kumar_2026

S. Kumar, J. D. Piel, C. H. Greene and N. Shivaram, “Broadband femtosecond lasers enable efficient two-photon excitation of the ultranarrow linewidth singlet 1s2s state in helium”, Phys. Rev. Research 8, 013009 (2026)

Source record · Catalogue · Review register

DOI: 10.1103/nfbf-h6hc

Source kind: theory

Recorded technique: An effective two-level (three-level for two colours) model of He 1s2 -> 1s2s 1S0 two-photon excitation by broadband femtosecond pulses: intermediate p states adiabatically eliminated, the continuum coupling of 1s2s in the Markov approximation (Eqs. 4-11, Appendix A), rotating-wave and two-photon rotating-wave approximations; field-free energies and dipole matrix elements from finite-volume variational R-matrix calculations; Eq. 7 integrated by an explicit Runge-Kutta method for Gaussian pulses at 120.27 nm (one colour) and 65 nm + 800 nm (two colours).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Pages are PDF pages (article 013009, pp. 1-10). Identity checked against the first page: Physical Review Research 8, 013009 (2026), not Phys. Rev. A.

NOTHING TAKEN (the maintainer, 2026-10-08, TC-872): the coefficients of Table I (p. 7, tbl_a107b6829704, checked against the image) and Table II (p. 8, tbl_6e9725e0885b) stay in these notes. Table I, the quantities of Eq. 7 at 120.27 nm (hbar omega_P = 10.31 eV), ‘Expression (in a.u.)’ with E_0 the peak field of I_0 = (1/2) eps_0 c E_0^2 (p. 2): S_g = -0.424664 E_0^2 (Eq. 8), S_e = 1.13668 E_0^2 (Eq. 8), Omega_ge^P = 0.886278 E_0^2 (Eq. 9), delta E_e/hbar = 0.840524 E_0^2 (Eq. 10), Gamma_e = 0.869215 E_0^2 (Eq. 11); at 10 TW/cm^2 -0.000120979, 0.000323822, 0.000252485, 0.000239451, 0.000247624 a.u. and -5.0015, 13.3872, 10.4381, 9.8992, 10.2371 ‘THz’ (rates in 10^12 s^-1: a.u. divided by 2.41888e-17 s, no 2 pi; reproduced 2026-10-08). The a.u. columns imply E_0^2 = 2.84882e-4 at 10 TW/cm^2, 0.02 % below the CODATA 2.84945e-4 (I_au = 3.50945e16 W/cm^2): immaterial.

CONVENTIONS (Eq. 7): i dc/dt = H c with H_ge = Omega_ge^P*/2 (the off-diagonal is half the two-photon Rabi frequency, Eq. 9 a sum over p states with the factor 1/(2 hbar^2) and eps_P^2) and H_ee = S_e + delta E_e/hbar - (i/2) Gamma_e. The amplitude decays as exp(-Gamma_e t/2), so |c_e|^2 decays as exp(-Gamma_e t): Gamma_e is the population (ionisation) rate of 1s2s, consistent with Eq. 11, Gamma = (pi/(2 hbar)) |eps_P|^2 |<e|mu.e_P|E>|^2, Fermi’s golden rule for the coupling mu eps_P/2 with an energy-normalised continuum (Appendix A, Eqs. A9-A11).

THE IMPLIED 1s2s PHOTOIONISATION CROSS SECTION (computed 2026-10-08, not data): sigma = Gamma_e / Phi with Phi = I_0/(hbar omega). At 10 TW/cm^2, Gamma_e = 0.000247624 a.u. / 2.41888e-17 s = 1.02371e13 s^-1; hbar omega = 1239.842/120.27 = 10.3088 eV, Phi = 1e13/(10.3088 x 1.602177e-19) = 6.0545e30 cm^-2 s^-1; sigma(1s2s 1S0, 10.31 eV photon, 6.34 eV photoelectron) = 1.691e-18 cm^2 = 1.69 Mb (with Gamma_e = 0.869215 E_0^2 and the CODATA E_0^2 the same to 0.02 %). Table II gives, for the 19.06 eV (65.05 nm) XUV photon, Gamma_e^1 = 0.127529 E_XUV^2, 0.0000145323 a.u. at 4 TW/cm^2: 6.0079e11 s^-1 / 1.3099e30 cm^-2 s^-1 = 4.59e-19 cm^2 (0.46 Mb); and for the 1s4s 1S0 state at 1.54 eV (800 nm), Gamma_b^2 = 29.711 E_IR^2, 0.00846415 a.u. at 10 TW/cm^2: 8.63e-18 cm^2. The text’s ‘an order of magnitude smaller’ (p. 5) is the rate per E^2 (0.869215/0.127529 = 6.8); the cross sections differ by 3.7. Compared with kapralova_zdanska_2025’s gamma_1s2s (1.73 Mb at 120.3 nm): see that record and the register.

OTHER PRINTED VALUES: the 1s2 - 1s2s separation 20.62 eV (p. 2); at about 10 TW/cm^2 and 9 meV bandwidth (about 200 fs FWHM) and detuning 14.3 meV the transfer reaches about 28 %, the excitation rate (probability over FWHM duration) about 2e12 s^-1 atom^-1 (p. 4); 25-30 % at 120 nm and about 70 % for the XUV-IR scheme (abstract). Model results for chosen pulses, figures only.

FURTHER TWO-PHOTON DATA CITED: two-photon decay of the 1s2s 1S0 metastable state, A. Dalgarno and D. R. Bates, Mon. Not. R. Astron. Soc. 131, 311 (1966); G. W. F. Drake, G. A. Victor and A. Dalgarno, Phys. Rev. 180, 25 (1969); A. T. Bondy, D. C. Morton and G. W. F. Drake, Phys. Rev. A 102, 052807 (2020) (Refs. 23-25); the 2 1S0 lifetime, R. S. Van Dyck, C. E. Johnson and H. A. Shugart, Phys. Rev. A 4, 1327 (1971) (Ref. 16); none in the library. No two-photon excitation cross section of helium is cited.

Recorded bibliographic identity status: VALIDATED. 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.