Learning control of molecular systems

Abstract

Developing efficient algorithms is an important task in the learning control of quantum systems since most learning control problems for quantum systems involve a heavy requirement for computational resources. In this thesis, we first implement the learning control algorithm to construct a two-state wave packet for a HCN molecule in a fixed target state. Then, we demonstrate that the learning control algorithm with an adaptive target state can be more efficient for several classes of quantum control problems than traditional learning control algorithms using a fixed target state. In the algorithm, the target state is updated according to the renormalized fragmentary yield in the desired region (or subspace) throughout the learning iterations. We apply this adaptive target scheme to five significant quantum control tasks.

Another point worth considering is the robustness of the control field. For example, in laser-assisted collisions, a control field may fail if we cannot precisely synchronise the colliding particles and the laser pulse. Therefore, we aim to construct laser pulses which are robust to this circumstance by a sampling-based method to achieve a desired charge transfer probability with limited sensitivity to the arrival time of the laser pulses. An adaptive target scheme is used in the optimal control calculations based on an adiabatic two-state model of a H+D⁺ collision system. Several samples with different pulse arrival times are selected to construct robust fields at three different collision energies and the validity of these fields are examined by tests with additional samples.

Uncertainties also arise in some molecular parameters of the systems. When considering uncertainties in potential curves and laser amplitudes, we show that robust laser pulses can be obtained by a sampling-based method to achieve a desired photoassociation probability. Similarly, we use a small number of samples to construct a robust field and test the performance of this field using additional samples. Excellent outcomes are obtained based on the proposed method for different uncertainties. The robust control field achieves higher average photoassociation probabilities over the tested samples, in comparison with the probabilities achieved by the learned field designed without using the sampling-based method.