Quantum observable homotopy tracking control

This paper presents a new tracking method where the target observable < O(s,T)> at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s >= 0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique. (c) 2005 American Institute of Physics.