Enantioselective Topological Frequency Conversion

Abstract

Two molecules are enantiomers if they are non-superimposable mirror images of each other. Electric dipole-allowed cyclic transitions $|1⟩\to |2⟩\to |3⟩\to |1⟩$ obey the symmetry relation ${\mathcal{O}}^R=-{\mathcal{O}}^S$, where ${\mathcal{O}}^{R,S}=({\mu }_{21}^{R,S}{E}_{21})({\mu }_{13}^{R,S}{E}_{13})({\mu }_{32}^{R,S}{E}_{32})$, and $R,S$ label the two enantiomers. Here we generalize the concept of topological frequency conversion to an ensemble of enantiomers. We show that, within a rotating-frame, the pumping power between fields of frequency ${\omega }_1$ and ${\omega }_2$ is sensitive to enantiomeric excess, ${\mathcal{P}}_{2\to 1}=\hslash \frac{{\omega }_1{\omega }_2{C}_L^R}{2\pi }(N_R-N_S)$, where $N_i$ is the number of enantiomers $i$ and $C_L^R$ is an enantiomer-dependent Chern number. Connections with chiroptical microwave spectroscopy are made. Our work provides an underexplored and fertile connection between topological physics and molecular chirality.

Cited by in corpus (1)

• Topological power pumping in quantum circuits