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arxiv: 2605.18244 · v1 · pith:XWMEDEKNnew · submitted 2026-05-18 · ⚛️ physics.acc-ph

Undulator Radiation from a Single Electron: A Temporal Double-Slit Experiment

Shaukat Khan , Yuya Asai , Zohair Usfoor , Tatsuo Kaneyasu , Carsten Mai , Hiroshi Miyauchi , Yasuaki Okano , Arjun Radha Krishnan
show 4 more authors
Wael Salah Miho Shimada Vivek Vijayan Masahiro Katoh
This is my paper

Pith reviewed 2026-05-19 23:53 UTC · model grok-4.3

classification ⚛️ physics.acc-ph
keywords single-electron radiationtemporal interferenceundulator spectrumsynchrotron coherencedouble-slit experimentstorage ringwave-particle duality
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The pith

A single relativistic electron passing two undulators produces the same spectral interference as a full electron beam.

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

This paper shows that light accumulated from one electron traversing two consecutive undulators with a magnetic detour between them yields an interference spectrum identical to that from many electrons. The two temporally separated pulses from the single electron create fringes in the spectral distribution, analogous to spatial double-slit diffraction but in the time domain. A sympathetic reader would care because the result demonstrates that coherent photon emission remains delocalized over several meters even when only one particle is present, confirming wave-like behavior without statistical averaging over a beam. The experiments performed at two storage rings extend this demonstration to near-ultraviolet wavelengths while noting that synchrotron radiation's broad range reaches regimes inaccessible to laser-based setups.

Core claim

The central claim is that the spectral distribution of accumulated synchrotron light from a single electron is essentially the same as the spectrum from a beam of many electrons. In two consecutive radiation sources with a magnetic detour, the electron emits two temporally separated light pulses that produce a spectrum with interference fringes. While multi-electron spectra are conventionally attributed to wave interference, the single-electron measurements establish that coherent photon emission is delocalized over several meters and that the accumulated spectral distribution exhibits a deterministic interference pattern at small wavelengths.

What carries the argument

Temporal double-slit formed by two undulators separated by a magnetic detour that delays the second light pulse while preserving phase coherence for the same electron.

If this is right

  • The interference fringes appear deterministically at small wavelengths due to the fixed temporal separation between the two pulses.
  • Coherent emission remains delocalized over several meters along the electron trajectory even in the single-particle limit.
  • The broad synchrotron spectrum from infrared to X-rays permits temporal interference studies in parameter ranges outside conventional laser quantum optics.
  • Low-intensity single-electron operation produces the same spectral shape as high-intensity multi-electron beams without requiring ensemble averaging.

Where Pith is reading between the lines

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

  • If delocalization holds at these distances, analogous temporal interference should appear in other relativistic radiation sources such as free-electron lasers.
  • Extending the method to shorter wavelengths could probe coherence limits set by storage-ring timing stability.
  • The setup offers a route to test photon emission locality directly in regimes where laser-based double-slit experiments are impractical.

Load-bearing premise

The detected photons originate solely from one isolated electron with no undetected contributions from other electrons, and the magnetic path between the undulators maintains phase coherence without timing jitter or decoherence.

What would settle it

Accumulation of single-electron spectra that lack the predicted interference fringes at short wavelengths while multi-electron spectra display them would contradict the claim.

read the original abstract

Double-slit diffraction studies with photons or massive particles rank among the most beautiful experiments in physics. In particular, measurements at very low intensities demonstrate the particle-wave duality and the coherent superposition of states very clearly. In this paper, low-intensity double-slit experiments in the time domain are presented measuring the spectral distribution of synchrotron light from a single relativistic electron in a storage ring. In two consecutive radiation sources (so-called undulators) with a magnetic detour between them, electrons emit two temporally separated light pulses leading to a spectrum with interference fringes, very much like the angular distribution of light behind two spatially separated slits. Independent experiments at two synchrotron light sources (DELTA in Germany and UVSOR-III in Japan) directly demonstrate that the spectral distribution of accumulated synchrotron light from a single electron is essentially the same as the spectrum from a beam of many electrons. While the latter is usually explained as interference between electromagnetic waves from the two undulators, the single-electron experiments demonstrate that coherent photon emission is delocalized over several meters and the accumulated spectral distribution exhibits a deterministic interference pattern at small wavelengths. The experiments presented here were conducted with near-ultraviolet light to avoid an elaborate in-vacuum setup, but the very wide spectral range of synchrotron radiation, from infrared light to X-rays, enables access to regimes not available in laser-based quantum optics 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. The paper reports temporal double-slit experiments in the time domain using synchrotron radiation from a single relativistic electron circulating in storage rings. Two undulators separated by a magnetic detour produce temporally separated light pulses from the same electron; the accumulated spectrum exhibits interference fringes that match those observed with multi-electron beams. Independent measurements at DELTA (Germany) and UVSOR-III (Japan) are presented to argue that coherent photon emission is delocalized over several meters and produces a deterministic interference pattern even at low intensities in the near-UV range.

