Natural variables for controlling quantum dynamics

A quantum control landscape is the expectation value of an observable expressed as a function of the control variables, and the local geometry of the landscape for state-to-state transitions is explored for its implications upon practical searches for optimal controls. The gradient of the landscape with respect to the control field is shown to always lie in a low-dimensional subspace spanned by basis functions bearing specific knowledge of the system physics, thereby comprising a natural set of variables for the particular optimal control application. The enumeration of these basis functions provides an upper bound on the required number of properly identified control variables. A specific experimental protocol is suggested to utilize the geometric structure of the landscape for identifying a reduced set of control variables for practical laboratory implementation. Simulations on simple systems are used to illustrate the characteristics of the natural control variables and the prospective experimental protocol. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.