Pith. sign in

REVIEW 2 major objections 5 minor 38 references

Efficient Three-Dimensional Sub-Doppler Cooling of $^{40}$Ca$^+$ in a Penning Trap

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Dark-resonance laser cooling in a Penning trap drops a calcium ion's axial motion from 72 to 1.5 quanta in 800 microseconds, and parametric mode exchange extends sub-Doppler cooling to all three eigenmodes.

desk verdict Worth a look: a credible experimental demonstration of 3D sub-Doppler cooling in a Penning trap with a believable but under-justified semiclassical model; the experiment deserves refereeing even though the model needs work. read the letter →

arxiv 2602.02937 v1 pith:AMQPCK44 submitted 2026-02-03 physics.atom-ph quant-ph

Brian J. McMahon , Brian C. Sawyer This is my paper · ORCID
classification physics.atom-phquant-ph
keywords Penningtrapsub-Dopplercoolingdarkresonancecalcium-40ionparametricmodecouplingsemiclassicalmodelweakbindinglimitLamb-Dickeregime
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

Laser cooling usually slows ions in radiofrequency traps to their quantum ground state, but Penning traps—which hold ions with static magnetic and electric fields—have lagged behind. This paper shows that a narrow two-photon dark resonance, created by the same laser beams already used for Doppler cooling, can cool the axial motion of a single calcium-40 ion far below the Doppler limit: the mean thermal occupation falls from 72 to 1.5 quanta in 800 microseconds. Because the cooling beam pushes only along one axis, the paper then applies an oscillating electrode voltage that coherently swaps the axial mode's occupation with each radial mode, cooling all three eigenmodes sub-Doppler with a single beam axis. A semiclassical model—Lindblad master equation for the atom's internal state plus classical harmonic motion—reproduces the measured cooling trajectory over two orders of magnitude. If correct, this gives Penning-trap quantum information experiments a fast, simple cooling path that avoids the slow sideband-cooling sequences previously required.

What carries the argument

The central mechanism is the two-photon dark resonance formed between the 397B and 866 nm lasers, both shifted ~26 MHz to the blue of their Doppler-cooling resonances. The dark resonance, with a ~2 MHz linewidth, produces a velocity-dependent radiation pressure force: the effective wavevector k_eff = |k_397 − k_866|, combined with the counter-propagating geometry, makes the photon scatter rate strongly asymmetric between energy-removing and energy-adding axial sidebands. Cooling is modeled in the weak-binding limit, where the axial oscillation period (~5 μs) is longer than the internal-state equilibration time (<1 μs), so the atom's internal state adiabatically follows its instantaneous velo

What would settle it

Measure the axial cooling trajectory for the same ion at a higher axial frequency (e.g., ω_z = 2π × 1 MHz, where the oscillation period approaches the internal equilibration time) and compare against the semiclassical model; if the model fails to predict the cooling rate or final occupation there, the weak-binding assumption is the false step. Also, cooling repeated hundreds of times from an initial occupation near 72 should occasionally show heating trajectories consistent with the predicted 1:230,000 runaway probability; seeing runaway heating at a far higher rate would falsify the capture-r

Watch

Extended reading notes

Core claim

The paper demonstrates that dark-resonance cooling, with the 397 nm and 866 nm beams detuned about 26 MHz to the blue, reduces the axial mode of a single 40Ca+ ion in a 0.91 T Penning trap from a mean occupation of 72(23) to 1.5(3) in 800 μs, with a 1/e time constant of 108(8) μs, as measured by 729 nm carrier Rabi flopping. Combining this axial cooling with parametric mode-exchange pulses—an oscillating quadrupolar potential resonant with the sum or difference of mode frequencies—coherently transfers the cooled axial population to the magnetron and modified cyclotron modes, yielding final occupations of n_z = 0.12(6), n_+ = 15(2), and n_- = 21(4). The final radial occupations are limited by

Load-bearing premise

The model's agreement depends on the weak-binding timescale separation: the ion's internal state must reach equilibrium (under 1 microsecond) well within one axial oscillation period (about 5 microseconds), so the axial restoring force can be neglected; if the trap frequency were raised toward 1 MHz or the laser coupling strengthened, this separation would break down and the cooling dynamics would deviate from the model.

