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arxiv: 2605.04914 · v1 · submitted 2026-05-06 · 🪐 quant-ph

Transit Noise in Spin Squeezing Experiments with Coated Rubidium Vapor Cell

Yujie Ji , Peiying Li , Yanhong Xiao , Yuzhuo Wang , Junlei Duan This is my paper

Pith reviewed 2026-05-08 16:29 UTC · model grok-4.3

classification 🪐 quant-ph
keywords transit noisespin squeezingrubidium vapor cellprobe beam sizeLarmor frequencyatom-light interactionquantum projection noise
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The pith

Transit noise in rubidium vapor cells increases with smaller probe beams and lower Larmor frequencies, reducing spin squeezing.

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

This paper investigates the transit noise arising from atoms moving through regions of varying light intensity in a coated rubidium vapor cell during spin squeezing experiments. They demonstrate through theory and experiment that for a fixed cell, smaller probe beam areas produce more transit noise, and this noise becomes more significant when the atomic Larmor frequency falls below the transit noise linewidth. Measurements show a 2.7 dB difference in achieved spin squeezing between 2 mm and 0.6 mm beams, aligning with predictions of 3.0 dB. Understanding this helps explain why practical squeezing falls short of ideal limits set by quantum projection noise alone.

Core claim

The Gaussian profile of the optical probe beam causes position-dependent atom-light interactions as atoms transit the coated cell, generating additional noise that grows as beam spot area decreases and dominates when Larmor frequency is below the transit characteristic linewidth; this is confirmed by squeezing measurements differing by 2.7 ± 0.2 dB between beam diameters of 2 mm and 0.6 mm, close to the calculated 3.0 ± 0.3 dB.

What carries the argument

Position-dependent atom-light coupling from the finite Gaussian probe beam combined with finite atomic transit times across the coated cell.

Load-bearing premise

The theoretical model of position-dependent atom-light coupling and atomic transit times through the coated cell accurately captures all relevant noise sources without significant unmodeled contributions from wall collisions or coating imperfections.

What would settle it

If experiments showed no increase in measured noise or squeezing difference when reducing beam size from 2 mm to 0.6 mm, or no dependence on Larmor frequency relative to the transit linewidth, that would falsify the central claims.

Figures

Figures reproduced from arXiv: 2605.04914 by Junlei Duan, Peiying Li, Yanhong Xiao, Yujie Ji, Yuzhuo Wang.

Figure 1
Figure 1. Figure 1: Schematic diagram of atomic motion inside a rubidium vapor cell. The blue area is the region covered by the light spot; the dashed lines are the tangent and normal lines, respectively. We further consider the description of atomic collisions within the coated cell. During their high-speed motion, atoms experience both atom-atom and atom-wall collisions. Given that for our operating temperature the mean fre… view at source ↗
Figure 2
Figure 2. Figure 2: (a) Experimental setup for quantum nondemolition measurement. PBS: polarizing beam splitter; HWP: half-wave plate. (b) Energy level diagram of the interaction between the light fields and 87Rb atoms. The arrows indicate the energy levels coupled by the pump, repump, and probe beams; the circles (attached to the arrows) denote circularly polarized light. 4. Results The atomic spin noise spectra correspondin… view at source ↗
Figure 3
Figure 3. Figure 3: Atomic spin noise spectra at different Larmor frequencies and probe beam sizes. Experiment (left panels) for Larmor frequencies of (a) 30 kHz; (b) 100 kHz; (c) 500 kHz. Monte Carlo simulation (right panels) for Larmor frequencies of (d) 30 kHz; (e) 100 kHz; (f) 500 kHz. In our spin squeezing experiment, the Larmor precession frequency was set to 500 kHz. At this frequency, the transit noise was slightly lo… view at source ↗
Figure 4
Figure 4. Figure 4: Variation in atomic transit noise with Larmor frequency in experiments. 0. 4 0.8 1 . 2 1 . 6 2. 0      0 1 Squeezing (dB) d (mm) Experiment Theory 0. 4 0.8 1 . 2 1 . 6 2. 0 0. 4 0. 6 0.8 1 . 0 Squeezing d (mm) Experiment Theory (a) (b) view at source ↗
Figure 5
Figure 5. Figure 5: Calculated and measured spin squeezing at Larmor frequency of 500 kHz for different probe beam diameters. Both the experimental and theoretical values of the effective atom–light interaction strength κ are 1.61 ms−1/2, with total laser power fixed. Here, the squeezing was evaluated using a retrodictive estimator based on the past quantum state techniques, which improved the inference of the conditional ato… view at source ↗
Figure 6
Figure 6. Figure 6: Theoretical study of spin squeezing versus beam size under higher probe intensity condi￾tions (labeled with effective atom-light interaction strength κ, see text). At each κ, total laser power is fixed for different beam diameters. (a) Logarithmic scale; (b) linear scale. To fully exploit the advantages of strong atom-light coupling, the interaction must be made more spatially uniform, for example, by expa… view at source ↗
Figure 7
Figure 7. Figure 7: Theoretical study of atomic spin noise spectra for Gaussian probe beam and tophat probe beam for (a) low coupling strength κ = 1.61 ms−1/2; (b) high coupling strength κ = 25.45 ms−1/2 . 5. Conclusions In summary, we theoretically and experimentally investigated transit noise in a coated vapor cell and found good qualitative agreement between experiment and theory. We showed that the transit noise backgroun… view at source ↗
read the original abstract

