Achieving the laboratory control of quantum dynamics phenomena using nonlinear functional maps

This paper introduces a new algorithm for achieving closed-loop laboratory control of quantum dynamics phenomena. The procedure makes use of nonlinear functional maps to exploit laboratory control data for revealing the relat ionship between control fields and their effect on the observables of inter est. Control is achieved by (1) constructing the maps by performing laborat ory experiments during an initial learning phase and then (2) searching the maps for fields that drive the system to the desired target during a separ ate, offline optimization stage. Once the map is learned, additional labora tory experiments are not necessarily required if the control target is chan ged. Maps also help to determine the control mechanism and assess the robus tness of the outcome to fluctuations in the field since they explicitly mea sure the nonlinear response of the observable to field variations. To demon strate the operation of the proposed map based control algorithm, two illus trations involving simulated population transfer experiments are performed. (C) 2001 Elsevier Science B.V. All rights reserved.