Editorial extensions

If this is right

  • Penning-trap ion arrays can be sub-Doppler cooled with the same beam set used for Doppler cooling, eliminating the need for dedicated EIT or sideband beam configurations.
  • Axial ground-state cooling time drops from ~20 ms (sideband-only) to ~3.8 ms (dark resonance plus a few sideband pulses).
  • All three eigenmodes reach sub-Doppler occupation: axial near ground state (0.12), radial modes below ~25 quanta, limited by recoil heating.
  • The semiclassical model predicts a finite capture range (n < 900) and runaway heating above it, so optimal DR cooling requires trading capture range against cooling rate.
  • Radial mode occupations could be reduced below five quanta per uncooled mode with improved intensity and frequency stability, and continuous coupling during DR cooling is proposed as an avenue.

Reading between the lines

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

  • Editorial inference: The same dark-resonance scheme should work for other alkaline-earth-like ions (e.g., Sr+, Ba+) in Penning traps, since the cooling mechanism relies on the S–P and D–P two-photon structure common to that class.
  • Editorial inference: The weak-binding limit assumption sets an upper bound on the axial trap frequency for which this exact model holds; at higher frequencies (shorter oscillation period), the internal state may no longer adiabatically track velocity, and the model's predictions would require modification—this is a testable boundary.
  • Editorial inference: The parametric mode-exchange technique, used here after cooling, could be applied continuously during DR cooling; the paper notes initial attempts were unsuccessful, possibly due to micromotion, but improved compensation might enable simultaneous cooling of axial and radial modes.
  • Editorial inference: Because the capture range is finite, the scheme's reliability in a repeated quantum-information sequence depends on keeping the initial thermal occupation below the heating threshold; monitoring and feedback on initial temperature would be needed for robust operation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper demonstrates sub-Doppler cooling of all three eigenmodes of a single 40Ca+ ion in a compact Penning trap. Dark-resonance cooling along the axial direction, using the same 397/866 nm beams as Doppler cooling, reduces the axial thermal occupation from 72(23) to 1.5(3) in 800 μs with a 1/e time constant of 108(8) μs. A parametric mode-exchange drive then transfers axial coldness to the radial modes, yielding final occupations n_z = 0.12(6), n_+ = 15(2), and n_- = 21(4) after additional sideband cooling. The authors support the axial cooling curve with a semiclassical model combining Lindblad master-equation solutions for the internal dynamics with a classical equation for the axial velocity.

Significance. If the results hold, this is a practically significant advance: it demonstrates that a single axial cooling beam configuration can sub-Doppler cool all motional modes of a Penning-trapped ion, with a factor-of-five reduction in ground-state cooling time compared with prior sideband-only cooling. The experimental thermometry via 729 nm carrier/sideband Rabi flopping is a direct and well-established method, and the reported uncertainties are realistic. The paper also gives a concrete prediction for the DR cooling capture range. The main weakness is the theoretical model: the complex-amplitude equation used for the simulated cooling curves is not derived from the real equation of motion, so the claimed 'good agreement' between model and experiment is not yet fully supported. The experimental demonstration itself appears sound and is the principal value of the paper.

