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REVIEW 3 major objections 4 minor 69 references

Femtosecond and attosecond phase-space correlations in few-particle photoelectron pulses

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper directly reconstructs the phase-space distribution of two-electron pulses, revealing a Coulomb-induced bimodal structure, and shows that coherent inelastic electron-light scattering imprints controllable attosecond-scale…

desk verdict A real experimental step toward number-resolved two-electron phase-space maps, but the 'direct map' is more parametric than the abstract suggests; the bimodality is likely real, the fine shape needs error bars. read the letter →

arxiv 2412.11929 v2 pith:LQGFUCKE submitted 2024-12-16 cond-mat.mes-hall cond-mat.str-elphysics.acc-phphysics.app-phphysics.optics

Rudolf Haindl , Valerio Di Giulio , Armin Feist , Claus Ropers This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.str-elphysics.acc-phphysics.app-phphysics.optics
keywords few-electronstatesphase-spacereconstructioninelasticelectron-lightscatteringultrafasttransmissionelectronmicroscopyCoulombcorrelationsattosecondtemporalquantumwalkcathodoluminescence
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

The paper establishes that the joint energy and arrival-time structure of a two-electron pulse can be measured directly, and that it carries a clear fingerprint of Coulomb repulsion: the two electrons arrive separated by roughly 240 fs and 1.8 eV at the sample plane. It further shows that inelastic scattering of both electrons off a single long laser pulse imprints a controllable optical phase onto the pair, creating sub-optical-cycle (attosecond) correlations between their arrival times that depend on the final energies selected. If correct, this gives a practical way to tailor few-electron states for enhanced or suppressed excitation of a sample, relevant for dose-sensitive imaging and quantum electron-light experiments.

What carries the argument

The central object is the $N$-particle longitudinal phase-space density $\rho_N(\{t_i\},\{E_i\})$ and its two-electron marginal $\rho_2(t,E)$. The measurement principle is inelastic electron-light scattering (IELS) slicing: a short laser pulse acts as a multi-order spectral comb and temporal gate, so the recorded energy map is a convolution of the phase-space density with a known slicing function; the reconstruction inverts this for gain-scattered sidebands under a Gaussian-chirp ansatz for each sub-ensemble. For shaping, a long laser pulse acts as a global phase modulator, and the two-electron Wigner function is used to derive the projected coherence factor that enters the cathodoluminescence probability.

What would settle it

A direct, model-free measurement of the two-electron arrival-time difference distribution—for example by streaking the pair with a second time-resolved stage, or by performing IELS with two femtosecond-separated probe pulses—should reproduce the 240 fs separation and the sub-laser-period correlations predicted from the reconstructed density; a mismatch would falsify the reconstruction or the shaping claim.

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Extended reading notes

Core claim

The paper claims that the longitudinal phase-space density $\rho_2(t,E)$ of two-electron pulses emitted from a nanotip is bimodal, with the slower and faster electrons separated by 1.8 eV and 240 fs at the sample, and that this structure arises from Coulomb energy exchange during acceleration plus subsequent dispersion, not from initial photoemission correlations. It further claims that coherent inelastic electron-light scattering (IELS) with a laser pulse longer than the electron ensemble imprints a global phase on both electrons, producing a checkerboard spectral pattern (a two-particle quantum walk) and, for each pair of post-selected final energies, a distinct sub-cycle temporal correlation between the two electrons' arrival times. These correlations translate into a coherent modulation factor in the probability of cathodoluminescence emission from a downstream sample, enabling either enhancement or suppression that can be selected by choosing the detected electron energies.

Load-bearing premise

The reconstructed two-electron phase-space density assumes each of the two sub-ensembles has a Gaussian energy profile with a time-dependent chirp, so a non-Gaussian true distribution would make the extracted bimodal structure a model artifact rather than a measurement.

Editorial extensions

If this is right

  • Number-sorted phase-space reconstruction via IELS slicing can be extended to states with more than two electrons, and to the full $N$-particle density using multiple femtosecond-separated probe pulses.
  • Coherent IELS shaping produces attosecond inter-particle timing correlations without requiring dispersive bunching, so the shaping stage and the target can be placed without strict drift-length constraints.
  • Energy post-selection after coherent IELS provides a switch between enhancement and suppression of coherent excitations such as cathodoluminescence, giving a new control knob for ultrafast electron microscopy.
  • The measured Coulomb-induced chirp between the two lobes (130–140 fs/eV) is nearly independent of photocurrent, indicating the correlation gap is robust to stochastic interactions and set by the acceleration dynamics.
  • The framework connects IELS spectrograms to two-particle quantum walks, offering a route to probe decoherence and entanglement in few-electron beams.

