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 `__ · :doc:`Catalogue ` · :doc:`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 \|\\|^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 :doc:`review register ` for the checks and decisions.