major comments (2)
  1. [Sec. III, Eq. (9)] Equation (9) is presented as following from Eqs. (4) and (8), but it is not equivalent to Eq. (4) for complex A_v. With v_z = Re[A_v e^{iω_z t}], the real part of the diffusion term in Eq. (9) is Re[D/(A_v e^{iω_z t})] = D Re[A_v e^{iω_z t}]/|A_v|^2, whereas Eq. (4) contains D/Re[A_v e^{iω_z t}]. These differ whenever Im[A_v e^{iω_z t}] ≠ 0. The text only says the complex form 'avoids poles'; no derivation, asymptotic justification, or numerical convergence check against Eq. (4) with a standard regularization (e.g., D v_z/(v_z^2+ε^2)) is provided. Since the simulated trajectories and the quoted capture range n̄_z < 900 in Fig. 4 are produced by Eq. (9), the claimed quantitative model agreement is not yet established. Please either derive Eq. (9) as a controlled approximation with error estimates, or benchmark it against a regularized solution of Eq. (4).
  2. [Sec. III / Fig. 4] The simulation is stated to take experimental parameters as inputs, but the laser linewidths (Lorentzian white-noise assumption) and the exact 397B detuning used for the Fig. 4 curve are not reported. The 397B detuning is described as optimized experimentally, but the value that enters the simulation is not given. Since the simulated cooling curve and the capture-range prediction are sensitive to these quantities, the reader cannot reproduce the 'good agreement' from the information in the paper. Please provide a complete parameter list (linewidths, detunings, Rabi rates, decay rates, EOM sideband frequencies) and state which parameters are measured versus optimized.
minor comments (5)
  1. [General] Raw data for the cooling curves in Figs. 4-6 are not provided. A data availability statement or repository link would strengthen reproducibility.
  2. [Sec. II] The text says 'F ∼3000 for both wavelengths' for the reference cavity; it would be useful to give the cavity free spectral range and finesse at each wavelength, since the 866 nm and 397 nm coatings may differ.
  3. [Sec. III, Eq. (5)] Equation (5) appears without derivation of the factor of 2. A brief explanation of the 2/3-dimensional diffusion projection would help the reader.
  4. [Sec. II / Fig. 5] The blue shaded region in Fig. 5 is described as centered at 3.9(6) quanta, but the vertical center is not explicitly marked on the axis; please add a horizontal line or label for clarity.
  5. [Conclusion] The statement that 'approximately 1 : 230,000 of DR cooling attempts will lead to axial heating' is model-dependent and should be explicitly flagged as a prediction of the semiclassical model, given the caveats above.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the experimental demonstration is direct and the semiclassical model uses measured parameters as inputs; only minor self-citation to a prior trap paper appears, and it is not load-bearing for the cooling claim.

full rationale

The central demonstration—axial DR cooling from n_z = 72(23) to 1.5(3) in 800 μs with a 108(8) μs time constant—is a direct measurement via 729 nm carrier and sideband flops, not a fit to the model. The simulation is described as taking experimental parameters as inputs ('The solid blue line is the result of a semiclassical sub-Doppler cooling simulation that takes experimental parameters as inputs'), and the model was not fitted to the cooling data; agreement is shown over nearly two orders of magnitude, which is an independent check rather than a circular reduction. The Lindblad master equation (Eqs. 6–7) is a standard first-principles treatment with stated assumptions (white laser frequency noise, k_r = |k_397|, neglect of ~8% decays to D_3/2), and the cited sources for the approach [8, 37] are external. The only self-citation is Ref. [28] for the trap apparatus, which is peripheral to the cooling physics; the sub-Doppler cooling mechanism, parametric mode exchange, and final occupation measurements do not rest on that self-citation. The skeptical concern about the complexification in Eq. 9 (Re of the solution of the complex equation not obviously solving the real Eq. 4) is a correctness/numerical-regularization issue, not a circularity: the model is not being equated to its own output, and the central experimental claim does not depend on the model. Therefore no circular step meeting the required evidentiary standard can be identified.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central result is experimental; the model rests on standard quantum-optics approximations. No novel free parameters are explicitly fit to the cooling data, though the laser linewidths and detunings are not fully disclosed, so their role in the reported agreement cannot be assessed from the text alone.

