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REVIEW 3 major objections 4 minor 48 references

Attosecond tunneling time measurements through momentum squeezing in strong field ionization

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that the time an electron spends tunneling out of an atom is imprinted in the width of its photoelectron momentum distribution, so tunneling durations can be read directly from momentum images.

desk verdict The paper proposes a direct readout of tunneling times from transverse momentum widths, with strong TDSE support, but the central SFA derivation is omitted and needs to be shown. read the letter →

arxiv 2506.17483 v1 pith:K457UOT6 submitted 2025-06-20 physics.atom-ph quant-ph

Jonathan Dubois , Léonardo Rico , Camille Lévêque , Jérémie Caillat , Richard Taïeb This is my paper · ORCID
classification physics.atom-phquant-ph PACS 32.80.Rm32.80.Wr
keywords attosecondtunnelingtimephotoelectronmomentumdistributionstrong-fieldionizationattoclocktransversesqueezingcircularlypolarizedlasertraversalKeldyshparameter
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 claims that when a strong circularly polarized laser field pulls an electron out of an atom, the electron's momentum distribution carries a direct imprint of the time it spent under the barrier. In the direction perpendicular to the polarization plane, the distribution is a Gaussian whose width is set by the tunneling duration $\tau$; in the polarization plane, an analytically related width carries the same information after a known correction. The paper turns this into a measurement protocol: each photoemission angle fixes the exit time through $\theta = \omega t_0$, and a Gaussian fit to the transverse momentum profile fixes the duration. Applied to numerical simulations of hydrogen and argon and to published argon data, the protocol yields tunneling times of a few hundred attoseconds, growing as the instantaneous field weakens. If correct, the result resolves the longstanding question of whether strong-field tunneling is instantaneous by showing where the finite duration is recorded.

What carries the argument

The load-bearing object is the complex saddle-point time $t_\star=t_0+i\tau$, which encodes tunneling as an excursion into imaginary time. Expanding the strong-field-approximation wavefunction around the most probable momentum in cylindrical coordinates produces the Gaussian factorization of Eqs. (1a)-(1c), and a transcendental equation links $\tau$ to the instantaneous adiabaticity parameter $\gamma(t_0)=\omega\sqrt{2I_p}/F(t_0)$. The same $\tau$ emerges from the WKB wavefunction of a static barrier as the traversal time, so the transverse momentum squeezing is identified as the universal observable signature of the tunneling duration.

What would settle it

Measure photoelectron momentum distributions from a noble gas at high angular resolution and extract $\tau$ independently from the $p_z$ and the in-plane widths; the two values must lie on the curve of Eq. (1c) after the known Coulomb shift, otherwise the Gaussian-width interpretation fails. A cleaner test uses an atom with a short-range potential, where Coulomb corrections are absent, and checks that the extracted $\tau$ follows the predictions of Eq. (4) across intensity and angle; a mismatch would rule out the protocol.

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Extended reading notes

Core claim

The central claim is that the photoelectron momentum distribution from strong-field ionization by a circularly polarized pulse factorizes as $D(p,p_z;\theta)=D_z(p_z;\theta)D_p(p;\theta)$, with $D_z(p_z;\theta)\propto \exp(-m\tau(\theta)p_z^2/\hbar)$ and an analogous Gaussian along $p$ whose inverse width $\tilde{\tau}(\theta)$ is a known function of $\tau$, the laser frequency, and the adiabaticity parameter. The tunneling duration $\tau(\theta)$ is therefore observable as the inverse width of the momentum-space Gaussian once the emission angle is converted into an exit time via $\theta=\omega t_0$. The same Gaussian squeezing follows from a WKB treatment of a static three-dimensional barrier, where the width is controlled by the traversal time $\tau=\int_{x_{\mathrm{in}}}^{x_0} dx/\sqrt{2[V(x)-E]/m}$, showing that the effect is a general property of multidimensional tunneling rather than an artifact of the strong-field approximation. Numerical solutions of the time-dependent Schrödinger equation and re-analysis of experimental momentum distributions support the protocol, yielding durations of hundreds of attoseconds that increase as the instantaneous laser field decreases.

