Doppler-free ultrafast modulation spectroscopy with phase-conjugation geometry

We have studied theoretically a phase-conjugate ultrafast modulation spectroscopy (PCUMS) in a Doppler-broadened system. The pump beams consist of two frequency components which drive two different transitions. It is found that the four-wave-mixing (FWM) signal exhibits damping oscillation as the relative time delay between two pump beams is varied, from which the energy-level splitting can be deduced. We have considered the cases that pump beams have either narrow band or broadband linewidth and found that for both cases a Doppler-free precision in the measurement of the energy-level splitting can be achieved. The advantage of PCUMS is that the energy-level splitting between states can be widely separated. Finally, the relationship between PCUMS and other Doppler-free techniques in frequency and time domains has also been discussed.