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 · Catalogue · Review register

DOI: 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

No datasets are recorded.

Formulas

No formulas are recorded.

Corrections

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 review register for the checks and decisions.