Complete Controllability Despite Degeneracy: Quantum Control of Enantiomer-Specific State Transfer in Chiral Molecules

TL;DR

This paper demonstrates complete controllability of rotational states in chiral molecules despite degeneracy, enabling enantiomer-specific state transfer and advancing the goal of separating enantiomers using electric fields.

Contribution

It proves controllability for degenerate rotational states and constructs pulse sequences for enantiomer-specific transfer, overcoming a key obstacle in chiral molecule separation.

Findings

Achieved controllability for asymmetric top molecules with degenerate M-states.

Designed pulse sequences for enantiomer-specific population transfer.

Identified conditions for complete enantio-selective control.

Abstract

We prove complete controllability for rotational states of an asymmetric top molecule belonging to degenerate values of the orientational quantum number M. Based on this insight, we construct a pulse sequence that energetically separates population initially distributed over degenerate M-states, as a precursor for orientational purification. Introducing the concept of enantio-selective controllability, we determine the conditions for complete enantiomer-specific population transfer in chiral molecules and construct pulse sequences realizing this transfer for population initially distributed over degenerate M-states. This degeneracy presently limits enantiomer-selectivity for any initial state except the rotational ground state. Our work thus shows how to overcome an important obstacle towards separating, with electric fields only, left-handed from right-handed molecules in a racemic mixture.