Doppler- and recoil-free laser excitation of Rydberg states via three-photon transitions

Three-photon laser excitation of Rydberg states by three different laser beams can be arranged in a starlike geometry that simultaneously eliminates the recoil effect and Doppler broadening. Our analytical and numerical calculations for a particular laser excitation scheme 5S(1/2) -> 5P(3/2) -> 6S(1/2) -> nP in Rb atoms have shown that, compared to the one-and two-photon laser excitation, this approach provides much narrower linewidth and longer coherence time for both cold atom samples and hot vapors, if the intermediate one-photon resonances of the three-photon transition are detuned by more than respective single-photon Doppler widths. This method can be used to improve fidelity of Rydberg quantum gates and precision of spectroscopic measurements in Rydberg atoms.