Reading between the lines

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

  • If the Gaussian-chirp assumption biases the reconstructed widths, the 1.8 eV / 240 fs separation could be tested by comparing with streaking data or with the raw gain-filtered spectra without deconvolution; a mismatch would point to non-Gaussian energy distributions in the sub-ensembles.
  • The predicted energy-selectable attosecond correlations suggest a two-pulse experiment where the second sample is replaced by a second IELS gate or an optical streak, which would directly measure the pair-time correlation function and verify the Wigner-function prediction.
  • Because the coherent modulation factor $\eta$ can be negative for certain post-selected energies, the same setup could demonstrate destructive interference of two-electron excitation, effectively a two-electron 'anti-bunching' in excitation, which is not accessible with bunched beams.
  • The approach may extend to fermionic or bosonic statistics: the phase relation between two electrons is what matters for superradiance, so using identical electrons in the same spin state could reveal statistical effects on the correlation signal.
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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

3 major / 4 minor

Summary. The manuscript reports number-resolved measurements of one-, two-, and three-electron pulses generated by femtosecond photoemission from a Schottky emitter and detected with an event-based Timepix3 camera behind an energy filter in a UTEM. Using ultrafast gating via inelastic electron-light scattering (IELS), the authors reconstruct the marginalized longitudinal phase-space density ρ2(t,E) of two-electron pulses and find a bimodal structure with an energy separation of about 1.8 eV and a temporal separation of about 240 fs, attributed to Coulomb repulsion during acceleration and subsequent dispersion. The paper also develops a multi-electron IELS theory from a minimal-coupling Hamiltonian and a Jacobi-Anger expansion, supports the experiment with relativistic trajectory simulations, and proposes that long-pulse IELS can imprint sub-optical-cycle temporal correlations on two-electron states, enabling post-selection-controlled enhancement or suppression of cathodoluminescence. The experimental reconstruction is the central novelty; the attosecond-correlation and superradiance parts are theoretical predictions.

Significance. If the reconstruction is robust, the work offers a rare view of few-electron phase-space correlations in a UTEM and a concrete route toward coherent control of multi-electron pulses. The multi-electron IELS framework in Appendix B, connecting measured spectrograms to phase-space densities through a convolution, is a useful general contribution. The paper is also transparent about its key approximations: no entanglement in the beam, at-most-one-electron scattering per delay, and a Gaussian sub-ensemble model in the reconstruction. The trajectory simulations and the analytical derivation are internally consistent. The main risk is that the central experimental claim rests on a parametric inversion whose assumptions are not validated against the non-Gaussian distributions that the simulations themselves produce; if the authors add such a validation and report uncertainties, the significance of the work would be high.

