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 · Catalogue · 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.

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 review register for the checks and decisions.