Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

TL;DR

This paper introduces a direct optimal control method for laser-driven quantum particle dynamics, offering a robust alternative to traditional indirect methods by discretizing dynamical equations into a nonlinear optimization problem.

Contribution

It presents a novel direct optimal control approach for quantum systems, specifically applied to laser-driven wavepacket dynamics using a Gaussian parameterization.

Findings

The method is effective across various particle masses and control durations.

Optimized fields produce reasonable quantum control results in full wavepacket propagation.

Conditions are identified under which the Gaussian approximation remains valid.

Abstract

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.