Accumulative effects in the coherence of three-level atoms excited by femtosecond-laser frequency combs

We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\pi$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.