We demonstrate coherent Doppler-free three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ optical clock transition and the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ intercombination transition in free-space thermal clouds of
88Sr atoms. By appropriate orientation of the wave vectors of three lasers incident on the atoms, the first-order Doppler shift can be eliminated for all velocity classes. Three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition enables high-contrast Ramsey spectroscopy with interrogation times comparable to the $21\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ natural lifetime using a single near-resonant laser source. Three-photon spectroscopy on the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ clock transition, using only laser frequencies nearly resonant with the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, enables a reduction in Doppler broadening by two orders of magnitude and a corresponding $\ensuremath{\sim}470\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ linewidth without a confining potential.
We report on the saturation behavior of the
Na2 two-photon transition at 602.17
nm1,2 This transition has a dominant near-resonant intermediate level; the off-resonance
Delta is of the order of the Doppler width
DeltanuD. The dominant contribution to the Doppler-free two-photon line then cornea from two velocity packets of molecules which are Doppler-shifted into resonance. This results in some novel experimentally confirmed aspect, of the two-photon absorption: (i) the ratio of the amplitudes of the Doppler-free and Doppler-broadened two-photon lines is much larger than in the case
DeltaggDeltanuD, and (ii) the Doppler-free line saturates much stronger than the Doppler-broadened line. The resonant velocity packets of molecules are dominantly saturated on the ground-to-intermediate-level transition. The saturation power density is
sim0.5W/cm2; this value is consistent with a recent measurement of the Franck-Condon factors
involved3The method of Doppler – free comb – spectroscopy for dipole transitions was proposed. The numerical calculations for susceptibility spectrum for two-level system driving by strong counter propagating combs were made. The narrow peaks with homogeneous width arise on the background of Doppler counter. The contrast of these peaks is large for largest amplitudes of comb-components. Power broadening is increasing with increasing of field amplitudes. The amplitudes of peaks depend on the phase difference between carrier frequencies of combs. The spectral range of absorption spectrum is determined by the spectral range of comb generator and all homogeneous lines arise simultaneously. The spectral resolution is determined by the width of homogeneously –broadening lines. The physical nature of narrow peaks is in the existing of multi-photon transitions between manifolds of quasi-energy levels arising for different groups of atoms moving with velocities that satisfy to the resonant conditions 2kv= (n+l)Ω⁄j, where n, l, j-are integers and Ω - frequency difference between comb teeth.