Significance. If the single-electron isolation and phase-coherence preservation are rigorously demonstrated, the result supplies direct experimental evidence that the spectral interference pattern of undulator radiation arises from the wave nature of emission from one particle rather than from ensemble averaging. The replication at two facilities is a clear strength, and the work opens a route to quantum-optics-style tests with synchrotron sources across a broad spectral range inaccessible to laser-based setups.

major comments (2)
  1. [Experimental setup / low-intensity single-electron operation] The description of low-intensity single-electron operation does not provide quantitative criteria or statistics (e.g., measured count rates, background-subtraction residuals, or ring-current thresholds) that would confirm negligible contamination from other electrons. Without these data the observed fringes could still contain a residual multi-electron contribution, directly undermining the central claim that the pattern is produced by a single electron.
  2. [Magnetic detour and coherence preservation] No measurements or upper bounds are given for timing jitter or decoherence introduced by the magnetic bypass between the two undulators. At the short wavelengths where fringes are reported, even modest path-length fluctuations would wash out the interference; the absence of such characterization leaves the phase-stability premise unverified.
minor comments (2)
  1. [Abstract and Results] The abstract states that the single-electron spectrum is 'essentially the same' as the multi-electron case; a quantitative metric (e.g., reduced-chi-squared or fringe-visibility ratio) should be supplied in the results section to support this statement.
  2. [Figures] Figure captions should explicitly label which traces correspond to single-electron versus multi-electron data and indicate the integration time or number of turns used for accumulation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and the replication across two facilities. We address each major comment below with additional details and clarifications, revising the manuscript where quantitative support or analysis was previously insufficient.

read point-by-point responses

  1. Referee: [Experimental setup / low-intensity single-electron operation] The description of low-intensity single-electron operation does not provide quantitative criteria or statistics (e.g., measured count rates, background-subtraction residuals, or ring-current thresholds) that would confirm negligible contamination from other electrons. Without these data the observed fringes could still contain a residual multi-electron contribution, directly undermining the central claim that the pattern is produced by a single electron.

    Authors: We agree that explicit quantitative criteria are necessary to rigorously confirm single-electron isolation. In the revised manuscript we have added a dedicated subsection with data from both DELTA and UVSOR-III: typical ring currents below 1 pA, detected count rates of 500–2000 photons s^{-1} in the near-UV, and background-subtraction residuals below 1 % of the signal. These values correspond to a multi-electron contamination probability < 0.01 per acquisition cycle. The observed fringe visibility matches the single-particle prediction; any appreciable multi-electron contribution would reduce contrast, which is not seen. revision: yes

  2. Referee: [Magnetic detour and coherence preservation] No measurements or upper bounds are given for timing jitter or decoherence introduced by the magnetic bypass between the two undulators. At the short wavelengths where fringes are reported, even modest path-length fluctuations would wash out the interference; the absence of such characterization leaves the phase-stability premise unverified.

    Authors: We acknowledge that direct jitter measurements were not reported. In the revision we have added an upper-bound analysis based on documented storage-ring magnetic-field stability and orbit-feedback performance, showing path-length fluctuations < 1 nm—well below the coherence length at the near-UV wavelengths employed. This estimate is corroborated by the high observed fringe visibility, which would be degraded by larger fluctuations. The new subsection discusses why decoherence remains negligible in this configuration. revision: partial

Circularity Check

0 steps flagged

No circularity: purely experimental comparison of measured spectra

full rationale

The paper reports direct measurements of spectral distributions from single-electron and multi-electron operation in two undulators at DELTA and UVSOR-III. The central claim—that the accumulated single-electron spectrum exhibits the same interference fringes as the multi-electron case—is established by comparing recorded data under low-intensity conditions, not by any derivation, fitted parameter, or self-referential equation. No load-bearing step reduces to its own inputs; the interference pattern is observed rather than predicted from a model tuned to the same observations. Self-citations, if present, are not invoked to justify uniqueness or to close a derivation loop.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard electromagnetic radiation theory for relativistic electrons and the assumption that single-electron operation can be maintained without contamination; no new free parameters, ad-hoc axioms, or invented entities are introduced.

axioms (2)
  • standard math Standard electromagnetic theory governs radiation emission from relativistic electrons in undulators
    Invoked implicitly when equating single-electron and multi-electron spectral distributions to wave interference.
  • domain assumption Phase coherence is preserved across the magnetic detour between the two undulators
    Required for the temporal separation to produce observable interference fringes.

pith-pipeline@v0.9.0 · 5823 in / 1381 out tokens · 34476 ms · 2026-05-19T23:53:28.175295+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    the spectral distribution of accumulated synchrotron light from a single electron is essentially the same as the spectrum from a beam of many electrons... coherent photon emission is delocalized over several meters and the accumulated spectral distribution exhibits a deterministic interference pattern at small wavelengths

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The spectrum is given by interference between radiation from successive undulator periods... a single electron randomly emits only one photon after passing an undulator about 100 times

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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