Load-bearing premise

The protocol assumes that the Gaussian width measured at the detector is the unmodified imprint of the tunneling duration, meaning that post-barrier Coulomb attraction, focal-volume intensity averaging, and detector resolution do not appreciably reshape the transverse momentum distribution; the paper's own supplementary analysis shows that Coulomb effects shift extracted times by tens of attoseconds along the propagation axis at large angles and that the angle-to-time mapping would be modified there.

Editorial extensions

If this is right

  • Tunneling durations can be read from a single photoelectron momentum image by fitting Gaussian widths, with a time resolution of roughly $\delta\tau[\mathrm{asec}]\approx 0.01\,\delta\theta[\mathrm{deg}]\,\lambda[\mathrm{nm}]$.
  • The photoemission direction acts as a clock hand through $\theta=\omega t_0$, so no separate reference clock is needed to time the tunnel exit.
  • Because the Coulomb potential shifts the $p_z$-derived times more than the in-plane times, in-plane extraction is the more reliable route, and the Coulomb bias shrinks at higher ionization potentials or longer wavelengths.
  • In the long-pulse limit, above-threshold-ionization interference peaks modulate but do not change the Gaussian widths, so the protocol is not restricted to few-cycle pulses.
  • The extracted finite durations of hundreds of attoseconds reconcile the attoclock debate by showing where the tunneling time is recorded and why earlier near-zero readings arose.

Reading between the lines

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

  • The transverse-squeezing relation should apply to tunneling in other multidimensional settings, such as field emission from surfaces, where the transverse momentum width of emitted electrons could serve as a built-in clock.
  • An experiment that simultaneously measures both widths at a single angle, with high statistics, could check the ratio $\tilde{\tau}/\tau$ against Eq. (1c) and thereby isolate any post-barrier distortion source.
  • The protocol might extend to elliptical polarization or aligned molecules, where the barrier is anisotropic; the momentum width could then map the orientation-dependent barrier shape rather than a single duration.
  • Since the dispersion of $\tau$ across momentum components is below 1% in typical conditions, higher-order fits to the non-Gaussian wings of the distribution could in principle retrieve a distribution of tunneling times rather than a single most-probable value.
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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 claims that in strong-field ionization by a circularly polarized infrared pulse, the transverse photoelectron momentum distribution carries the tunneling duration in its width: along the light-propagation axis it is Gaussian in p_z with width set by the tunneling time tau(theta), and along the polarization-plane radius it is Gaussian in p around the most probable momentum with a modified width given by Eq. (1c). The paper derives these forms from the strong-field approximation and a WKB traversal-time argument, validates them against 3D TDSE simulations for hydrogen, a short-range model atom, and a model argon atom, and applies the p_z form to published argon experimental data to extract tunneling times of a few hundred attoseconds. It also proposes an angular resolution estimate and discusses the effect of the Coulomb potential, admitting that it up-shifts extracted times by tens of attoseconds along p_z.

Significance. If the central Gaussian-width identity holds, the paper offers a simple, parameter-free protocol for reading tunneling and exit times from photoelectron momentum distributions, with an estimated resolution of ~16 as at 800 nm and 2-degree angular resolution. The strengths are that the central relation has no fitted constants, is tested on several potentials and against one published experimental distribution, and the paper includes a resolution formula and an explicit long-pulse analysis. The main caveat is that the derivation of the Gaussian form from the saddle-point equations is not shown, and the admitted Coulomb systematics are of the same order as the claimed accuracy, so the quantitative claim is currently supported more by numerical agreement than by a complete analytic derivation.

