Doppler-free two-photon spectroscopy

We describe atomic transitions where two or more photons are simultaneously absorbed by an atom or a molecule (without any intermediate resonant level). We show theoretically and experimentally the possibilities of these transitions for numerous high-resolution spectroscopic studies. The principle of the method is discussed: the Doppler broadening is suppressed in two-photon transitions if the atoms are irradiated by two laser beams travelling in opposite directions, because the Doppler shift in one wave cancels that in the other. A generalization is made for multiphotonic transitions. Calculations of the multiphotonic transition probability are summarized and their hypotheses specified: one deals with line shape and orders of magnitude in practical conditions. The problem of light shifts is also discussed. A typical experimental set-up with a cw dye laser is described in detail. Typical recordings of two-photon transitions are given; they show line widths smaller than 4 MHz (on a Doppler width of 2000 MHz). Other experiments show the possibility of increasing the transition probability by using two lasers with slightly different wave lengths. One experiment with a three-photon Doppler-free transition is also described. In conclusion, we make a brief comparison with the saturated absorption technique.