The examples of quantum-state manipulation and coherent excitation discussed in this monograph present idealizations of actual quantum systems, simplifications that allow straightforward theoretical description. As one moves beyond the models of isolated atoms, few essential states, and transform-limited pulses to deal with more realistic models that can describe experimental reality, the basic tools described hitherto require elaboration and extension. Theoretical treatments of large molecules and chemical reactions involving laser-induced changes rely upon numerical simulation more than on analytic solutions. This final chapter discusses two of the themes applicable to that work: control theory and optimization.

Control theory

Classical control theory, as followed by mathematicians and engineers, deals with procedures for manipulating the input (the “controls”) of a dynamically changing system to obtain a desired output of the system. In a closed-loop control system some device measures the output and, using a feedback loop, alters the input (via a control element) to bring the output closer to conformity with a goal. These techniques typically find application in control of experiments but they also work for theoretical modeling. An open-loop control system is one without such feedback; the controls are adjusted in accord with some established plan. Design of a suitable control mechanism (a control function ratioing output to input) must ensure that the system is stable (i.e. a finite input signal produces a finite output signal) and controllable (i.e. it is possible to obtain the desired output).