Complex probability amplitudes of three states in a V-type system with two orthogonal sub-states

We theoretically analyzed the complex probability amplitudes of three states in a V-type system with two orthogonal energy sub-states. With rotating-wave approximation, the non-damped analytic solutions of the complex probability amplitudes equations with resonant excitation were deduced. The effective transition dipole moments and effective input pulse area were introduced and their expressions were given. Itʹs revealed that both amplitudes and frequencies of the population oscillations on the two orthogonal sub-states could be manipulated by the polarization angle of the excitation and the initial distribution of populations.