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 `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.60\.1287 `__ **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 \ for \|t1 \- t2\| \< 1/omega\_bar and 0 otherwise\. \- Eq\. \(4\)\: P = \(1/hbar^4\) \|\/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 \/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 :doc:`review register ` for the checks and decisions.