fushitani_2015#
M. Fushitani, C.-N. Liu, A. Matsuda, T. Endo, Y. Toida, M. Nagasono, T. Togashi, M. Yabashi, T. Ishikawa, Y. Hikosaka, T. Morishita and A. Hishikawa, “Femtosecond two-photon Rabi oscillations in excited He driven by ultrashort intense laser fields”, Nat. Photon. 10, 102-105 (2016); published online 30 November 2015
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Photoelectron spectroscopy (magnetic bottle, about 1 mm detection length) of helium excited to 1s2p 1P1 by the SCSS test-accelerator EUV free-electron laser (58.4 nm, about 100 fs, about 10 uJ, linearly polarised, 40 um 1/e^2 diameter), then driven 30 ps later by a linearly polarised Ti:sapphire pulse (795 nm, 45 fs, up to 10 TW/cm2, 160 um 1/e^2 diameter, Rayleigh length about 25 mm, so a near-uniform intensity over the detection volume; intensity uncertainty 10 %); a weak 250 nm pulse (about 100 fs, about 2 uJ) normalises the 1s2p population; the angle between the EUV and NIR polarisations selects M = 0 or M = +-1 about the NIR axis. Theory: TDSE in the single-active-electron approximation (length gauge, l up to 200, r0 = 2000 au, squared-sine field envelope of 45 fs), checked against a two-electron hyperspherical TDSE below 3 TW/cm2; and a four-level model (2p, 3d, 5f, 6f) with the ponderomotive shift on 5f and 6f (pp. 1-3 and Methods, PDF p. 5).
Materials in structured entries: He
Dataset quantities: radiative_lifetime, transition_dipole_moment
Contents: 4 datasets; 0 formulas.
Curation notes#
Identity checked on the first page (PDF p. 1): the library copy is the ADVANCE ONLINE PUBLICATION, ‘PUBLISHED ONLINE: 30 NOVEMBER 2015 | DOI: 10.1038/NPHOTON.2015.228’, pages numbered 1-5 (Methods on PDF p. 5); received 22 May 2015, accepted 19 October 2015. The issue version is Nat. Photon. 10, 102-105 (2016) (the library’s validated metadata: volume 10, issue 2, pp. 102-105); the id keeps the library’s 2015, the online date. Page numbers below are the PDF’s. The Supplementary Information (Supplementary Figs. 1-4, the M dependence of the Rabi period) is not in the library. Every number below was read on the PDF’s text layer and Fig. 1’s drawing.
WHAT IS DRIVEN. A TWO-photon Rabi oscillation between two EXCITED levels: 1s2p 1P1 (M = +-1, prepared by the EUV pulse) and the Rydberg level 1s6f 1F3 (NIST 1s.6f 1F*3, 195262.429 cm^-1), at 795 nm (1.5595 eV, vacuum), through the near-resonant intermediate 1s3d 1D2 (186104.964 cm^-1). The two-photon resonance is detuned by delta = 0.13 eV at zero field (recomputed from NIST: 2 x 1.55955 - 2.99143 = 0.1277 eV) and is brought into resonance by the ponderomotive (Freeman) shift of the Rydberg levels during the pulse; 1s5f 1F3 (193921.128 cm^-1) and 1s7f also take part. Fig. 1b’s energies above 2p, 1.86 (3d), 2.83 (5f) and 2.99 eV (6f), and 3.37 eV (the ionisation threshold), are NIST’s 1.8561, 2.8251, 2.9914 and 3.3694 eV. The 5f and 6f lie 0.54 and 0.38 eV below threshold (p. 1; NIST 0.5442 and 0.3779). The intermediate detuning Delta = 0.30 eV (Fig. 5; NIST 1.8561 - 1.5595 = 0.2965 eV).
THE NUMBERS (pp. 1-3, Methods): - photoelectron peaks of three-photon ionisation from 2p at E_kin = 0.97 and 1.14 eV, constant up to 5.9 TW/cm2 (Freeman resonance through 5f and 6f; field-free one-photon ionisation of 5f and 6f gives 1.015 and 1.182 eV, recomputed; the kinetic-energy calibration is +-0.10 eV, Methods); spectra at 5.9, 3.8, 2.5, 1.9 and 0.9 TW/cm2 (Fig. 2); - Up = 0.3 eV at 5 TW/cm2 (p. 1; recomputed 0.295 eV from the Methods’ formula); Methods: Up[eV] = 9.334 x 10^-14 I[W/cm2] (lambda[um])^2, against 9.3373 x 10^-14 from e^2 E0^2 / (4 m omega^2) with I = eps0 c E0^2 / 2 (0.04 % low); - ‘the population oscillation occurs twice at ~6 TW cm-2 within the 45 fs NIR laser pulse’, an effective two-photon Rabi frequency Omega^(2)/2pi = 2/(45 fs) = 44 THz, period 23 fs (recomputed 44.4 THz, 22.7 fs); ‘about half’ of the three-level value Omega^(2)/2pi = Omega_2p-3d Omega_3d-6f / (4 pi Delta) = 83 THz, attributed to the 5f state (p. 2); - the total bound population falls by only 22 % at 6 TW/cm2 (TDSE, Fig. 3c); - the four-level model’s dipoles (Methods), ‘adopted from the line strengths’ of Wiese and Fuhr (J. Phys. Chem. Ref. Data 38, 565 (2009), not in the library), ‘for the M = +-1 states’: |mu_2p-3d| = 2.1645 au, |mu_3d-6f| = 0.7425 au, |mu_3d-5f| = 1.338 au (the datasets); - the 2 1P radiative lifetime ‘560 ps’ (Fig. 1 caption, no source given; a dataset, check); - Fig. 4: at 5 TW/cm2 the 6f peak is largest at theta = 90 degrees (M = +-1) and smallest at 0 (M = 0), the 5f peak the reverse; the TDSE reproduces both (the M dependence of the Rabi period, and an extra Stark shift from 1s3s in the M = 0 manifold).