Spin squeezing can suppress quantum projection noise via interparticle entanglement, therefore enabling measurement sensitivities beyond the standard quantum limit. In practice, however, the Gaussian and finite intensity profiles of the optical probe beam induce spatially inhomogeneous atom-light interactions. As polarized atoms move within a vapor cell, they experience position-dependent optical intensities, generating transit noise that limits spin squeezing performance. Here, we investigate the transit noise in a coated rubidium vapor cell through combined theoretical analysis and experimental measurements. By varying the probe beam diameter, we quantify the dependence of transit noise on beam size and atomic Larmor frequency. Our results show that, for a vapor cell with fixed dimensions, the transit noise increases as the probe beam spot area decreases. Moreover, when the Larmor frequency is below the characteristic linewidth of the transit noise, the noise contribution becomes larger. We further calculated and measured spin squeezing for different beam sizes and found an experimental difference of $2.7 \pm 0.2$ dB between 2~mm and 0.6~mm, similar to the theoretical prediction of $3.0 \pm 0.3$ dB. Theoretical analysis under conditions of stronger squeezing shows that transit noise becomes an even more critical limiting factor. These results provide practical guidance for optimizing probe beam parameters and suppressing transit noise in spin squeezing experiments.

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.

Referee Report

2 major / 2 minor

Summary. This paper investigates transit noise in spin squeezing experiments with a coated rubidium vapor cell. Through theoretical modeling of position-dependent atom-light coupling and atomic transit times, combined with experiments varying probe beam diameter, the authors claim that transit noise increases as beam spot area decreases for fixed cell dimensions, and becomes larger when Larmor frequency falls below the transit noise linewidth. They report an experimental squeezing difference of 2.7 ± 0.2 dB between 2 mm and 0.6 mm beams, close to the theoretical prediction of 3.0 ± 0.3 dB, and note that transit noise limits performance more severely under stronger squeezing conditions.

Significance. If the central claims hold, the work supplies concrete guidance on probe beam sizing to suppress transit noise in vapor-cell spin squeezing, a practical issue for pushing sensitivities beyond the standard quantum limit. The reported quantitative agreement between independent experimental data and theory for the squeezing difference is a strength, as is the focus on a scalable noise source that grows more relevant at higher squeezing levels.