free parameters (2)
  • 397B laser detuning during DR cooling = ~26 MHz blue of Doppler resonance (empirically optimized)
    The detuning is hand-optimized to maximize cooling (Sec. II A, Fig. 3). It is an experimental control input to the simulation, not fitted to the final cooling curve.
  • Laser linewidths in Lindblad simulation
    The simulation assumes white frequency noise (Lorentzian linewidths) for the 397 nm and 866 nm lasers, but the numerical values are not reported (Sec. III). If these were adjusted to match the data, they would be free parameters.
assumptions (5)
  • domain assumption Lindblad master equation with Markovian spontaneous emission and white laser frequency noise.
    Sec. III Eq. 7: the Liouvillian includes jump operators for spontaneous decay and laser frequency fluctuations; white noise (Lorentzian linewidths) is assumed without reporting numerical values.
  • domain assumption Neglect of the axial restoring force (weak binding limit): the ion is treated as a free particle with instantaneous velocity on the timescale of internal dynamics.
    Sec. III: 'We neglect the Penning trap axial restoring force in Eq. 4 since... the axial oscillation period > internal state dynamics timescale.' This is load-bearing for the velocity-ansatz model.
  • domain assumption Recoil heating approximated by k_r=|k_397|, neglecting the ~8% of spontaneous decays to the D_3/2 manifold.
    Sec. III: stated approximation after Eq. 4.
  • domain assumption Equipartition of radial kinetic energy between the modified cyclotron and magnetron modes after axial DR cooling.
    Sec. III: 'we assume equipartition of the radial kinetic energy between the modified cyclotron and magnetron modes' following Eq. 5.
  • standard math Harmonic oscillator velocity ansatz v_z(t)=Re[A_v(t) e^{iω_z t}] with slowly varying complex amplitude.
    Sec. III Eq. 8; this mathematical ansatz is used to avoid numerical poles at zero velocity, a standard technique in semiclassical cooling models.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Three-Dimensional Sub-Doppler Cooling of $^{40}$Ca$^+$ in a Penning Trap." pith.science (2026). https://pith.science/paper/AMQPCK44

@misc{pith2026260202937,
  author       = {Pith},
  title        = {Pith review of: Efficient Three-Dimensional Sub-Doppler Cooling of $^40$Ca$^+$ in a Penning Trap},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AMQPCK44}},
  note         = {Machine review of arXiv:2602.02937}
}
abstract

We demonstrate efficient sub-Doppler laser cooling of the three eigenmodes of a $^{40}$Ca$^+$ ion confined in a compact Penning trap operating with a magnetic field of 0.91 T. Using the same set of laser beams as required for the initial Doppler laser cooling operation, we detune the laser frequencies to produce a narrow two-photon dark resonance. The process achieves a 1/e cooling time constant of 108(8) $\mu$s, ultimately reducing the mean thermal axial mode occupation from 72(23) to 1.5(3) in 800 $\mu$s as measured by resonantly probing an electric quadrupole transition near 729 nm. A parametric drive is applied to the trap electrodes which coherently exchanges the axial mode occupation with that of each radial mode, allowing for three-dimensional sub-Doppler cooling using only the axially-propagating laser beams. This sub-Doppler cooling is achieved for an axial oscillation frequency of $\omega_z = 2\pi~\times~$221 kHz, which places the motion well outside of the Lamb Dicke confinement regime at the Doppler laser cooling limit. Our measured cooling rate and final mode occupation are in good agreement with a semiclassical model which combines a Lindblad master equation solution for ion-photon interactions with classical harmonic oscillator motion of the trapped ion.

Figures

Figures reproduced from arXiv: 2602.02937 by the authors.

Figure 1
Figure 1. FIG. 1. Cross-section view of the in-vacuum permanent mag [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Measured axial mode occupation (points with error [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Measured axial mode occupation ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

38 extracted references · 1 linked inside Pith

  1. [1]

    S. Jain, T. Sägesser, P. Hrmo, C. Torkzaban, M. Stadler, R. Oswald, C. Axline, A. Bautista-Salvador, C. Os- pelkaus, D. Kienzler, and J. Home, Nature627, 510 (2024)

    2024

  2. [2]

    J. P. Gaebler, T. R. Tan, Y. Lin, Y. Wan, R. Bowler, A.C.Keith, S.Glancy, K.Coakley, E.Knill, D.Leibfried, andD.J.Wineland,Phys.Rev.Lett.117,060505(2016)