THE CONVENTION AND THE IMPLIED |M| (computed here). The paper’s Omega^(2) = Omega_1 Omega_2 / (2 Delta), with Omega_i = mu_i E0 / hbar for E = E0 cos(omega t) (Gentile et al.’s three-level form, the paper’s ref. 10): this is OEP 8’s full two-photon Rabi frequency Omega_R = |M| |E+|^2 / hbar (section 4.5), with M = 2 mu_1 mu_2 / Delta (OEP 8’s kernel, Eq. 2, for one intermediate, both orderings) and E+ = E0 / 2; the off-diagonal element |H_fg| = (1/2) |M| |E+|^2 is half of it (the naming trap of TC-990, which Kaufman et al.’s and Toth et al.’s ‘two-photon Rabi frequency’ falls into; this paper’s does not). Recomputed with I = eps0 c E0^2 / 2 (1 au of field = 3.5094 x 10^16 W/cm2): - the printed dipoles and Delta = 0.30 eV give |M| = 2 x 2.1645 x 0.7425 / (0.30 / 27.2114) = 291.6 au, and Omega_R / 2pi = 82.0 THz at 6 TW/cm2; NIST’s Delta = 0.2965 eV gives |M| = 295.0 au and 83.0 THz. So the printed 83 THz is the three-level formula at 6 TW/cm2 (6.00 TW/cm2 with NIST’s Delta), and the intensity is the peak; - the TDSE’s effective 44 THz at 6 TW/cm2 corresponds to an effective |M| = 156 au (158 au from 2/(45 fs) unrounded), half the three-level value; its basis, two cycles in ‘45 fs’, counts the pulse as flat. If 45 fs is the intensity FWHM of the Methods’ squared-sine field envelope, the integral of I(t) over the pulse is 1.03 x FWHM x I_peak, so ‘two cycles in 45 fs’ is a pulse area of 4 pi at a peak Omega_R / 2pi of about 43 THz; if it is the full width, the peak would be 118 THz. The paper does not say which.
FOR OEP 8. Not a direct test of OEP 8’s two-photon coupling -(1/2) M_f (E+)^2 (Eq. 6): - the lower level is an excited 1P1 level in M = +-1, not the J = 0 ground state, so the coupling is not two_photon_transition_amplitude (ground to bound level only, TC-1040) and no strength in TC-952’s per-level convention follows; - the adiabatic elimination of OEP 8 section 4.3 fails: its field-strength condition |d E0| / (2 hbar D) << 1 is 1.30 for 2p-3d at 6 TW/cm2 (0.45 for 3d-6f, 0.80 for 3d-5f), so the admixture 2 (d E0 / 2 hbar D)^2 is not small; the intermediate 3d is strongly dressed (the a.c. Stark shift of 2p that the paper’s Fig. 5 discussion invokes for negative Delta). The three-level Omega_R (83 THz) overestimates the TDSE’s effective 44 THz by about 2, which the paper assigns to 5f; the strong-field regime alone would also break the eliminated form (inference); - what it does test is the structure of Eq. (6)-(7) far from the weak field: a level shift that tunes the two-photon resonance during the pulse, -alpha_f |E+|^2, with the Rydberg level’s polarisability that of a free electron, alpha_f = -e^2 / (m omega^2), which makes -alpha_f |E+|^2 = e^2 E0^2 / (4 m omega^2) = Up exactly (derived here); Rabi flopping (two cycles) faster than the ionisation (22 % loss); and the M (polarisation) dependence of the coupling. A tier-3 TDSE validation case for a future excited-level extension, not a check of the curated strengths.