major comments (3)
  1. [Appendix C, Eq. (C1); Fig. 4] The reconstruction of ρA/B(t,E) is not model-free. Assumption (ii) in Appendix C postulates a Gaussian energy envelope with a time-independent width σ_inc and a time-dependent center E_chirp(t); the chirp is then read off from a single Fourier component of the gain-filtered spectra. For a non-Gaussian or asymmetric conditional distribution, the phase of that Fourier component yields an effective center rather than the true mean, and the Gaussian envelope fit returns an effective width. Because the bimodal separation (1.8 eV, 240 fs) and the inter-lobe slope (130–140 fs/eV) are central quantitative claims, the authors should validate the inversion by applying it to synthetic IELS spectrograms generated from their own trajectory simulations (Appendix A), which naturally produce non-Gaussian ρ2, and compare the recovered and true distributions. They should also report uncertainties on the extracted separations and chirps. Without this, the reconstructed bimodal density in Fig. 4 is a model output rather than a direct measurement.
  2. [Main text around Eq. (2) and Fig. 3f] The reduction of Eq. (1) to the one-dimensional convolutions in Eq. (2) assumes that at most one electron undergoes IELS at a given delay. Figure 3f explicitly shows that the gain contributions of the two electrons overlap at small delays, and the text notes this overlap without quantifying it. The reconstructed density near zero delay, including the reported nonlinear flattening and the sub-ensemble chirps, can be biased by events in which both electrons scatter or by gain-selection misassignment. The paper should specify the temporal separation criterion quantitatively (for example, the fraction of double-scattering events as a function of delay) and either exclude affected delays or model the overlap in the inversion.
  3. [Results, Fig. 4] The quantitative comparisons that support the interpretation are presented without error bars. In particular, the difference between the within-sub-ensemble chirp (about 300 fs/eV at higher current) and the inter-lobe slope (about 140 fs/eV) is the basis for claiming that the energy difference emerges during propagation; the paper should quantify the uncertainty of these slopes and of the 240 fs temporal separation before drawing that conclusion. This is especially important because the within-lobe chirp at higher current is extracted from the same delay range where the overlap of gain contributions in Fig. 3f is largest.
minor comments (4)
  1. [Abstract and Introduction] The phrase 'directly map' in the abstract overstates the procedure described in Appendix C, which is a model-based deconvolution under explicit Gaussian and short-pulse assumptions; recommend wording such as 'reconstruct via a model-based deconvolution'.
  2. [Appendix B, Eq. (B3)] In Eq. (B3), the sum indices m, m′ and the variable n are introduced inside the final expression; the notation should be defined before use, and λ should be written explicitly as a function of ℓ, m, and m′ (or of n).
  3. [Appendix D, Eq. (D2)] The condition 'Δ_L/σ ≫ 1' uses a symbol σ that is not defined in the appendix; if σ refers to the electron temporal width Δ_c, this should be stated explicitly.
  4. [Figs. 2 and 3] The color scales in Figs. 2e–g and 3f are labeled 'arb. u.'; for a quantitative reconstruction, the relative normalization between the two-electron sub-ensembles (pink vs. green) should be specified, because Eq. (2) assumes a fixed 1/2 prefactor.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase-space reconstruction is a model-dependent deconvolution, not a fit to the predicted correlations, and the attosecond-correlation claim is derived from the IELS Hamiltonian.

full rationale

The central experimental claim is the reconstruction of the two-electron phase-space density via inelastic electron-light scattering. The reconstruction in Appendix C does assume a parametric form ρ_A/B(t,E) = η(t) exp[-(E - E_chirp(t) - E_bar)^2/(2σ_inc^2)] and then extracts E_chirp(t) from the Fourier phase at the photon frequency and σ_inc from the Gaussian envelope. This is a model-dependent deconvolution, and the skeptic's concern about skew or time-dependent widths is a legitimate correctness risk, but it is not circularity: the parameters are extracted from the measured spectrogram, not set equal to the target bimodal separation or attosecond correlations. The bimodal energy splitting (1.8 eV) is directly visible in the raw pair histogram (Fig. 3a), and the temporal separation (240 fs) emerges from the fitted time profiles η_A/B, which are not assumed to be separated by that value. The theoretical claims about attosecond inter-particle correlations follow from the Jacobi-Anger expansion of the minimal-coupling Schrödinger solution in Appendix B, not from the experimental reconstruction. The superradiance formula in Eq. (3) is derived in Appendix D from the two-electron Wigner function, and references to prior work on the degree of coherence are contextual, not load-bearing for the new measurement. No equation in the paper is equivalent by construction to its inputs, and no fitted parameter is renamed as a prediction. Therefore no circular step is identified.

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

The central claims rest on a set of modeling assumptions rather than on new physical entities. The main free parameters are the reconstructed energy width and the electron coherence time, both determined from data. The most consequential assumption is the absence of entanglement, which underlies the entire theoretical treatment of the two-electron state.

