Quantum Tracking Control With No Singular Points
Alicia Magann, Princeton University
Quantum tracking control aims to identify a control field to steer an observable along a desired path in time. The field can be generated by simply inverting the dynamical equation for the observable, making tracking control a computationally attractive alternative to traditional quantum optimal control. However, unlike in optimal control, fields found by inverting the dynamical equation are often plagued by singular points that can derail the control effort. In this poster we take a step toward realizing the potential of tracking control to accelerate quantum control simulations. Namely, we demonstrate the existence of one class of problems that is free of singular points: tracking dipoles in quantum systems whose Hamiltonians are unbounded. General analytical expressions are presented for the tracking control fields and the structure of the expressions ensures that the fields they produce will be smooth and free of singular points. We illustrate this concept using a planar molecular rotor whose dipole vector corresponds directly to its orientation. A series of simulations are presented to drive the rotor orientation along desired trajectories in time using two orthogonal control electric fields with no singular points. We highlight that tracks defined by analytical functions as well as arbitrary data points can be followed.
Abstract Author(s): Alicia Magann, Tak-San Ho, Herschel Rabitz