meshulach_1999#
D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses”, Phys. Rev. A 60, 1287 (1999)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Perturbative theory of N-photon and Raman transitions driven by phase-shaped pulses (Sec. II), tested by two-photon fluorescence (460 nm) of the caesium 6S1/2-8S1/2 transition (411 nm) excited by 31 fs FWHM transform-limited sech^2 pulses (23 nm FWHM) at 822 nm, shaped in a 4-f shaper (1200 lines/mm, 100 mm achromats, 128-element liquid-crystal modulator, 97 um pixels) and focused by a 50 mm lens; and, for the broad-line limit, by two-photon fluorescence of Coumarin 6H in ethanol (absorption maximum 396 nm, FWHM about 60 nm) with 50 fs pulses (14 nm FWHM) at 814 nm (Sec. III, pp. 1290-1291). The shaping is a pi spectral phase step at detuning delta from the carrier.
Materials in structured entries: None recorded.
Dataset quantities: None recorded.
Contents: 0 datasets; 0 formulas.
Curation notes#
Context only, no datasets: caesium and the dye are not optmat materials, and the measurements are normalised fluorescence (Figs. 6-7, raster). Identity checked on the PDF: Phys. Rev. A 60, 1287-1292 (August 1999), Meshulach and Silberberg (Weizmann Institute), received 1 October 1998. It is the full paper of meshulach_1998.
Atom and transition: Cs 6S1/2 -> 8S1/2 at 411 nm, photons near 822 nm; hyperfine doublets treated as one two-level system (Fig. 3 caption). The paper prints no intermediate level or detuning: the intermediate states are ‘all far from resonance’ (p. 1288), and the transition is called nonresonant, ‘i.e., a transition with no intermediate state’ (p. 1287).
What it derives (Sec. II, p. 1288), compared with OEP 8 section 4: - Eq. (2): second-order amplitude a_f = -(1/hbar^2) sum_n mu_fn mu_ng double time-ordered integral of eps(t1) eps(t2) exp(i omega_fn t1) exp(i omega_ng t2), real field eps(t). This is the time-domain form of OEP 8 Eqs. (1)-(2) before the rotating-wave selection. - Eq. (3): closure with an ‘appropriately weighted average energy’ hbar omega_bar (after Bebb and Gold): the intermediate sum is replaced by <f|mu^2|g> for |t1 - t2| < 1/omega_bar and 0 otherwise. - Eq. (4): P = (1/hbar^4) |<f|mu^2|g>/omega_bar|^2 |integral eps^2(t) exp(i omega_0 t) dt|^2. Against OEP 8: the pair form c_f = (i/2hbar) M S_2(Omega_f) with hbar M = 2 sum_n d_fn d_ng / D_n gives |c_f|^2 = (1/hbar^4) |sum_n d_fn d_ng/D_n|^2 |S_2|^2. Eq. (4) is the same, with the same 1/hbar^4, once the sum over D_n is replaced by <f|mu^2|g>/omega_bar, and since the only part of eps^2 near +omega_0 is (E+)^2 the time integral is OEP 8’s S_2(omega_0) (same sign of the exponent, E+ ~ exp(-i omega t)). The closure (3) is the assumption kappa = 0 of OEP 8 Eq. (4): M independent of the split; the box in time drops the phase i of the exact 1/(i D_n). The authors call the derivation ‘rather crude’, without ac Stark shifts (p. 1288). - Eq. (5): N photons, P ~ |integral eps^N exp(i omega_0 t) dt|^2. - Eq. (6): S_2 = |integral eps^2 exp(i omega_0 t) dt|^2 = |integral eps~(omega_0/2 + Omega) eps~(omega_0/2 - Omega) dOmega|^2; Meshulach’s S_2 is OEP 8’s |S_2|^2, and the frequency form drops the 2 pi of the convolution (proportionality only). Transform limit maximises it; antisymmetric phases leave it unchanged. - Eq. (8): impulsive Raman, the resonant component of the intensity. - Eqs. (9)-(11): an inhomogeneous line broad compared with the spectrum gives S_2 = integral I^2(t) dt (N photons: integral I^N dt). This is OEP 8’s Check 2 / OEP 6 section 4 identity, P = (1/2 pi) integral K |S_2|^2 dOmega, with K constant and Parseval’s theorem.
Measurements testing the pair-spectrum dependence: - Fig. 2 (calculated only): N = 2, 3, 4 with a pi step; each curve vanishes at N values of delta / Delta omega; the step at delta = 0 is antisymmetric and leaves N = 2 unchanged. - Fig. 6 (Cs, measured and calculated from Eq. (6) with transform-limited 31 fs sech^2): signal constant for large |delta / Delta omega|, nearly zero (‘dark pulses’) at delta / Delta omega = +-0.31 (p. 1291), and at delta = 0 it ‘almost reproduced’ the transform-limited value (about 0.9, read by eye). Read by eye from the raster figure: the minima are about 0.1 (negative delta) and 0.02 (positive delta), and the measured signal stays at 1 out to |delta / Delta omega| about 1 while the calculation falls from about 1.5; the paper does not comment on either difference. - Fig. 7 (Coumarin 6H): the coherent feature at delta = 0 is absent, the dip (about 0.3) follows integral I^2 dt. No intermediate-resonance test is made; dudovich_2001 extends Eq. (2) to a resonant intermediate level.
Cited, not in optmat: H. B. Bebb and A. Gold, Phys. Rev. 143, 1 (1966) (in the library as Bebb_1966_MultiphotonIonizationHydrogen, no record).
Register: TC-987.
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.