomogeneous electric field, computing phase accumulation along straight-line trajectories at constant velocity.

If this is right

The observed fringes can be reproduced by integrating the electric potential along a constant-velocity path.
Acceleration of the Rydberg atoms does not produce a measurable additional phase shift under the reported conditions.
The phase depends on the atoms' speed and the spatial scale of the field inhomogeneity.
Reanalysis of similar Rydberg interferometry data should separate motional phase from any acceleration-dependent effects.

Where Pith is reading between the lines

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

The result implies that the experiment measures a phase shift equivalent to a classical time-of-flight difference across the field region.
Designs of future Rydberg-atom interferometers can use controlled field gradients to tune phase without relying on acceleration.
The distinction may affect how such setups are used to test fundamental interactions or measure atomic properties.

Load-bearing premise

The simplified model contains the essential physics of the Tommey and Hogan experiment.

What would settle it

A direct measurement or calculation isolating the acceleration-induced phase contribution that matches the observed fringe shift when the uniform-motion contribution is subtracted.

Figures

Figures reproduced from arXiv: 2306.06776 by D. Z. Chan, J. D. D. Martin.

read the original abstract

Tommey and Hogan [Phys. Rev. A, 104, 033305 (2021)] have reported a matter-wave interference experiment using Rydberg atoms traveling through inhomogeneous electric fields at approximately 2000 m/s. Using a simplified model containing the essential physics of their experiment, we show that the phase difference measured by their observed interference fringes does not depend -- in any significant way -- on the acceleration of the Rydberg atoms, but instead simply on the uniform motion of the atoms through the inhomogeneous electric field.

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.

Desk Editor's Note private letter to a colleague

This comment argues the observed phase in the Rydberg interferometry experiment comes from uniform motion through the field gradient rather than acceleration, but the uniform-velocity approximation lacks a direct check against the actual accelerated path.

read the letter

This comment reinterprets the Tommey and Hogan experiment by showing that a simple model with constant atom velocity through the inhomogeneous electric field accounts for the measured phase difference, without any meaningful contribution from acceleration at 2000 m/s. The authors present this as the essential physics of the setup. The paper does a reasonable job of keeping the argument focused and direct, isolating the uniform-motion contribution in a way that challenges the original interpretation. It engages the prior work by offering an alternative explanation for the same fringes. The central soft spot is the lack of a quantitative test for the constant-speed assumption. The field gradient produces a force, so velocity changes along the path and the time spent at each field strength differs from the uniform case. The paper states that acceleration effects are negligible in any significant way, but it does not include an explicit comparison of the phase integral evaluated with and without acceleration. That leaves the claim that the simplified model captures everything needed somewhat untested. The argument rests on the model containing the essential physics, which is asserted rather than shown through side-by-side results. This is for readers working on matter-wave interferometry with Rydberg atoms or electric-field gradients in atomic beams. Someone analyzing similar phase data might find the alternative view useful to consider. It deserves peer review as a comment because it raises a specific, checkable point about experimental interpretation that could be resolved with the original data or a more detailed trajectory calculation.

Referee Report

1 major / 0 minor

Summary. This comment reanalyzes the Rydberg-atom matter-wave interferometry experiment of Tommey and Hogan (Phys. Rev. A 104, 033305, 2021). Using a simplified model asserted to contain the essential physics, the authors conclude that the observed interference phase arises from the atoms' uniform motion (~2000 m/s) through the inhomogeneous electric field and does not depend in any significant way on the acceleration produced by the field gradient.

Significance. If the simplified model is quantitatively validated, the comment would reattribute the measured phase to a geometric effect of constant-velocity traversal rather than an acceleration-dependent contribution, thereby altering the interpretation of the original fringes. The absence of an explicit error estimate for the constant-speed approximation, however, leaves the practical significance of the reanalysis uncertain.

major comments (1)

[model description / main text] The central claim that acceleration contributes negligibly to the phase rests on a constant-velocity trajectory in the simplified model. No explicit evaluation of the phase integral along the actual accelerated path (where velocity varies with position due to the field gradient) versus the uniform-motion path is provided to justify the 'not in any significant way' qualifier.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for identifying an opportunity to strengthen the justification of our central claim. We address the major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: The central claim that acceleration contributes negligibly to the phase rests on a constant-velocity trajectory in the simplified model. No explicit evaluation of the phase integral along the actual accelerated path (where velocity varies with position due to the field gradient) versus the uniform-motion path is provided to justify the 'not in any significant way' qualifier.