free parameters (3)
  • sigma_inc (incoherent energy envelope width) = not stated numerically; fitted to Fourier envelope
    Appendix C: 'sigma_inc is obtained by fitting the envelope of the absolute value of the Fourier transform to a Gaussian function.' The reconstructed phase-space density depends on this fitted width.
  • electron coherence time Delta_c = 1.29 fs (simulation); derived from 0.6 eV spectral width
    Derived from the non-stochastically broadened single-electron spectrum at low power. Enters the IELS sideband envelope and the Wigner-function predictions in Appendix D.
  • Initial simulation spreads sigma_0,t and sigma_0,E = 80 fs and 0.35 eV
    Trajectory simulation in Appendix A uses these as initial temporal and energy spreads, chosen to match the photoemission laser pulse and initial spectrum. They affect the simulated phase-space evolution.
assumptions (5)
  • domain assumption No quantum entanglement between the two electrons in the beam
    Appendix B states: 'we tacitly exclude the presence of quantum correlations, i.e., entanglement, in the beam.' This justifies solving independent single-electron Schrodinger equations and is critical for the Wigner-function and quasiprobability predictions of attosecond correlations.
  • domain assumption The IELS slicing function factorizes as a product of single-electron Gamma functions
    Eq. (1) writes P({t0,i},{E0,i}) = prod_i Gamma(tL - t0,i, Ei - E0,i), assuming each electron interacts independently with the optical near field within the interaction region.
  • domain assumption Coulomb repulsion is negligible close to the Si membrane and during the IELS interaction
    Appendix B explicitly neglects 'Coulomb repulsion close to the Si membrane' when solving the Schrodinger equation for each electron, which is necessary for the factorized solution.
  • standard math Standard approximations: linearized electron dispersion, no spin flips, no ponderomotive forces, small velocity differences
    Appendix B introduces the linearized Hamiltonian and neglects terms of order |v-vi|/c ~ 1e-5. These are standard simplifications in electron-light interaction theory.
  • standard math Jacobi-Anger expansion and semi-monochromatic laser pulse
    Used in Appendix B to expand the phase factor into Bessel functions and to model the laser as a Gaussian envelope with carrier frequency omega_L.

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Cite this review

Pith. "Pith review of Femtosecond and attosecond phase-space correlations in few-particle photoelectron pulses." pith.science (2026). https://pith.science/paper/LQGFUCKE

@misc{pith2026241211929,
  author       = {Pith},
  title        = {Pith review of: Femtosecond and attosecond phase-space correlations in few-particle photoelectron pulses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQGFUCKE}},
  note         = {Machine review of arXiv:2412.11929}
}
read the original abstract

Temporal correlations in pulsed electron beams reflect the microscopic dynamics of emission and interparticle interaction. In femtosecond electron emission from nanoscale field emitters, Coulomb interactions result in structured few-electron states with strong correlations in energy, time, and transverse momentum. Interactions with external fields may be used to both probe and further manipulate these correlated states. Here, we combine femtosecond-gated, event-based detection with inelastic electron-light scattering to directly map the photoelectron phase-space distribution of two-electron states. Our experiments demonstrate a bimodal structure in longitudinal phase space, with distinct contributions from interparticle interaction and dispersion. Moreover, we theoretically reveal that global phase modulation coherently shapes the few-electron phase-space distribution to exhibit attosecond temporal correlations. This controlled phasing of few-electron states can be harnessed to produce tailored excitations and super-radiance via two-electron energy post-selection.

Figures

Figures reproduced from arXiv: 2412.11929 by the authors.

Figure 1
Figure 1. Generation and propagation of two-electron pulses [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Inelastic electron-light scattering of few-electron [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Phase-space reconstruction of double-electron states via inelastic electron-light scattering. a) Spectrum (top), scheme [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Reconstructed marginalized phase-space densities [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: Coherent shaping of two-electron pulses enables attosecond inter-particle correlations and coherent modulation [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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Reference graph

Works this paper leans on

69 extracted references · 59 canonical work pages

  1. [64]

    Two-electron quantum walks can probe entanglement and decoherence in an electron microscope

    O. Tziperman, D. Nabben, R. Ruimy, J. Holder, E. Nussinson, Y. Fang, A. Gorlach, D. Kazenwadel, A. Karnieli, I. Kaminer, and P. Baum, Two-electron quantum walks can probe entanglement and decoherence in an electron microscope (2025), arXiv:2505.03707

    work page Pith review arXiv 2025

  2. [1]

    Boersch, Zeitschrift f¨ ur Physik139, 115 (1954)

    H. Boersch, Zeitschrift f¨ ur Physik139, 115 (1954)

    work page 1954

  3. [2]

    Loeffler, Zeitschrift f¨ ur angewandte Physik 27, 145 (1969)

    KH. Loeffler, Zeitschrift f¨ ur angewandte Physik 27, 145 (1969)

    work page 1969

  4. [3]

