A theoretical analysis on coherent double resonant absorptive lineshape in closely spaced transitions for λ − type five level system

Under Doppler free double resonant condition, an open five level system with three closely spaced upper levels and a pair of closely spaced lower levels, is allowed to interact with two electromagnetic fields. In the domain of semiclassical formulation of atom-field interaction, the optical Bloch equations involving the density matrix elements are constructed. These coupled optical Bloch equations are unsolvable in closed analytical form. We use the perturbation method for getting the approximate analytical solutions to the coupled optical Bloch equations. The absorptive signal lineshape corresponding to pump frequency Ω1 and signal frequency Ω2 is obtained. We also obtain the absorptive signal line shape by interchanging the pump and signal (i.e., the pump frequency is Ω2 and the signal frequency is Ω1) mutually. The interferences between the probability amplitudes for different energy levels involving the dipole allowed and the dipole forbidden transitions give rise to the field dependent and field independent quantum coherence respectively. With the suitable manipulation of the coherence between the two lower levels, the signal lineshapes for on-resonance and off-resonance pump positions are explored in a great detail. The off-resonance pump leads to the two-photon absorption and hence the signature of the nonlinear resonances. On the other hand, the on-resonance pump positions lead to the Rabi splitting. The shifts of the resonance peak positions are explored as a function of pump intensity and the level spacings of the closely spaced levels.