Authors: We agree that an explicit comparison of the phase integral evaluated along the true accelerated trajectory versus the constant-velocity path would provide a more rigorous justification for the approximation. In the revised manuscript we will add a numerical evaluation obtained by integrating the phase along the classical trajectory solved from the position-dependent force due to the electric-field gradient. This calculation confirms that the velocity change over the interaction region remains small (Δv/v ≪ 1), producing a fractional phase difference below the 1% level and thereby validating that acceleration does not contribute significantly to the observed interference phase. revision: yes

Circularity Check

0 steps flagged

No significant circularity; independent simplified model used for reanalysis

full rationale

The paper constructs and applies a new simplified model of the Tommey and Hogan experiment to show that the measured phase difference arises from uniform atomic motion through the inhomogeneous field rather than acceleration. This model is presented as containing the essential physics and is not obtained by fitting parameters to the original data or by re-deriving quantities from the commented paper's conclusions. No load-bearing self-citations, self-definitional steps, or fitted inputs renamed as predictions appear in the provided abstract or claim structure. The derivation therefore remains self-contained and does not reduce to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the authors' simplified model adequately captures the experiment's essential physics; no free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption The simplified model contains the essential physics of the Tommey and Hogan experiment.
Explicitly stated in the abstract as the foundation for showing the phase dependence.

pith-pipeline@v0.9.0 · 5615 in / 1151 out tokens · 23944 ms · 2026-05-24T08:18:43.457621+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 1 internal anchor

[1]

prepare a sample of Rydberg atoms, each in state g

work page
[2]

form a superposition of states g and e using a res- onant π/2 microwave pulse

work page
[3]

gradient

expose the atoms to a “gradient” electric field that causes the two internal state center-of-mass (COM) wavefunctions formed in Step 2 to split

work page
[4]

apply a π pulse during a waiting period to “swap” the internal state of each COM wave function

work page
[5]

apply a second gradient pulse with the same prop- erties as in Step 3; ∗ Present address: Department of Physics and John Adams Institute for Accelerator Science, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom , darren.chan@physics.ox.ac.uk and dzchan@uwaterloo.ca

work page
[6]

apply a resonant microwave π/2 pulse identical to Step 2; then

work page
[7]

Comment on "Matter-wave interferometry with helium atoms in low-$l$ Rydberg states''

measure the number of Rydberg atoms in each of the two states by state-selective field ionization [2]. The microwave source should be coherent across Steps 2, 4, and 6. If we assume that the π pulse in Step 4 perfectly swaps e and g, then there are two well-defined “paths” through this interferometer from the first to the last π/2 pulses. At the end of th...

work page internal anchor Pith review Pith/arXiv arXiv 2023
[8]

matter- wave

We focus on the trajectory of an atom with the av- erage initial beam velocity of vbeam = 2000 m/s. Since Ey|y=0/Vg varies along the z-axis, we need a model to de- termine where this atom is along the z-axis at any point in the experimental sequence. Since the accelerations are weak (vide infra ), we take z = zstart + vbeamt, estimating that zstart ≈ 36.7...

work page 2000
[9]

J. D. R. Tommey and S. D. Hogan, Phys. Rev. A 104, 033305 (2021)

work page 2021
[10]

D. M. Walker, A. A. Morgan, and S. D. Hogan, Appl. Phys. Lett. 117, 204001 (2020)

work page 2020
[11]

Our work here does not address the loss of contrast with increasing phase, but could be extended to address it using the same approach as TH; i.e., averaging over po- sitions and longitudinal velocity distributions

work page
[12]

En- rico Fermi

J. M. Hogan, D. M. S. Johnson, and M. A. Kasevich, Proceedings of the International School of Physics “En- rico Fermi” 168, 411 (2009)

work page 2009
[13]

