Control protocol of finite dimensional quantum systems using alternating square pulse

Control protocol to drive finite dimensional quantum systems to an arbitrary target state using square pulses is proposed explicitly. It is a multi-cycle control process and in each cycle we apply square pulses to cause single or a few transitions between energy levels. Systems with equal energy gaps except the first one, four dimensional system with equal first and third energy gaps and different second energy gap, and systems with all equal energy gaps of dimension three, are investigated in detail. The control parameters, the interaction time between systems and control fields and free evolution times between cycles, are connected with the probability amplitudes of target states via trigonometric functions and are determined analytically.