  In this paper, an exact analytical solution is presented for achieving
coherent population transfer and creating arbitrary coherent superposition
states in a five-state chainwise system by a train of coincident pulses. We
show that the solution of a five-state chainwise system can be reduced to an
equivalent three-state $\Lambda$-type one with the simplest resonant coupling
under the assumption of adiabatic elimination (AE) together with a requirement
of the relation among the four incident pulses. In this method, all of four
incident pulses at each step all have the same time dependence, but with
specific magnitudes. The results show that, by using a train of appropriately
coincident incident pulses, this technique enables complete population
transfer, as well as the creation of arbitrary desired coherent superposition
between initial and final states, while the population in all intermediate
states is effectively suppressed. The complete physical explanation of the
underlying mechanism is presented. The results are of potential interest in
applications where high-fidelity multi-state quantum control is essential,
e.g., quantum information, atom optics, formation of ultracold molecules,
cavity QED, nuclear coherent population transfer, light transfer in waveguide
arrays, etc.