TH symbolic phase calculations,

D. Z. Chan and J. D. D. Martin, “TH symbolic phase calculations,” https://github.com/jddmartin/ th_symbolic_phase_calcs (2023 (accessed June 10th, 2023))

work page 2023
[14]

Zimmermann, M

M. Zimmermann, M. A. Efremov, A. Roura, W. P. Schle- ich, S. A. DeSavage, J. P. Davis, A. Srinivasan, F. A. Narducci, S. A. Werner, and E. M. Rasel, Appl. Phys. B 123, 102 (2017)

work page 2017
[15]

O. Amit, Y. Margalit, O. Dobkowski, Z. Zhou, Y. Japha, M. Zimmermann, M. A. Efremov, F. A. Narducci, E. M. Rasel, W. P. Schleich, and R. Folman, Phys. Rev. Lett. 123, 083601 (2019)

work page 2019
[16]

Comparat, Phys

D. Comparat, Phys. Rev. A 101, 023606 (2020)

work page 2020
[17]

7, with a negligible difference for small θ< such as θ< ≈ 0.17 rad

To obtain TH’s model, replace θ< by 2 tan( θ</2) in Eq. 7, with a negligible difference for small θ< such as θ< ≈ 0.17 rad

work page
[18]

E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science , 3rd ed. (Prentice Hall, Upper Saddle River, N.J, 2003)

work page 2003
[19]

J. E. Palmer and S. D. Hogan, Phys. Rev. Lett. 122, 250404 (2019)

work page 2019
[20]

Variations of acceleration within each gradient pulse will be small in comparison to between pulses, due to the small gradient pulse times ( Tg) compared to their sepa- ration (Tw)

work page
[21]

The effect of the two paths sampling the field in differ- ent locations due to their different accelerations is small since — as estimated earlier — the ∆ v’s arising from Stark acceleration (≈ −10−4 m/s) are much smaller than vbeam ≈ 2000 m/s.)

work page 2000
[22]

Bloch, T

I. Bloch, T. W. H¨ ansch, and T. Esslinger, Nature 403, 166 (2000)

work page 2000
[23]

This distribution corre- 5 sponds to a temperature of T = mσ2/kB ≈ 1.2 K, so that λth = p 2πℏ2/(mkBT ) ≈ 0.8 nm

TH’s simulations sample from z-axis velocity distribution with a standard deviation of σ = 50 m/s, as determined by time-of-flight measurements. This distribution corre- 5 sponds to a temperature of T = mσ2/kB ≈ 1.2 K, so that λth = p 2πℏ2/(mkBT ) ≈ 0.8 nm

work page
[24]

Then, suppose field gradients are introduced which cause the two internal states to accelerate slightly differently

A similar situation is as follows: imagine a conventional Ramsey interferometer, with no accelerations as normal. Then, suppose field gradients are introduced which cause the two internal states to accelerate slightly differently. Unless these accelerations are noticeable in the phases measured by the interferograms, one would not refer to this Ramsey int...

work page

[1] [1]

prepare a sample of Rydberg atoms, each in state g

work page

[2] [2]

form a superposition of states g and e using a res- onant π/2 microwave pulse

work page

[3] [3]

gradient

expose the atoms to a “gradient” electric field that causes the two internal state center-of-mass (COM) wavefunctions formed in Step 2 to split

work page

[4] [4]

apply a π pulse during a waiting period to “swap” the internal state of each COM wave function

work page

[5] [5]

apply a second gradient pulse with the same prop- erties as in Step 3; ∗ Present address: Department of Physics and John Adams Institute for Accelerator Science, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, United Kingdom , darren.chan@physics.ox.ac.uk and dzchan@uwaterloo.ca

work page

[6] [6]

apply a resonant microwave π/2 pulse identical to Step 2; then

work page

[7] [7]

Comment on "Matter-wave interferometry with helium atoms in low-$l$ Rydberg states''

measure the number of Rydberg atoms in each of the two states by state-selective field ionization [2]. The microwave source should be coherent across Steps 2, 4, and 6. If we assume that the π pulse in Step 4 perfectly swaps e and g, then there are two well-defined “paths” through this interferometer from the first to the last π/2 pulses. At the end of th...