    Borrelli, T

    S. Borrelli, T. C. H. de Raadt, S. B. van der Geer, P. H. A. Mutsaers, K. A. H. van Leeuwen, and O. J. Luiten, Phys- ical Review Letters 132, 115001 (2024)

    work page 2024

  5. [4]

    Kiesel, A

    H. Kiesel, A. Renz, and F. Hasselbach, Nature 418, 392 (2002)

    2002

  6. [5]

    Kodama, N

    T. Kodama, N. Osakabe, and A. Tonomura, Physical Re- view A 83, 063616 (2011)

    work page 2011

  7. [6]

    Kuwahara, Y

    M. Kuwahara, Y. Yoshida, W. Nagata, K. Nakakura, M. Furui, T. Ishida, K. Saitoh, T. Ujihara, and N. Tanaka, Physical Review Letters 126, 125501 (2021)

    work page 2021

  8. [7]

    Keramati, W

    S. Keramati, W. Brunner, T. J. Gay, and H. Batelaan, Physical Review Letters 127, 180602 (2021)

    work page 2021

Show all 69 references
  1. [8]

    Haindl, A

    R. Haindl, A. Feist, T. Domr¨ ose, M. M¨ oller, J. H. Gaida, S. V. Yalunin, and C. Ropers, Nature Physics 19, 1410 (2023)

    2023

  2. [9]

    Hommelhoff, Y

    P. Hommelhoff, Y. Sortais, A. Aghajani-Talesh, and M. A. Kasevich, Physical Review Letters 96, 077401 (2006)

    2006

  3. [10]

    Ropers, D

    C. Ropers, D. R. Solli, C. P. Schulz, C. Lienau, and T. El- saesser, Physical Review Letters 98, 043907 (2007)

    2007

  4. [11]

    Barwick, C

    B. Barwick, C. Corder, J. Strohaber, N. Chandler-Smith, C. Uiterwaal, and H. Batelaan, New Journal of Physics 9, 142 (2007)

    2007

  5. [12]

    Meier, J

    S. Meier, J. Heimerl, and P. Hommelhoff, Nature Physics 19, 1402 (2023)

    2023

  6. [13]

    S. A. Koppell, J. W. Simonaitis, M. A. R. Krielaart, W. P. Putnam, K. K. Berggren, and P. D. Keathley, New Journal of Physics 27, 023012 (2025)

    2025

  7. [14]

    Gover and A

    A. Gover and A. Yariv, Physical Review Letters 124, 064801 (2020)

    2020

  8. [15]

    Zhao, X.-Q

    Z. Zhao, X.-Q. Sun, and S. Fan, Physical Review Letters 126, 233402 (2021)

    2021

  9. [16]

    Karnieli, N

    A. Karnieli, N. Rivera, A. Arie, and I. Kaminer, Physical Review Letters 127, 060403 (2021)

    2021

  10. [17]

    F. J. Garc ´ ıa de Abajo and V. Di Giulio, ACS Photonics 8, 945 (2021)

    2021

  11. [18]

    R¨ atzel, D

    D. R¨ atzel, D. Hartley, O. Schwartz, and P. Haslinger, Physical Review Research 3, 023247 (2021)

    2021

  12. [19]

    Zhang, D

    B. Zhang, D. Ran, R. Ianconescu, A. Friedman, J. Scheuer, A. Yariv, and A. Gover, Physical Review Let- ters 126, 244801 (2021)

    2021

  13. [20]

    Ruimy, A

    R. Ruimy, A. Gorlach, C. Mechel, N. Rivera, and I. Kaminer, Physical Review Letters 126, 233403 (2021)

    2021

  14. [21]

    O. Kfir, V. Di Giulio, F. J. G. de Abajo, and C. Ropers, Science Advances 7, eabf6380 (2021)

    2021

  15. [22]

    Di Giulio, O

    V. Di Giulio, O. Kfir, C. Ropers, and F. J. Garc ´ ıa de Abajo, ACS Nano 15, 7290 (2021)

    2021

  16. [23]

    Gorlach, O

    A. Gorlach, O. Reinhardt, A. Pizzi, R. Ruimy, G. Baranes, N. Rivera, and I. Kaminer, Physical Review A 109, 023722 (2024)