    2016

  3. [3]

    C. J. Ballance, T. P. Harty, N. M. Linke, M. A. Sepiol, and D. M. Lucas, Physical Review Letters117, 060504 (2016)

    2016

  4. [4]

    C. R. Clark, H. N. Tinkey, B. C. Sawyer, A. M. Meier, K. A. Burkhardt, C. M. Seck, C. M. Shappert, N. D. Guise, C. E. Volin, S. D. Fallek, H. T. Hayden, W. G. Rellergert, and K. R. Brown, Physical Review Letters 127, 130505 (2021)

    2021

  5. [5]

    C. H. Baldwin, B. J. Bjork, M. Foss-Feig, J. P. Gae- bler, D. Hayes, M. G. Kokish, C. Langer, J. A. Sedlacek, D. Stack, and G. Vittorini, Physical Review A: Atomic, Molecular, and Optical Physics103, 012603 (2021)

    2021

  6. [6]

    C. F. Roos, D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, Physical Review Letters85, 5547 (2000)

    2000

  7. [7]

    Lechner, C

    R. Lechner, C. Maier, C. Hempel, P. Jurcevic, B. P. Lanyon, T. Monz, M. Brownnutt, R. Blatt, and C. F. Roos, Physical Review A: Atomic, Molecular, and Opti- cal Physics93, 053401 (2016)

    2016

  8. [8]

    D. T. C. Allcock, T. P. Harty, M. A. Sepiol, H. A. Janacek, C. J. Ballance, A. M. Steane, D. M. Lucas, and D. N. Stacey, New Journal of Physics18, 023043 (2016)

    2016

Show all 38 references
  1. [9]

    Scharnhorst, J

    N. Scharnhorst, J. Cerrillo, J. Kramer, I. D. Leroux, J. B. Wübbena, A. Retzker, and P. O. Schmidt, Phys. Rev. A 98, 023424 (2018)

    2018

  2. [10]

    L. Feng, W. Tan, A. De, A. Menon, A. Chu, G. Pagano, and C. Monroe, Physical Review Letters125, 053001 (2020)

    2020

  3. [11]

    J. J. Wu, P.-Y. Hou, S. D. Erickson, A. D. Brandt, Y. Wan, G. Zarantonello, D. C. Cole, A. C. Wilson, D. H. Slichter, and D. Leibfried, Physical Review A: Atomic, Molecular, and Optical Physics111, 043109 (2025)

    2025

  4. [12]

    J. P. Bartolotta, B. Estey, M. Foss-Feig, D. Hayes, and C. N. Gilbreth, Laser cooling trapped-ion crystal modes beyond the Lamb-Dicke regime (2024)

    2024

  5. [13]

    Huang, C

    C. Huang, C. Wang, H. Zhang, H. Hu, Z. Wang, Z. Mao, S. Li, P. Hou, Y. Wu, Z. Zhou, and L. Duan, Physical Review Letters133, 113204 (2024)

    2024

  6. [14]

    Jordan, K

    E. Jordan, K. A. Gilmore, A. Shankar, A. Safavi-Naini, 8 J. G. Bohnet, M. J. Holland, and J. J. Bollinger, Physical Review Letters122, 053603 (2019)

    2019

  7. [15]

    P. Hrmo, M. K. Joshi, V. Jarlaud, O. Corfield, and R. C. Thompson, arXiv:1907.02406 [physics, physics:quant-ph] (2019)

    1907 arXiv

  8. [16]

    Goodwin, G

    J. Goodwin, G. Stutter, R. Thompson, and D. Segal, Physical Review Letters116, 143002 (2016)

    2016

  9. [17]

    J. M. Cornejo, J. Brombacher, J. A. Coenders, M. Von Boehn, T. Meiners, M. Niemann, S. Ulmer, and C. Ospelkaus, Physical Review Research6, 033233 (2024)

    2024

  10. [18]

    Mordini, A

    C. Mordini, A. Ricci Vasquez, Y. Motohashi, M. Müller, M. Malinowski, C. Zhang, K. K. Mehta, D. Kienzler, and J. P. Home, Physical Review X15, 011040 (2025)