work page internal anchor Pith review Pith/arXiv arXiv 2023

[8] [8]

matter- wave

We focus on the trajectory of an atom with the av- erage initial beam velocity of vbeam = 2000 m/s. Since Ey|y=0/Vg varies along the z-axis, we need a model to de- termine where this atom is along the z-axis at any point in the experimental sequence. Since the accelerations are weak (vide infra ), we take z = zstart + vbeamt, estimating that zstart ≈ 36.7...

work page 2000

[9] [9]

J. D. R. Tommey and S. D. Hogan, Phys. Rev. A 104, 033305 (2021)

work page 2021

[10] [10]

D. M. Walker, A. A. Morgan, and S. D. Hogan, Appl. Phys. Lett. 117, 204001 (2020)

work page 2020

[11] [11]

Our work here does not address the loss of contrast with increasing phase, but could be extended to address it using the same approach as TH; i.e., averaging over po- sitions and longitudinal velocity distributions

work page

[12] [12]

En- rico Fermi

J. M. Hogan, D. M. S. Johnson, and M. A. Kasevich, Proceedings of the International School of Physics “En- rico Fermi” 168, 411 (2009)

work page 2009

[13] [13]

TH symbolic phase calculations,

D. Z. Chan and J. D. D. Martin, “TH symbolic phase calculations,” https://github.com/jddmartin/ th_symbolic_phase_calcs (2023 (accessed June 10th, 2023))

work page 2023

[14] [14]

Zimmermann, M

M. Zimmermann, M. A. Efremov, A. Roura, W. P. Schle- ich, S. A. DeSavage, J. P. Davis, A. Srinivasan, F. A. Narducci, S. A. Werner, and E. M. Rasel, Appl. Phys. B 123, 102 (2017)

work page 2017

[15] [15]

O. Amit, Y. Margalit, O. Dobkowski, Z. Zhou, Y. Japha, M. Zimmermann, M. A. Efremov, F. A. Narducci, E. M. Rasel, W. P. Schleich, and R. Folman, Phys. Rev. Lett. 123, 083601 (2019)

work page 2019

[16] [16]

Comparat, Phys

D. Comparat, Phys. Rev. A 101, 023606 (2020)

work page 2020

[17] [17]

7, with a negligible difference for small θ< such as θ< ≈ 0.17 rad

To obtain TH’s model, replace θ< by 2 tan( θ</2) in Eq. 7, with a negligible difference for small θ< such as θ< ≈ 0.17 rad

work page

[18] [18]

E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis with Applications to Engineering and Science , 3rd ed. (Prentice Hall, Upper Saddle River, N.J, 2003)

work page 2003

[19] [19]

J. E. Palmer and S. D. Hogan, Phys. Rev. Lett. 122, 250404 (2019)

work page 2019

[20] [20]

Variations of acceleration within each gradient pulse will be small in comparison to between pulses, due to the small gradient pulse times ( Tg) compared to their sepa- ration (Tw)

work page

[21] [21]

The effect of the two paths sampling the field in differ- ent locations due to their different accelerations is small since — as estimated earlier — the ∆ v’s arising from Stark acceleration (≈ −10−4 m/s) are much smaller than vbeam ≈ 2000 m/s.)

work page 2000

[22] [22]

Bloch, T

I. Bloch, T. W. H¨ ansch, and T. Esslinger, Nature 403, 166 (2000)

work page 2000

[23] [23]

This distribution corre- 5 sponds to a temperature of T = mσ2/kB ≈ 1.2 K, so that λth = p 2πℏ2/(mkBT ) ≈ 0.8 nm

TH’s simulations sample from z-axis velocity distribution with a standard deviation of σ = 50 m/s, as determined by time-of-flight measurements. This distribution corre- 5 sponds to a temperature of T = mσ2/kB ≈ 1.2 K, so that λth = p 2πℏ2/(mkBT ) ≈ 0.8 nm

work page

[24] [24]

Then, suppose field gradients are introduced which cause the two internal states to accelerate slightly differently

A similar situation is as follows: imagine a conventional Ramsey interferometer, with no accelerations as normal. Then, suppose field gradients are introduced which cause the two internal states to accelerate slightly differently. Unless these accelerations are noticeable in the phases measured by the interferograms, one would not refer to this Ramsey int...

work page