Fast chiral resolution with optimal control

TL;DR

This paper formulates and solves an optimal control problem to achieve the fastest possible perfect chiral resolution using boundary control fields, providing analytical and numerical pulse sequences that outperform existing methods.

Contribution

It introduces a novel optimal control framework for minimal-time chiral resolution, deriving explicit pulse sequences and analyzing their dependence on control bounds.

Findings

Optimal control fields are boundary or zero (singular)

Identified three-stage symmetric pulse sequences for larger control bounds

Achieves faster resolution than existing pulsed protocols

Abstract

In this work, we formulate the problem of achieving in minimum-time perfect chiral resolution with bounded control fields, as an optimal control problem on two non-interacting spins-$1/2$. We assume the same control bound for the two Raman fields (pump and Stokes) and a different bound for the field connecting directly the two lower-energy states. Using control theory, we show that the optimal fields can only take the boundary values or be zero, the latter corresponding to singular control. Subsequently, using numerical optimal control and intuitive arguments, we identify some three-stage symmetric optimal pulse-sequences, for relatively larger values of the ratio between the two control bounds, and analytically calculate the corresponding pulse timings as functions of this ratio. For smaller values of the bounds ratio, numerical optimal control indicates that the optimal pulse-sequence loses its symmetry and the number of stages increases in general. In all cases, the analytical or numerical optimal protocol achieves a faster perfect chiral resolution than other pulsed protocols, mainly because of the simultaneous action of the control fields. The present work is expected to be useful in the wide spectrum of applications across the natural sciences where enantiomer separation is a crucial task.