meshulach_1998 ============== D\. Meshulach and Y\. Silberberg, "Coherent quantum control of two\-photon transitions by a femtosecond laser pulse", Nature 396, 239 \(1998\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1038/24329 `__ **Source kind:** measurement **Recorded technique:** Two\-photon fluorescence \(about 460 nm, through 7P\) of the caesium 6S1/2\-8S1/2 two\-photon transition \(411 nm; omega\_0/2 at 822 nm\) excited by 31 fs FWHM transform\-limited sech^2 pulses \(23 nm FWHM spectrum\) centred at 822 nm from a Ti\:sapphire laser, shaped by a 4\-f pulse shaper \(1200 lines/mm gratings, 100 mm achromats\) with a 128\-element liquid\-crystal phase modulator; photomultiplier and lock\-in \(pp\. 240\-241, Figs\. 1\-2\)\. Phase\-only filters Theta\(Omega\) = alpha cos\(beta Omega \+ phi\), beta about 220 fs, leave the power spectrum and energy unchanged\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Context only, no datasets\: caesium is not an optmat material, and the paper gives normalised fluorescence only \(Fig\. 3, raster\)\. Identity checked on the PDF\: Nature 396, 239\-242 \(19 November 1998\), Meshulach and Silberberg \(Weizmann Institute\); the letter starts at the foot of p\. 239 after another letter, and p\. 242 carries the start of a third \(Riseman et al\.\), which is why the library's observed title differs\. Atom and transition\: Cs 6S1/2 \-\> 8S1/2, omega\_0 at 411 nm \(3\.0166 eV\), each photon near 822 nm \(1\.5083 eV\); the hyperfine doublets are treated as one two\-level system \(Fig\. 1 caption\)\. Intermediate states\: the paper calls the transition 'non\-resonant \(that is, a transition with no intermediate states\)' \(p\. 240\) and prints no intermediate level or detuning; Fig\. 1 shows only 6S1/2, 7P \(the cascade\) and 8S1/2\. The spectrum's FWHM, 23 nm, is 42\.2 meV of photon energy \(computed here\); 31 fs sech^2 at the sech^2 time\-bandwidth product gives 42\.0 meV, consistent\. What it derives \(p\. 240, Eq\. \(1\)\)\: the transition probability is proportional to S\_2 = \|integral E\(omega\_0/2 \+ Omega\) E\(omega\_0/2 \- Omega\) dOmega\|^2, with E\(omega\) = A\(omega\) exp\[i Phi\(omega\)\] the Fourier transform of the field e\(t\); every pair omega\_1 \+ omega\_2 = omega\_0 contributes\. Against OEP 8\: this is the squared modulus of OEP 8's pair spectrum S\_2\(Omega\_f\) = integral exp\(i Omega t\) E\+\(t\)^2 dt \(section 4\.1, Check 2; section 4\.2\) written in the frequency domain at Omega\_f = omega\_0, the same within conventions\: Meshulach's S\_2 is OEP 8's \|S\_2\|^2, and the 2 pi and the factor 2 of the change of variable are dropped because only proportionality is claimed\. The kernel M of OEP 8 Eqs\. \(1\)\-\(2\) is taken as a constant \(no derivation here; see meshulach\_1999, Eqs\. \(2\)\-\(4\)\)\. Consequences stated\: the transform\-limited pulse maximises S\_2 for a given power spectrum; any phase antisymmetric about omega\_0/2, Phi\(omega\_0/2 \+ Omega\) = \-Phi\(omega\_0/2 \- Omega\), leaves it unchanged; 'dark pulses' cancel it\. Measurements testing the pair\-spectrum dependence \(Fig\. 3, p\. 241; calculated curves from Eq\. \(1\) with a sech spectrum, 'without adjustable parameters'\)\: \- Fig\. 3a, symmetric phase alpha cos\(beta Omega\)\: the fluorescence vanishes first near alpha = 1\.2 \(dark pulse, Fig\. 3b\: a pulse train\), then oscillates; related to J0\(2 alpha\_0\) = 0, and for a square spectrum of width Delta omega, S\_2 = 0 exactly at beta = 2 pi / Delta omega and alpha\_0 = 1\.2024\. \- Fig\. 3a, antisymmetric phase alpha sin\(beta Omega\)\: theory is constant; the measured signal falls slowly with alpha \(to about 0\.4 at alpha = 6, read by eye from the raster figure\), attributed by the authors to 'inherent loss and imperfect antisymmetry' of the discrete modulator; at alpha = 1\.2 it drops only 'by a few per cent'\. Note for OEP 8\: a split\-dependent kernel M\(nu\) \(OEP 8 Eqs\. \(3\)\-\(5\)\) also breaks the antisymmetric\-phase invariance; the paper does not consider it and gives no intermediate detunings to estimate it\. \- Fig\. 3c, the modulation phase phi at alpha = 1\.2 \(symmetric to antisymmetric\)\: contrast 'better than 1 in 200'\. No intermediate\-resonance test is made here; dudovich\_2001 is the resonant case\. Text slip \(p\. 241, not a value\)\: 'where Theta is the frequency deviation from omega\_0/2' should name Omega\. Reference 17 \(Salour and Cohen\-Tannoudji, Phys\. Rev\. Lett\. 38, 757\) is printed with the year 1997\. Register\: TC\-986\. **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.