major comments (2)
  1. [Results section] Results section (squeezing measurements): The central claim rests on the 2.7 ± 0.2 dB experimental difference matching the 3.0 ± 0.3 dB theory for the two beam sizes, yet the manuscript provides neither the underlying noise spectra, raw squeezing data, nor the explicit error-propagation steps used to obtain the quoted uncertainties. This omission makes it impossible to verify that beam-size-dependent effects other than transit noise have been excluded.
  2. [Theoretical model] Theoretical model (transit noise derivation): The model attributes the observed scaling entirely to position-dependent coupling and finite transit times, but does not derive or bound possible residual contributions from coating imperfections or multiple wall bounces. Without such bounds or auxiliary measurements (e.g., cell transmission vs. beam size), the attribution to pure transit noise remains untested and could be confounded by unmodeled effects that scale similarly with beam area.
minor comments (2)
  1. [Abstract] Abstract: The statement that the squeezing difference is 'similar' to theory would be more precise if the beam diameters were stated explicitly, as they are in the main text.
  2. [Figures] Figure captions: Ensure every panel explicitly labels the beam diameters and Larmor frequencies used, and add a note on how the theoretical curves were generated from the transit-time model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment below and are prepared to revise the manuscript to improve clarity and transparency where appropriate.

read point-by-point responses

  1. Referee: [Results section] Results section (squeezing measurements): The central claim rests on the 2.7 ± 0.2 dB experimental difference matching the 3.0 ± 0.3 dB theory for the two beam sizes, yet the manuscript provides neither the underlying noise spectra, raw squeezing data, nor the explicit error-propagation steps used to obtain the quoted uncertainties. This omission makes it impossible to verify that beam-size-dependent effects other than transit noise have been excluded.

    Authors: We acknowledge that the main text does not include the full raw noise spectra or step-by-step error propagation to keep the presentation concise. The quoted uncertainties were obtained from repeated measurements of the squeezing level (typically 5–10 independent runs per beam size) with standard error propagation from the variance in the detected photocurrent noise relative to the shot-noise limit. In the revised manuscript we will add a supplementary figure showing the noise spectra for both the 2 mm and 0.6 mm beams, tabulate the raw squeezing values, and provide an explicit description of the error-propagation procedure. This addition will allow direct verification that the observed difference arises from transit noise rather than other beam-size-dependent systematics, as all other experimental parameters (optical power, detuning, cell temperature) were held fixed. revision: yes

  2. Referee: [Theoretical model] Theoretical model (transit noise derivation): The model attributes the observed scaling entirely to position-dependent coupling and finite transit times, but does not derive or bound possible residual contributions from coating imperfections or multiple wall bounces. Without such bounds or auxiliary measurements (e.g., cell transmission vs. beam size), the attribution to pure transit noise remains untested and could be confounded by unmodeled effects that scale similarly with beam area.

    Authors: Our model is constructed from the position-dependent atom-light coupling (Gaussian intensity profile) and the distribution of atomic transit times across the probe beam, which directly follows from the cell geometry and atomic velocity distribution. The quantitative match between the predicted 3.0 dB and measured 2.7 dB difference provides strong empirical support that transit noise dominates the beam-size dependence. We did not explicitly bound coating imperfections or multiple-bounce contributions in the original text. In the revision we will add a dedicated paragraph that (i) recalls the anti-relaxation coating specifications used in the cell, (ii) notes that the measured optical transmission remained >95 % and showed no measurable dependence on beam diameter within experimental precision, and (iii) derives an upper bound on residual coating-induced noise by comparing the observed transit-noise linewidth with the known spin-relaxation rate. These additions will clarify why other effects are not expected to mimic the observed scaling. revision: partial

Circularity Check

0 steps flagged

No significant circularity; model predictions validated against independent experimental measurements

full rationale

The derivation of transit noise from position-dependent atom-light coupling and atomic transit times through the coated cell is presented as a first-principles model. It is then used to predict beam-size dependence and squeezing differences, which are compared to separate experimental data (2.7 dB measured vs 3.0 dB predicted). The values are close but not identical, and no equations reduce the reported differences to parameters fitted from the same dataset. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard models of atom-light interaction and atomic diffusion in a coated cell; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard quantum optics description of position-dependent AC Stark shifts and atomic transit through a Gaussian beam
    Invoked for theoretical calculation of transit noise spectrum.

pith-pipeline@v0.9.0 · 5551 in / 1246 out tokens · 40550 ms · 2026-05-08T16:29:46.285669+00:00 · methodology

discussion (0)

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