A theoretical analysis of the relative intensities of the Doppler-free signals in saturation spectroscopy, velocity selective optical pumping (VSOP) spectroscopy, polarization spectroscopy and a mixing of saturation and polarization spectroscopies is presented using the approximation of a single cycle of optical pumping in a four-level system. An optical pumping process in the Zeeman sublevels is taken into account owing to the important role of spontaneous emission even if the sublevels are degenerate. Arbitrary polarization combinations are considered for pump and probe beams. The similarities and differences between three kinds of spectroscopy are made clear. Both circular and linear optical anisotropies induced by the pump beam are considered in this theoretical calculation. The magnitude and sign of Doppler-free resonances in each spectroscopy are quite different owing to the polarizations of the pump and probe beams. The four-level system is important as a three-level approximation. The results obtained from the four-level optical pumping theory are in good agreement with experimental reports.
We have observed that spectral lines obtained in sodium vapor can be strongly distroted when using two-photon spectroscopy with a resonant intermediate state. In some cases, the spectral lines appear to be split into two components. We demonstrate that these effects are due to velocity-selective optical pumping of the atomic ground state; the line shapes reflect the velocity distribution of atoms in the excited intermediate state. We have analyzed the effects using the time-dependent solutions of the rate equations which describe the time evolution of optical pumping for the various atomic velocity groups, and we obtain good agreement with experiment. Optical-pumping problems are often analyzed with the use of steady-state rate equations which incorporate phenomenological relaxation; such approaches are not capable of describing our observations. Velocity-changing collisions are shown to suppress the effects and they explain why these effects were not previously observed; the previous experiments were carried out with slight amounts of a buffer gas in the vapor cell. The effects reported here must be accounted for when carrying out laser-induced line-narrowing experiments in atoms or molecules that can be optically pumped; they can also be used as a new and more sensitive probe of optical pumping in vapors.
Theoretical analysis of D 1 lines of most stable alkali atoms in velocity selective optical pumping (VSOP) spectroscopy is presented by using the approximation of a single cycle of optical pumping in a four-level system. VSOP spectroscopy is clearly compared with polarization spectroscopy and then it is shown that the results obtained for polarization spectroscopy can be applied to the theory in VSOP spectroscopy. The relative signal intensities of Na D 1 line in polarization spectroscopy have been theoretically calculated and experimentally confirmed to be in good agreement with those in VSOP spectroscopy. The first-order theory in VSOP spectroscopy can be applied to the cases of the D 1 lines of the other alkali atoms. It is expected that the theoretical analysis can be useful for future experiments of the Doppler-free D lines in the alkali atoms.
We report computational results for the time evolution of the velocity distribution P(V,t) for two-level and multilevel ``Doppler'' laser cooling. We compare results obtained from the semiclassical (SC) Fokker-Planck equation and from generalized optical Bloch equations applied to density matrices over a basis of products of internal and quantized translational states (QDM). Computer memory requirements are optimized to make large-scale QDM calculations feasible. QDM and SC agree well except for two cases: (a) atoms in the wells of the light-shift potential (with kinetic energy less than the well depth,
U0), and (b) atoms with recoil energy
ER comparable to or greater than the natural linewidth \ensuremath{\Elzxh}\ensuremath{\Gamma}. Transient dips occur in P(V,t) at V=0 in QDM results due to slow cooling of atoms in the light-shift potential wells. Dips in P(V,t) occur at velocity-tuned-resonance (Doppleron) velocities but disappear over long interaction times as atoms accumulate near points where the force is zero. When
ER\ensuremath{\approxeq}\ensuremath{\Elzxh}\ensuremath{\Gamma}, sharp peaks occur in P(V,T) at V=\ifmmode\pm\else\textpm\fi{}
VR from velocity-selective population quasitrapping not previously found in a two-level transition. Sharp features in P(V,t) occur also for J\ensuremath{\rightarrow}J+1 transitions with J>0, small
U0/
ER, and sufficiently large detuning, from transitions between individual quantum states in the periodic potential.
We study the influence of optical pumping on Doppler-broadened alkali-metal-atom
D line spectra by solving the time-dependent density matrix for an open two-level system. The time-dependent absorption is averaged over the distribution of interaction times obtained from the three-dimensional beam geometry and atomic velocity distribution and over the longitudinal velocity distribution. The optical pumping is significant at much lower intensities than saturation and depends strongly on the intensity, beam radius, vapor cell length, and spontaneous-decay branching ratio. The result is in agreement with our earlier steady-state solution for a wide range of parameters and predicts two interesting line-shape features.
The effect of an intense pump beam on the intensity of the phase-conjugated emission is studied in the case of a three-level atom. We first extend to the case of cross-polarized pump beams the dressed-atom model that we have presented previously [Phys. Rev. A 34, 4008 (1986)] for the case of two-level atoms. The range of validity of our theory is \ensuremath{\Gamma} (natural width) ${\ensuremath{\Omega}}_{1}$ (Rabi frequency of the intense pump) ku (Doppler width). We have studied the line shape in degenerate four-wave mixing, the influence of a static magnetic field, and the resonances that appear in nondegenerate four-wave mixing. Experiments are done in a neon discharge using cw dye lasers. The experimental results are in good agreement with the theoretical predictions. In degenerate four-wave mixing, we have shown that the saturating dip disappears when the weak beams have orthogonal polarizations. In the presence of a static magnetic field and in the nearly degenerate case, narrow resonances corresponding to transitions between energy levels of the dressed atom are observed. The intensity and the width of these resonances are in very good agreement with the predictions of the theoretical model.