toth_2023
=========

A\. Tóth, S\. Borbély, Y\. Zhou and A\. Csehi, "Role of dynamic Stark shifts in strong\-field excitation and subsequent ionization", Phys\. Rev\. A 107, 053101 \(2023\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/toth_2023.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.107\.053101 <https://doi.org/10.1103/PhysRevA.107.053101>`__

**Source kind:** theory

**Recorded technique:** Strong\-field two\-photon excitation and \(2\+1\)\-photon ionisation of Na \(3s \-\> 4s, 1\.589 eV photons\) and Li \(2s \-\> 4s, 2\.169 eV\) in a single\-active\-electron model, at three levels\: minimal two\- and three\-state models with the nonessential states adiabatically eliminated \(dynamic Stark shifts, two\-photon Rabi frequency, ionisation width; Eqs\. 5\-15\), a multilevel expansion in 55\-67 field\-free bound states \(and 500 continuum states for Li\) without continuum\-continuum couplings \(Eq\. 3\), and a velocity\-gauge TDSE on a radial grid \(Eqs\. 16\-28; Hellmann pseudopotential for Na, Klapisch model potential for Li\)\.

**Materials in structured entries:** None recorded.

**Dataset quantities:** None recorded.

**Contents:** 0 datasets; 0 formulas.

Curation notes
--------------

Nothing extracted\: Na and Li only; optmat has no material for them, and no noble\-gas number is printed\. THE LIBRARY COPY is the APS author proof \('AC12314 PRA April 26, 2023'; 15 PDF pages\: pp\. 1\-3 the proof notice, pp\. 4\-15 the article as 'Physical Review A 00, 003100 \(2023\)', pages 003100\-1 to \-12, DOI placeholder 10\.1103/PhysRevA\.00\.003100\), not the version of record \(Phys\. Rev\. A 107, 053101\)\. Pages below are PDF pages \(article page = PDF page \- 3\)\. Equations 5\-7 and 12 were read from the page image \(p\. 6\)\. Not checked against the published version\.

CONVENTIONS \(pp\. 5\-7\)\. Atomic units, hbar = 1; V = \-mu E\(t\) with E\(t\) = E\_0 g\(t\) cos\(omega t\), I\_0 = E\_0^2/\(8 pi alpha\_fs\) \(that is \(1/2\) eps\_0 c E\_0^2\), g\(t\) = exp\(\-t^2/\(2 tau^2\)\) \(Eq\. 1\)\. After adiabatic elimination \(citing kaufman\_2020\) and the two\-photon RWA \(Eqs\. 5, 14\-15\)\: the off\-diagonal element IS Omega\_2\(t\) = \-sum\_m mu\_Rm mu\_mI E\_0^2 g^2 / \(4 \(omega\_mI \- omega\)\) \(Eq\. 6\), the Stark shifts S\_k = \-sum\_m \|mu\_km\|^2 E\_0^2 g^2 omega\_mk / \(2 \(omega\_mk^2 \- omega^2\)\) \(Eq\. 7; the sum\-integral over m includes continuum states\), and the resonant level carries \-\(i/2\) Gamma\(t\) with Gamma\_0 = 2 pi \|mu\_R,eps E\_0/2\|^2, 'the total ionization rate' \(Eq\. 12, energy\-normalised continuum, local approximation\)\. The pi\-pulse condition for complete inversion is Theta = integral \|Omega\_2\| dt = pi/2 \(Eq\. 10\), confirming that Omega\_2 is half the Rabi frequency\.

