dudovich_2001 ============= N\. Dudovich, B\. Dayan, S\. M\. Gallagher Faeder and Y\. Silberberg, "Transform\-limited pulses are not optimal for resonant multiphoton transitions", Phys\. Rev\. Lett\. 86, 47 \(2001\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevLett\.86\.47 `__ **Source kind:** measurement **Recorded technique:** Fluorescence \(about 420 nm, through 6P\) of the rubidium 5S\-5D two\-photon transition, resonant through 5P, excited by Ti\:sapphire pulses \(18 nm FWHM spectrum, 'corresponding to 50 fs transform\-limited pulses', 150 mW, 80 MHz\) centred on omega\_fg/2 at 778\.1 nm and shaped in a 4\-f shaper with a 128\-element liquid\-crystal modulator \(resolution below 0\.3 nm\) or an adjustable slit at its Fourier plane \(pp\. 48\-49, Fig\. 1\)\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Context only, no datasets\: rubidium is not an optmat material, and the measurements are normalised fluorescence \(Figs\. 2\-3\)\. Identity checked on the PDF\: Phys\. Rev\. Lett\. 86, 47\-50 \(1 January 2001\), Dudovich, Dayan, Gallagher Faeder and Silberberg \(Weizmann Institute\), received 8 August 2000\. Atom and transition\: Rb 5S \-\> 5D, 'dominated by resonant transitions through the 5P level' \(p\. 48\)\. Printed wavelengths\: omega\_fg/2 at 778\.1 nm, 5S\-5P \(omega\_ig\) at 780\.2 nm, 5P\-5D \(omega\_fi\) at 776\.0 nm \(Fig\. 1 caption\)\. Computed here from them\: photon energies 1\.59342, 1\.58913 and 1\.59773 eV, so the intermediate detuning in OEP 8's variable D = E\_5P/hbar \- Omega\_f/2 is \-4\.29 meV \(\-34\.6 cm^\-1; 5P lies below half the two\-photon energy\), and the spectrum's FWHM, 18 nm, is 36\.9 meV\: \|D\| is 0\.12 of the FWHM, the pole inside the spectrum\. \(18 nm and 50 fs agree with a Gaussian time\-bandwidth product, 36\.5 meV, not a sech^2 one; the paper does not state the shape\.\) Only 5P is named; the 5P fine structure is not discussed\. What it derives \(p\. 47\)\: \- Eq\. \(1\)\: the second\-order amplitude, as meshulach\_1999 Eq\. \(2\), the pulse 'shorter than all lifetimes'\. \- Eq\. \(2\), nonresonant\: a\_f ~ \-\(1/\(i hbar^2\)\) sum\_n mu\_fn mu\_ng / \(omega\_ng \- omega\_fg/2\) integral E\(omega\) E\(omega\_fg \- omega\) d omega\. This is OEP 8's pair form c\_f = \(i/2hbar\) M\(Omega\_f\) S\_2\(Omega\_f\) at nu = 0, hbar M = 2 sum\_n d\_fn d\_ng / D\_n\: the prefactor \-1/i = i and the denominators D\_n agree; Dudovich's integral over E\(omega\) lacks OEP 8's 1/\(2 pi\), which the unstated Fourier normalisation of E\(omega\) absorbs\. \- Eq\. \(3\), one resonant level i\: a\_f ~ \-\(1/\(i hbar^2\)\) mu\_fi mu\_ig \[i pi E\(omega\_ig\) E\(omega\_fg \- omega\_ig\) \+ P integral E\(omega\) E\(omega\_fg \- omega\) / \(omega\_ig \- omega\) d omega\]\. This is OEP 8 Eqs\. \(1\)\-\(2\) for one intermediate level, with the two time orderings combined by the symmetry of E\(omega\)E\(Omega\_f \- omega\) and the pole taken causally, 1/\(omega\_ig \- omega \- i0\) = P/\(omega\_ig \- omega\) \+ i pi delta\(omega\_ig \- omega\)\. The same within conventions; OEP 8 Eq\. \(2\) does not state the \-i0 \(or the level width\) that a pole inside the spectrum needs, because OEP 8 section 4\.3 excludes that regime\. The paper notes the on\-resonance term is pi/2 out of phase with the rest, and that photons red and blue of the resonance contribute with opposite signs, so a transform\-limited pulse cancels the principal\-value part once the bandwidth exceeds \|omega\_ig \- omega\_fg/2\|\. Measurements testing the pair\-spectrum dependence \(the resonant\-intermediate case; calculated curves from Eq\. \(3\)\)\: \- Fig\. 2, a slit blocking bands symmetric about omega\_fg/2\: as the cutoffs approach the resonances the fluorescence doubles, while the average power falls by 71 % and the pulse broadens to 390 fs, the peak intensity reduced by a factor 38 \(Fig\. 2 caption and p\. 49; the abstract rounds to 40\)\. The pair form, with M fixed, cannot rise when spectrum is removed\. \- Fig\. 3, a pi/2 phase on a 4 nm window scanned across the spectrum\: enhancement by a factor 7 \('600 %'\) with the window centred on 778\.1 nm, its edges near 780\.2 and 776\.0 nm, which inverts the sign of E\(omega\)E\(omega\_fg \- omega\) over about 8 nm around omega\_ig; peak intensity 26 % lower\. An adaptive optimisation reached the same factor\. Under the pair form any phase\-only shaping gives at most the transform\-limited value, so a factor 7 is a direct demonstration that the pair form fails with an intermediate resonance in the spectrum\. For OEP 8\: the bound\-level D\_eff rule \(section 4\.2\) and the adiabatic elimination \(section 4\.3\) do not apply here \(2 kappa sigma^2 with kappa = 1/D^2 and sigma = 15\.7 meV, the Gaussian rms of the stated FWHM, is about 27\); the experiment shows the size and sign structure of the failure, not a noble\-gas number\. Register\: TC\-988\. **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.