Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field

TL;DR

This paper introduces new monotonically convergent algorithms for optimal control of quantum systems with nonlinear electromagnetic interactions, ensuring algorithm stability and practical pulse implementation.

Contribution

It proposes a novel algorithmic approach for nonlinear quantum control problems with guaranteed convergence and applicability to pure and mixed states.

Findings

Algorithms demonstrate monotonic convergence numerically.

Optimal pulses are experimentally feasible.

Method effectively handles nonlinear interactions of order 3.

Abstract

We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.