DATASETS. - mu_2p_3d, mu_3d_6f, mu_3d_5f (transition_dipole_moment, au, label, reproduced from Wiese and Fuhr 2009): the |z| elements between the M = +-1 sublevels (the NIR polarisation the quantisation axis). A plausibility check (computed here, a model, not data): hydrogenic radial integrals (Z = 1) times the angular factor sqrt(((l+1)^2 - m^2) / ((2l+1)(2l+3))) give, for m = 1, 2.123 (2p-3d), 0.860 (3d-6f) and 1.587 au (3d-5f), and for m = 0 2.452, 0.912 and 1.683. The printed 2p-3d is 2 % above the hydrogenic m = 1 element, confirming the M = +-1 reading; DOUBT, the printed 3d-6f and 3d-5f lie 14 % and 16 % below it, though d-f transitions of He’s singlets are expected to be nearly hydrogenic. Wiese and Fuhr’s line strengths are not in the library, and the held NIST lines cover 40-60 nm only, so the conversion cannot be checked here. - tau_2p (radiative_lifetime, check): 560 ps, Fig. 1 caption, no source. NIST’s 1/A(2 1P -> 1 1S) = 1/1.7989e9 s^-1 = 555.9 ps (the held He_I_lines.tsv), an upper bound since the 2 1P -> 2 1S branch is not held; johansson_2003 measured 0.57 +- 0.03 ns.
NOT TAKEN: - the Rabi frequencies (44 and 83 THz), the period (23 fs), the implied |M| (291.6-295.0 and 156 au) and the intensities: no quantity holds an excited-to-excited two-photon coupling (two_photon_transition_amplitude is ground-state only; a continuum or excited-level amplitude is not proposed); - the detunings (0.13, 0.30 eV), level energies and binding energies: NIST’s, which optmat holds; - the photoelectron energies (0.97, 1.14 eV), Up’s coefficient and Figs. 2-5 (yields in arbitrary units, raster TDSE populations): no quantity, and nothing printed beyond the text’s numbers.
References the paper cites that the library does not hold: T. R. Gentile, B. J. Hughey, D. Kleppner and T. W. Ducas, Phys. Rev. A 40, 5103 (1989) (one- and two-photon Rabi oscillations, the three-level formula); A. F. Linskens et al., Phys. Rev. A 54, 4854 (1996) (two-photon Rabi oscillations); O. Kittelmann et al., Phys. Rev. Lett. 76, 2682 (1996) (coherent two-photon excitation of krypton by femtosecond UV pulses); W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref. Data 38, 565 (2009) (He transition probabilities); C. N. Liu, A. Hishikawa and T. Morishita, Phys. Rev. A 86, 053426 (2012) (the hyperspherical TDSE).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
fushitani_2015/mu_2p_3d#
{
"id": "mu_2p_3d",
"material": "He",
"table": "text",
"quantity": "transition_dipole_moment",
"unit": "au",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref. Data 38, 565 (2009)"
],
"parameters": {
"states": "1s2p 1P1 - 1s3d 1D2",
"component": "z between the M = +1 (or -1) sublevels, the NIR's linear polarisation the axis; magnitude"
}
}
1 inline points in the source record.
Methods (PDF p. 5): ‘|mu_2p-3d| = 2.1645 au’, ‘adopted from the line strengths’ of Wiese and Fuhr 2009 (ref. 30), ‘for the M = +-1 states’; the four-level model’s input. Hydrogenic m = 1 element 2.123 au (the record’s notes). No uncertainty stated.
fushitani_2015/mu_3d_6f#
{
"id": "mu_3d_6f",
"material": "He",
"table": "text",
"quantity": "transition_dipole_moment",
"unit": "au",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref. Data 38, 565 (2009)"
],
"parameters": {
"states": "1s3d 1D2 - 1s6f 1F3",
"component": "z between the M = +1 (or -1) sublevels, the NIR's linear polarisation the axis; magnitude"
}
}
1 inline points in the source record.
Methods (PDF p. 5): ‘|mu_3d-6f| = 0.7425 au’, from Wiese and Fuhr’s line strengths, M = +-1. Hydrogenic m = 1 element 0.860 au, 14 % above (the record’s doubt). No uncertainty stated.
fushitani_2015/mu_3d_5f#
{
"id": "mu_3d_5f",
"material": "He",
"table": "text",
"quantity": "transition_dipole_moment",
"unit": "au",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"W. L. Wiese and J. R. Fuhr, J. Phys. Chem. Ref. Data 38, 565 (2009)"
],
"parameters": {
"states": "1s3d 1D2 - 1s5f 1F3",
"component": "z between the M = +1 (or -1) sublevels, the NIR's linear polarisation the axis; magnitude"
}
}
1 inline points in the source record.
Methods (PDF p. 5): ‘|mu_3d-5f| = 1.338 au’, from Wiese and Fuhr’s line strengths, M = +-1. Hydrogenic m = 1 element 1.587 au, 16 % above (the record’s doubt). No uncertainty stated.
fushitani_2015/tau_2p#
{
"id": "tau_2p",
"material": "He",
"table": "text",
"quantity": "radiative_lifetime",
"unit": "ps",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "quoted without a source (rounded)"
}
}
1 inline points in the source record.
Fig. 1 caption (PDF p. 2): ‘the 1s2p (2 1P) excited state (radiative lifetime 560 ps)’, quoted without a source and rounded; context for the 30 ps EUV-NIR delay. NIST 1/A to the ground state 555.9 ps; johansson_2003 measured 0.57 +- 0.03 ns. No uncertainty stated.
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.