major comments (3)
  1. The central result is obtained by substituting the saddle-point conditions into the SFA wave packet and expanding around (p0,0), but the manuscript only states that this happens 'after several steps of mathematical (and somehow tedious) rewriting' and does not show the expansion of the prefactor C(p,t*) in Eq. (B3) or of the real-time action contribution. Since C contains the initial-state momentum dependence through |p+A(t*)|, and the action S(p,t*) contributes p_z-dependent phase factors, the statement that D_z(p_z;theta) is Gaussian with width exactly m tau(theta)/hbar requires that these contributions either cancel or are negligible. Because Eq. (1a) is used to convert the published argon widths into tunneling times in Fig. 3, this omitted step is load-bearing for the absolute calibration. Please provide the complete saddle-point expansion, including the p_z dependence of the prefactor and the real-time phase, and state the approximations and their validity range.
  2. The supplementary material states that the Coulomb potential up-shifts the extracted times by tens of attoseconds along p_z and would modify Eq. (2) at large angles, yet the experimental retrieval in Fig. 3 uses exactly the p_z channel. The text says the Coulomb effect 'does not hamper the validity of our SFA-based interpretations,' but an up-shift of tens of attoseconds is of the same order as the claimed precision and as the differences between the experimental points and Eq. (4). Please quantify the Coulomb correction for the argon conditions used in Fig. 3, or restrict the quantitative claims to the p channel where the Coulomb effect is stated to be smaller, or provide a systematic correction procedure.
  3. The figure caption reads 'using Eq. 1b' while the text explicitly says the argon extraction uses Eq. (1a); since Eqs. (1a) and (1b) correspond to different momentum channels, this inconsistency must be resolved.
minor comments (4)
  1. The long-pulse analysis in Eq. (B8) keeps C(p,t*) inside the interference sum but the subsequent claim that the ATI peaks are 'modulated by the distribution (1b)' ignores possible p-dependence of C(p,t*) in the interference sum; please add a sentence explaining why C does not affect the width.
  2. The sentence 'the less straightforward tau-dependency of the PMD width along p ... boils down to a bijective one-to-one map' is grammatically awkward; please rephrase for clarity.
  3. There are several small language issues: 'gaz' should be 'gas', 'conforts' should be 'confirms', and 'envelop' should be 'envelope' in the methods and figure captions.
  4. Reference [39] is cited in the text alongside [38] for the Ammosov-Delone-Krainov rate, but [39] is the experimental Arissian et al. paper; please verify the citation numbering.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the tunneling-time/width relation is derived from the SFA saddle-point expansion and tested against independent TDSE and published experimental data.

full rationale

The paper's central relation—Eqs. (1a)-(1c), connecting transverse PMD widths to the tunneling duration—is derived within the SFA saddle-point approximation rather than fitted. In SM B.1, tau is defined as the saddle-point imaginary time at the distribution maximum via Eq. (B5d), and the subsequent expansion of the action produces an explicit exponential term -F^2/omega^2 tau sigma_z^2, which is -tau p_z^2 after rescaling sigma_z = omega p_z/F. The Gaussian width is therefore a mathematical consequence of the model, not an input parameter renamed as a prediction. The protocol then extracts widths from TDSE simulations and from the published Ar PMDs of Ref. [39], both of which are external to the derivation. The TDSE simulations do not assume the SFA Gaussian form, so agreement with Eq. (4) provides independent support. The experimental data are likewise used as an external benchmark. The only self-citation, Ref. [44], supports the minor and explicitly verified point that initial-state symmetry plays a small role for Ar ('we verified with SFA-based simulations'); it is not load-bearing for the main derivation or the angle-to-time mapping. No external uniqueness theorem is imported from the authors' prior work, and no fitted parameter is presented as a prediction. The SM's phrase 'after several steps of mathematical (and somehow tedious) rewriting' indicates an omitted algebraic derivation, but an omitted expansion is a completeness issue, not circularity. Accordingly, the paper is self-contained against external benchmarks and merits a circularity score of 0.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central analytic result uses the SFA saddle-point approximation, the slowly varying envelope approximation, a Gaussian truncation of the wavepacket around the most probable momentum, and the identification of the complex-time imaginary part with the Buttiker-Landauer traversal time. The TDSE validation adds model-potential parameters (A and b) calibrated to the ionization potentials of H and Ar. No new physical entities are introduced.