    2024

  17. [24]

    Di Giulio, R

    V. Di Giulio, R. Haindl, and C. Ropers, Nanophotonics 1–14, 1 (in press)

  18. [25]

    E. J. VandenBussche and D. J. Flannigan, Nano Letters 19, 6687 (2019)

    2019

  19. [26]

    J. J. Axelrod, J. T. Zhang, P. N. Petrov, R. M. Glaeser, and H. M¨ uller, Current Opinion in Structural Biology 86, 102805 (2024)

    2024

  20. [27]

    Kfir, Physical Review Letters 123, 103602 (2019)

    O. Kfir, Physical Review Letters 123, 103602 (2019)

    2019

  21. [28]

    Talebi and I

    N. Talebi and I. Bˇ rezinov´ a, New Journal of Physics23, 063066 (2021)

    2021

  22. [29]

    Koneˇ cn´ a, F

    A. Koneˇ cn´ a, F. Iyikanat, and F. J. Garc ´ ıa de Abajo, Sci- ence Advances 8, eabo7853 (2022)

    2022

  23. [30]

    Kazakevich, H

    E. Kazakevich, H. Aharon, and O. Kfir, Physical Review Research 6, 043033 (2024)

    2024

  24. [31]

    Henke, H

    J.-W. Henke, H. Jeng, and C. Ropers, Phys. Rev. A 111, 012610 (2025)

    2025

  25. [32]

    Henke, H

    J.-W. Henke, H. Jeng, M. Sivis, and C. Ropers, Obser- vation of quantum entanglement between free electrons and photons (2025), arXiv:2504.13047

    2025 arXiv

  26. [33]

    Preimesberger, S

    A. Preimesberger, S. Bogdanov, I. C. Bicket, P. Rembold, and P. Haslinger, Experimental verification of electron- photon entanglement (2025), arXiv:2504.13163

    2025 arXiv

  27. [34]

    A. H. Zewail, Science 328, 187 (2010)

    2010

  28. [35]

    Feist, N

    A. Feist, N. Bach, N. Rubiano da Silva, T. Danz, M. M¨ oller, K. E. Priebe, T. Domr¨ ose, J. G. Gatzmann, S. Rost, J. Schauss, S. Strauch, R. Bormann, M. Sivis, S. Sch¨ afer, and C. Ropers, Ultramicroscopy 176, 63 (2017)

    2017

  29. [36]

    N. Bach, T. Domr¨ ose, A. Feist, T. Rittmann, S. Strauch, C. Ropers, and S. Sch¨ afer, Structural Dynamics6, 014301 (2019)

    2019

  30. [37]

    P. K. Olshin, M. Drabbels, and U. J. Lorenz, Structural Dynamics 7, 054304 (2020)

    2020

  31. [38]

    C. Zhu, D. Zheng, H. Wang, M. Zhang, Z. Li, S. Sun, P. Xu, H. Tian, Z. Li, H. Yang, and J. Li, Ultrami- croscopy 209, 112887 (2020)

    2020

  32. [39]

    Shiloh, T

    R. Shiloh, T. Chlouba, and P. Hommelhoff, Physical Re- view Letters 128, 235301 (2022)

    2022

  33. [40]

    Kuttruff, D

    J. Kuttruff, D. Nabben, A.-C. Zimmermann, A. Ryabov, and P. Baum, Science Advances 10, eadl6543 (2024)

    2024

  34. [41]

    Schr¨ oder, A

    A. Schr¨ oder, A. Wendeln, J. T. Weber, M. Mukai, Y. Kohno, and S. Sch¨ afer, Laser-driven cold-field emis- sion source for ultrafast transmission electron microscopy (2024), arXiv:2410.23961

    2024 arXiv

  35. [42]

    D. H. Dowell and J. F. Schmerge, Physical Review Spe- cial Topics - Accelerators and Beams 12, 074201 (2009)

    2009

  36. [43]

    B. Cook, M. Bronsgeest, K. Hagen, and P. Kruit, Ultra- microscopy 109, 403 (2009)

    2009

  37. [44]

    Herink, D

    G. Herink, D. R. Solli, M. Gulde, and C. Ropers, Nature 483, 190 (2012)

    2012

  38. [45]

