Hyperpolarizability, two-photon resonances and quadratic Stark effects in Doppler free spectra for a four level system

Using pump-probe spectroscopy, a four level system (FLS) with a double V-type configuration is investigated under Doppler-free conditions. The semiclassical description of the atom-field interaction is used to derive the optical Bloch equations (OBE). Under steady-state and rotating wave approximation, the coupled OBE reduces to a system of simultaneous equations. The analytical expressions for the signal absorption are parametrically computed using theoretical data. The signal lineshapes exhibit two perfectly symmetric Lorentzians corresponding to two signal resonance frequencies when the pump position is exactly in the middle of the two signal resonance frequencies. These two Lorentzians repel each other and, hence, the shifts of the signal peak frequencies. For on-resonant pump, the ac (dynamic) Stark splittings are obtained. The off-resonant pump produces the two-photon resonances. The nonlinear polarization and hence the hyperpolarizability involving the lower pair of levels exhibit interesting results. The hyperpolarizability is synonymous with those of the quadratic Stark effects.