free parameters (2)
  • Amplitude A of short-range potential = set to yield ground-state energy -0.5 a.u.
    Model potential V(r)=-A exp(-r^2) for pseudo-hydrogen; calibrated to Ip=13.6 eV, not fitted to the tunneling-time claim.
  • Regularization parameter b of soft-Coulomb potential = set to yield ground-state energy -0.58 a.u.
    Model potential V(r)=-(r^2+b^2)^-1/2 for Ar; calibrated to Ip=15.7 eV, not fitted to the central result.
assumptions (6)
  • standard math SFA saddle-point approximation of the ionization amplitude
    The PMD derivation starts from the Lewenstein ansatz and approximates the time integral by saddle points at complex times t_star=t0+i*tau (Eqs. B1-B4 in SM). This is a standard asymptotic technique, but its accuracy is uncontrolled in the present parameter regime.
  • domain assumption Slowly varying envelope approximation F(t0+i*tau) approximately F(t0)
    Used to obtain Eq. (B5c)-(B5d) and the simple angle-time mapping theta=omega*t0; breaks down when the pulse envelope changes on the scale of the complex time excursion.
  • domain assumption Single-active-electron model potentials
    The TDSE simulations use one-electron model potentials (Coulomb, short-range, soft-Coulomb) and neglect multi-electron correlation and core dynamics.
  • domain assumption Identification of SFA imaginary time tau with Buttiker-Landauer traversal time
    The paper equates tau in the saddle-point exponent with the traversal-time integral of Eq. (5); the WKB derivation supports the same Gaussian form for static barriers, but the equality for a time-dependent field is an interpretive step rather than a proved theorem.
  • domain assumption Neglect of Stark shift and dressing effects
    SM B.3 states that Stark shifts are not accounted for in Eqs. (1a)-(1c) and would require a finer model; this limits the accuracy at the largest intensities near theta=0.
  • domain assumption Gaussian truncation of the wavepacket around the most probable momentum
    The expansion of phi(p) to second order around (p0,0) yields the exponential forms (1a)-(1b); if the true PMD is non-Gaussian at the measured level, fitted widths would not correspond to tau.

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Cite this review

Pith. "Pith review of Attosecond tunneling time measurements through momentum squeezing in strong field ionization." pith.science (2026). https://pith.science/paper/K457UOT6

@misc{pith2026250617483,
  author       = {Pith},
  title        = {Pith review of: Attosecond tunneling time measurements through momentum squeezing in strong field ionization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K457UOT6}},
  note         = {Machine review of arXiv:2506.17483}
}
read the original abstract

Tunneling of a particle through a potential barrier is a fundamental physical process and a major thought-provoking outcome of quantum physics. It is at the basis of multiple scientific and technological advances and strongly influences both the structuring and the dynamics of matter at the microscopic scale. Without a classical counterpart, it defies our intuitive perception and understanding of the motion of a particle. Thus, the temporal characterization of tunneling, typically in terms of the time spent "under the barrier", referred to as tunneling time, raises several debates and questions on its interpretation and measurability. Here we show that an electron wavepacket tunneling out of an atom through the potential barrier induced by a strong electric field, carries in its momentum profile the value of the corresponding tunneling time, in a self-probing manner. In a revisited interpretation of the attoclock setup, we view a circularly polarized light pulse as a temporal prism which maps the barrier configuration, and hence the tunneling dynamics, onto different photoelectron ejection directions. From our simulations, we find that tunneling times in the infrared regime are of the order of hundreds of attoseconds, in agreement with previous theories.

Figures

Figures reproduced from arXiv: 2506.17483 by the authors.

Figure 1
Figure 1. FIG. 1. Illustrative photoelectron momentum distributions [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Tunneling times in simulated strong field ionization. (a) Correlation between the inverse widths of the PMD cuts along [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Tunneling durations [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Width of the photoelectron momentum distribution [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of the tunneling times in Ref. [35] and the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Tunneling time as a function of the angle at 800 nm for different laser intensities obtained from three-dimensional [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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