Nonlinear effects of third-and fifth-order on polarization beats in a four-level system

We have employed second-order coherence function theory to study the nonlin ear effects of third-and fifth-order on polarization beats in a four-level system (TPBFS and FPBFS). It is found that the different temporal behavior; of the beat signal in TPBFS and FPBFS depends on the stochastic properties of the lasers and transverse relaxation rate of the transition. We have con sidered the cases that pump beams have either narrow band or broadband line width and found that for both cases a Doppler-free precision can be achieve d in the measurement of the energy-level difference between two excited sta tes which are dipolar forbidden from the ground state. We also discussed th e spatiall modulation behavior of the beat signal.