Control in a dissipative environment: the example of a Cope rearrangement

In this work, we present optimal control calculations in a dissipative environment. To this end, the auxiliary density matrix method describing the dissipative quantum dynamics is combined with optimal control theory. The resulting approach, which is nonperturbative in the laser-system interaction, is applied to model the control of Cope's isomerization of the methyl-cyclopentadienylcarboxylate dimer, described as the motion along a one-dimensional reaction path. The construction of the reaction path model as well as the dipole moments required for the laser interaction are obtained from DFT quantum chemistry calculations. As a main result, we show that the proposed methodology, which includes the environment at the design stage of the control, leads to control fields which can react on dissipative effects during the dynamics and lead to an increased control objective, as compared to control fields obtained without dissipation. The chosen example is analyzed in detail, and the physical mechanisms of the control under dissipation are elucidated.