Optimal control of coherent wave functions: A linearized quantum dynamical view

We present an optimal control approach to study a linearized quantum dynamical system. Using quadratic forms for the physical objective of a target coherent wave function and for the physical penalties, we derive analytical expressions for the optimal fields. It is shown that the optimal fields can be decomposed into a finite number of monochromatic component fields. The numerical results suggest that the qualitative behavior of the optimal field is strongly dependent upon the cost functional weight factors. Moderate weight factors placed on the physical constraints can lead to excellent control of the desired target wave function. The effect of target time on the properties of the optimal field is also investigated. The numerical studies indicate that the optimal field is affected by the overall absolute phase of the target wave function, which provides a certain degree of additional flexibility in choosing the optimal fields. In all the cases studied only negligible direct current components appear in the fields.