    2025

  11. [19]

    Z. Xing, H. M. Rivy, V. Natarajan, A. M. Kolhatkar, G. Beck, and K. K. Mehta, Rapid multi-mode trapped- ion laser cooling in a phase-stable standing wave (2025), arXiv:2512.10900 [physics]

    2025

  12. [20]

    Roghani and H

    M. Roghani and H. Helm, Physical Review A: Atomic, Molecular, and Optical Physics77, 043418 (2008)

    2008

  13. [21]

    E. A. Cornell, R. M. Weisskoff, K. R. Boyce, and D. E. Pritchard, Physical Review A41, 312 (1990)

    1990

  14. [22]

    D. J. Gorman, P. Schindler, S. Selvarajan, N. Daniilidis, and H. Häffner, Physical Review A89, 062332 (2014)

    2014

  15. [23]

    W. M. Itano and D. J. Wineland, Physical Review A25, 35 (1982)

    1982

  16. [24]

    M. J. Jensen, T. Hasegawa, and J. J. Bollinger, Physical Review A70, 033401 (2004)

    2004

  17. [25]

    K. Koo, J. Sudbery, D. M. Segal, and R. C. Thompson, Physical Review A69, 043402 (2004)

    2004

  18. [26]

    D. J. Wineland and W. M. Itano, Physical Review A: Atomic, Molecular, and Optical Physics20, 1521 (1979)

    1979

  19. [27]

    H. F. Powell, S. R. d. Echaniz, E. S. Phillips, D. M. Se- gal, and R. C. Thompson, Journal of Physics B: Atomic, Molecular and Optical Physics36, 961 (2003)

    2003

  20. [28]

    B. J. McMahon, K. R. Brown, C. D. Herold, and B. C. Sawyer, Physical Review Letters133, 173201 (2024)

    2024

  21. [29]

    R. J. Hendricks, E. S. Phillips, D. M. Segal, and R. C. Thompson, J. Phys. B: At. Mol. Opt. Phys41, 35301 (2008)

    2008

  22. [30]

    Savard, S

    G. Savard, S. Becker, G. Bollen, H.-J. Kluge, R. Moore, T. Otto, L. Schweikhard, H. Stolzenberg, and U. Wiess, Physics Letters A158, 247 (1991)

    1991

  23. [31]

    H. F. Powell, D. M. Segal, and R. C. Thompson, Physical Review Letters89, 093003 (2002)

    2002

  24. [32]

    S. Guan, M. C. Wahl, and A. G. Marshall, The Journal of Chemical Physics100, 6137 (1994)

    1994

  25. [33]

    E. S. Phillips, R. J. Hendricks, A. M. Abdulla, H. Ohadi, D. R. Crick, K. Koo, D. M. Segal, and R. C. Thompson, Physical Review A78, 032307 (2008)

    2008

  26. [34]

    Morigi, Physical Review A67, 033402 (2003)

    G. Morigi, Physical Review A67, 033402 (2003)

    2003

  27. [35]

    We remove this tilt with a waveform that differentially charges the azimuthally-segmented electrodes

    Our trap PCB electrodes produce an electrostatic quadrupole that is slightly tilted with respect to the trap magnetic field. We remove this tilt with a waveform that differentially charges the azimuthally-segmented electrodes. This means that a uniform oscillating volt- age ap...

  28. [36]

    5 reflects an elevated background ax- ial mode heating rate due to technical noise

    The data of Fig. 5 reflects an elevated background ax- ial mode heating rate due to technical noise. We have recently removed this technical noise source by electroni- cally disconnecting the axialization inputs from the trap when not performing Doppler cooling

  29. [37]

    H. A. Janacek,Optical Bloch equations for simulating trapped-ion qubits, phd, University of Oxford (2015)

    2015

  30. [38]

    Lau and M

    H.-K. Lau and M. B. Plenio, Physical Review B94, 054305 (2016)

    2016

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.