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 · Catalogue · 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.

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.