Optimal Control Theory and the design of Laser pulses to control molecular motion

Abstract

Laser pulses can now routinely be designed in the laboratory, through the use of feedback mechanisms, to optimise the yield of a desired photofragmentation product. The ideas and impetus for these developments came originally from the Optimal Control Theory papers of Herschel Rabitz. We have developed a Born-Oppenheimer like separation called the electricnuclear Born-Oppenheimer (ENBO) approximation. In this approximation variations of both the nuclear geometry and of the external electric field are assumed to be slow compared with the speed at which the electronic degees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei, but also on the electric field strength and on the orientation of the molecule with respect to the electric field. Through the use of this approach it has been possible for the first time to include the effects of polarizability into the Optimal Control Theory design of laser pulses [1,2]. We have also found analytic ways of designing laser pulses to achieve population transfer to specified quantum states in certain simple cases [3]. Our new method is applicable to homonuclear diatomic molecules, whereas previous similar methods required the existence of a non-zero transition dipole matrix element connecting the two quantum states. Laser pulses can also be designed to create aligned or oriented molecular populations [4], and we have designed such pulses both analytically and using Optimal Control Theory. Current projects involve applications to control in biologically related molecules (carboxy-myoglobin, AADH), to photodissociation processes and to the control of branching at conical intersections.