Revival, Supression and Maximization of Coherent Control through a Change of Basis

Coherent control relies on the interference between different pathways created by the preparation of initial superpositions. However, interference is a basis-dependent quantity, and so is coherent control. To address this, we introduce a novel formalism, the Coherent Control Scattering (CCS) matrix. This matrix allows us to analyze the modifications in interference structure and controllability resulting from a change of basis. We show that the change in controllability can be linked to the non-commutativity of the transformation matrix with the CCS matrix, and the non-orthogonality of the transformation. Furthermore, we find that minimal interference is associated with the CCS eigenbasis, while the Fourier basis of the eigenvectors yields maximal interference, leading to optimal coherent control. To illustrate the impact of a basis change on controllability, we provide an example involving ⁸⁵Rb+ ⁸⁵Rb scattering. Additionally, we apply this developed formalism to interpret recent experimental findings on He + D₂ inelastic scattering, highlighting the presence or absence of interference based on the chosen basis.