COMPARISON WITH OEP 8 AND kumar\_2026 \(derived 2026\-10\-09, not data\)\. \(a\) Eq\. 6 equals OEP 8's H\_fg = \-\(1/2\) M\_f \(E^\+\)^2 for one colour \(\|H\_fg\| = sum d d E\_0^2/\(4 D\_n\)\), and equals kumar\_2026's off\-diagonal Omega\_ge^P/2 \(its Eq\. 9 has 1/\(2 hbar^2\)\)\: Toth et al\.'s Omega\_2 = OEP 8's Omega\_R/2 = Kumar's Omega\_ge^P/2\. \(b\) Eq\. 7 is OEP 8's \-alpha\_k \|E^\+\|^2/hbar with the full \(co\- and counter\-rotating\) polarisability, and is kumar\_2026's Eq\. 8 term for term\. \(c\) Gamma\_0 = 2 pi \|mu E\_0/2\|^2 = \(pi/2\) \|mu\|^2 E\_0^2 is kumar\_2026's Eq\. 11 identically, and Knight et al\.'s Eq\. 2\.12 \(knight\_1990\); with Phi = I/\(hbar omega\) it is sigma^PI Phi with sigma^PI = 4 pi^2 alpha omega \|mu\|^2 \(a\.u\.\), and the amplitude decays as \-\(i/2\) Gamma, so Gamma is a population rate, OEP 8's Gamma^PI\_f\. Kumar's continuum level shift delta E\_e \(its Eq\. 10\) is not in this paper\: Toth et al\. put the continuum into S\_R through the sum\-integral of Eq\. 7\.

VALIDITY \(pp\. 4, 8\-12\)\. The elimination is justified when no intermediate state is one\-photon resonant and the pulse 'supports many cycles' \(p\. 4\)\. Two\-level and multilevel populations agree for long pulses \(a few hundred fs FWHM\); for short pulses the larger bandwidth and peak intensity \(at fixed area pi/2\) bring in the 3p \(Na\) and 2p \(Li\) intermediates and the one\-photon resonant 7p \(Na\) and 4d \(Li\) levels \(Fig\. 3, p\. 9\)\. For the \(2\+1\) model in Li 2\-ps pulses are used; below about 200 fs FWHM the 2s \-\> 2p \-\> 4d \-\> continuum path dominates the photoelectron spectrum \(p\. 12\)\. RATE OF THE LIGHT SHIFT\: with a transform\-limited Gaussian pulse the transfer is maximised at a two\-photon detuning Delta\_opt = 0\.76 x delta S\_0, delta S\_0 the peak relative Stark shift \(Figs\. 2\-3, p\. 8\-9; the proof's text prints 'Delta = \+\-0\.76' for the same optimum\); the transition\-frequency shift seen in REMPI lies between 0 and delta S\_0 depending on the envelope \(76 % for the Gaussian\)\. For OEP 8 \(comment, 2026\-10\-09\)\: the Bloch model \(its Eq\. 7\) carries the time\-dependent shift \(Re alpha\_f \- alpha\_g\) \|E^\+\|^2 and so includes this; a rate model with a fixed line centre would need such an envelope\-dependent factor\. For Li at 2 ps\: Gamma \<\< \|Omega\_2\| = \|delta S\|/3 = Sigma/7 \(Sigma = S\_I \+ S\_R; p\. 11\)\: the light shift exceeds the two\-photon coupling\. The Stark shifts, Rabi frequencies and pulse\-duration dependences are in the Supplemental Material \(ref\. 66\), which is not in the library\.

FURTHER REFERENCES CITED, not in the library\: C\. Trallero\-Herrero, D\. Cardoza, T\. C\. Weinacht and J\. L\. Cohen, Phys\. Rev\. A 71, 013423 \(2005\) \(ref\. 10, two\-photon phase matching with Stark shifts\); P\. V\. Demekhin and L\. S\. Cederbaum, Phys\. Rev\. A 83, 023422 \(2011\) \(ref\. 58, the local approximation\); S\. Nandi et al\., Nature 608, 488 \(2022\) \(ref\. 47, Rabi dynamics in resonant two\-photon ionisation of He by an XUV free\-electron laser\); X\. Zhang et al\., Phys\. Rev\. A 106, 063114 \(2022\) \(ref\. 48, the role of nonessential states in the Autler\-Townes doublet after two\-photon ionisation\)\. No noble\-gas two\-photon strengths, polarisabilities or widths are printed\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
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No datasets are recorded.

Formulas
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No formulas are recorded.

Corrections
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No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.