Line shape and frequency shift of Lamb dip and crossover-resonance dip in closely spaced transitions

The line shape of a pair of Doppler-broadened closely spaced transitions sharing a common lower level and under the effect of a standing-wave monochromatic radiation field is studied. The eight steady-state optical Bloch equations are solved analytically to obtain the polarization by retaining terms up to the third power in the electric-field amplitude. The absorption coefficient derived for the standing-wave case consists of two Lamb dips for the two allowed transitions at ω₁ and ω₂ and a crossover resonance dip at the intermediate frequency ωc=(ω₁+ω₂)/2. The Lamp-dip peak frequencies show intensity-dependent shifts. Numerical computations are presented for different values of Rabi frequencies and relaxation linewidth parameters, which are small compared to the frequency difference {Δ}=ω₂-ω₁. The computed line shape and frequency shift are compared with the observed results in the Balmer H_α line of hydrogen and the infrared Zeeman spectra of methane.