    Kr¨ uger, M

    M. Kr¨ uger, M. Schenk, and P. Hommelhoff, Nature475, 78 (2011)

    2011

  39. [46]

    Hergert, R

    G. Hergert, R. Lampe, A. W¨ oste, and C. Lienau, Nano Letters 24, 11067 (2024)

    2024

  40. [47]

    Cook and P

    B. Cook and P. Kruit, Applied Physics Letters 109, 151901 (2016)

    2016

  41. [48]

    Kuwahara, Y

    M. Kuwahara, Y. Nambo, K. Aoki, K. Sameshima, X. Jin, T. Ujihara, H. Asano, K. Saitoh, Y. Takeda, and N. Tanaka, Applied Physics Letters 109, 013108 (2016)

    2016

  42. [49]

    Meier and P

    S. Meier and P. Hommelhoff, ACS Photonics 9, 3083 (2022)

    2022

  43. [50]

    C. T. Hebeisen, G. Sciaini, M. Harb, R. Ernstorfer, T. Dartigalongue, S. G. Kruglik, and R. J. D. Miller, Optics Express 16, 3334 (2008)

    2008

  44. [51]

    Koz´ ak, J

    M. Koz´ ak, J. McNeur, K. J. Leedle, H. Deng, N. Sch¨ onen- berger, A. Ruehl, I. Hartl, J. S. Harris, R. L. Byer, and P. Hommelhoff, Nature Communications8, 14342 (2017). 11

    2017

  45. [52]

    D. Epp, B. Schr¨ oder, M. M¨ oller, and C. Ropers, Struc- tural Dynamics 11, 024306 (2024)

    2024

  46. [53]

    S. T. Park, O.-H. Kwon, and A. H. Zewail, New Journal of Physics 14, 053046 (2012)

    2012

  47. [54]

    F. O. Kirchner, A. Gliserin, F. Krausz, and P. Baum, Nature Photonics 8, 52 (2014)

    2014

  48. [55]

    Barwick, D

    B. Barwick, D. J. Flannigan, and A. H. Zewail, Nature 462, 902 (2009)

    2009

  49. [56]

    F. J. Garc ´ ıa de Abajo, Reviews of Modern Physics 82, 209 (2010)

    2010

  50. [57]

    Feist, K

    A. Feist, K. E. Echternkamp, J. Schauss, S. V. Yalunin, S. Sch¨ afer, and C. Ropers, Nature521, 200 (2015)

    2015

  51. [58]

    Ballabriga, M

    R. Ballabriga, M. Campbell, and X. Llopart, Nuclear In- struments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 878, 10 (2018)

    2018

  52. [59]

    J. P. van Schayck, E. van Genderen, E. Maddox, L. Rous- sel, H. Boulanger, E. Fr¨ ojdh, J.-P. Abrahams, P. J. Pe- ters, and R. B. Ravelli, Ultramicroscopy 218, 113091 (2020)

    2020

  53. [60]

    D. A. Plemmons, S. Tae Park, A. H. Zewail, and D. J. Flannigan, Ultramicroscopy 146, 97 (2014)

    2014

  54. [61]

    F. J. Garc ´ ıa de Abajo, Rev. Mod. Phys.82, 209 (2010)

    2010

  55. [62]

    S. V. Yalunin, A. Feist, and C. Ropers, Physical Review Research 3, L032036 (2021)

    2021

  56. [63]

    F. J. Garc ´ ıa de Abajo and C. Ropers, Physical Review Letters 130, 246901 (2023)

    2023

  57. [65]

    S. T. Park, M. Lin, and A. H. Zewail, New J. Phys. 12, 123028 (2010)

    2010

  58. [66]

    F. J. Garc ´ ıa de Abajo, A. Asenjo-Garcia, and M. Kociak, Nano Lett. 10, 1859 (2010)

    2010

  59. [67]

    G. M. Vanacore, I. Madan, G. Berruto, K. Wang, E. Po- marico, R. J. Lamb, D. McGrouther, I. Kaminer, B. Bar- wick, F. J. Garc ´ ıa de Abajo, and F. Carbone, Nat. Com- mun. 9, 2694 (2018)

    2018

  60. [68]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of Mathe- matical Functions (Dover, New York, 1972)

    1972

  61. [69]

    Wigner, Phys

    E. Wigner, Phys. Rev. 40, 749 (1932)

    1932

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