Manipulation of Multi-Level Quantum Systems via Unsharp Measurements and Feedback Operations

The recently proposed quantum control method called self-fulfilling prophesy is investigated in multi-level cases, based on a sequence of measurement-feedback operations. The feedback operation is elaborately designed with respect to the eigenstates of the density matrix of the target state and its post-measurement state. This design procedure is suitable for the generation of any predefined coherent superpositions of multiple quantum states and elicitation of desired quantum dynamics. For the sake of clearness, arbitrarily prescribed superposition states in three- and four-level systems are prepared, and quantum dynamics achieved as desired. The simulation results indicate that the scheme tolerates modest imprecisions of feedback operation and is robust against sudden perturbations. Thus, the scheme enables new insight on quantum manipulations in a variety of multi-level systems to be achieved.