Quantum optimal control of molecular coherent states

Abstract In this paper, we address the optimal control problem in molecular systems, focusing on transitions within coherent states characterised by complex coefficients. Employing Hölder's inequality, we establish a mathematical relationship between the energy requirement and the distance separating the initial and the target coherent states. A key part of our study is the application of this framework to the $\text{H}_2\text{O}$ molecule, specifically examining the local OH bond. Here, we demonstrate how energy requirements for the state transitions are influenced by the distance between these states. Furthermore, we investigate the effects of a heat bath coupled to the system, by analysing its impact on transferring the molecular system to different final coherent states. These coherent states are defined as \textit{almost} eigenvectors of the Generalised Heisenberg Algebra (GHA) annihilation operator. By using the Perolomov approach, another type of coherent states for the Morse potential associated with the GHA can be constructed. By leveraging the GHA structure, we revisit and analyse Morse coherent states previously established for certain diatomic molecules, offering a deeper insight into the dynamics of state transitions under various conditions.