Femtosecond-pulse two-photon resonant difference-frequency mixing in gases: A technique for tunable vacuum-ultraviolet femtosecond-pulse generation and a spectroscopic tool for studying atoms in strong laser fields

Two-photon resonant and near-resonant four-wave difference-frequency mixing in gases in the interaction regime when laser pulse durations are comparable to or shorter than the medium polarization relaxation time $T_2^{\prime }$ is investigated. The results of experimental studies of the process in Ar and Kr using pump pulses from the ArF-excimer laser are presented demonstrating a generation of tunable short pulse radiation in the range 102–124 nm. The results are discussed in terms of a theoretical model based on a self-consistent solution of the Bloch equations for the atomic transitions and the Maxwell equations for the fields. This enables one to interpret specific nonstationary resonant and quasiresonant phenomena involved in the frequency conversion process. It is shown that the femtosecond-pulse four-wave frequency-mixing technique with probe pulses significantly shorter than the pump pulses makes it possible to study the coherent dynamics of an atomic transition exposed to an intense field. Using atomic Kr as the nonlinear medium, coherent Rabi oscillations and the subsequent phase relaxation of excitation were observed under the condition of two-photon interaction of Kr with femtosecond 193-nm laser pulses. The obtained information is important for controlling and optimizing processes of two-photon resonant frequency conversion and for time-resolved studies of Rydberg states in atoms and molecules.