Quantum optimal control of multiple targets: Development of a monotonically convergent algorithm and application to intramolecular vibrational energy redistribution control

Abstract

An optimal control procedure is presented to design a field that transfers a molecule into an objective state that is specified by the expectation values of multiple target operators. This procedure explicitly includes constraints on the time behavior of specified operators during the control period. To calculate the optimal control field, we develop a new monotonically and quadratically convergent algorithm by introducing a quadruple space that consists of a direct product of the double (Liouville) space. In the absence of the time-dependent constraints, the algorithm represented in the quadruple-space notation reduces to that of the double-space notation. This simplified formulation is applied to a two dimensional system which models intramolecular vibrational energy redistribution (IVR) processes in polyatomic molecules. An optimal pulse is calculated that exploits IVR to transfer a specific amount of population to an optically inactive state, while the other portion of the population remains in the initial state at a control time. Using trajectory plots in quantum-number space, we numerically analyze how the control pathway changes depending on the amount of the excited population.