Adiabatic creation of coherent superposition states via multiple intermediate states

We consider an adiabatic population transfer process that resembles the well-established stimulated Raman adiabatic passage. In our system, the states have nonzero angular momentums J, therefore, the coupling laser fields induce transitions between the magnetic sublevels of the states. In particular, we discuss the possibility of creating coherent superposition states in a system with coupling pattern J = 0 double left right arrow1 and 1 double left right arrow 2. Initially, the system is in the J = 0 state. We show that by, applying two delayed overlapping laser pulses, it is possible to create any final superposition state of the magnetic sublevels \2, -2], \2, 0], \2, +2]. Moreover, we find that the relative phases of the applied pulses influence not only the phases of the final superposition state but also the probability amplitudes. We show that if we fix the shape and the time delay between the pulses, the final state space can be entirely covered by varying the polarizations and relative phases of the two pulses. Performing numerical simulations we find that our transfer process is nearly adiabatic for the whole parameter set.