Coherent superpositions of states in coupled Hilbert-space using step by step Morris-Shore transformation

Creation of coherent superpositions in quantum systems with Na states in the lower set and Nb states in the upper set is presented. The solution is drived by using the Morris-Shore transformation, which step by step reduces the fully coupled system to a three-state Λ-like system and a set of decoupled states. It is shown that, for properly timed pulse, robust population transfer from an initial ground state (or superposition of M ground states) to an arbitrary coherent superposition of the ground states can be achieved by coincident pulses and/or STIRAP techniques.