Enantioselective Topological Frequency Conversion.

Two molecules are enantiomers if they are nonsuperimposable mirror images of each other. Electric dipole-allowed cyclic transitions |1⟩ → |2⟩ → |3⟩ → |1⟩ obey the symmetry relation O R = - O S , where O R , S = (μ 21 R , S E 21 )(μ 13 R , S E 13 )(μ 32 R , S E 32 ) and R and S label the two enantiomers. Herein, 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 ω 1 and ω 2 is sensitive to enantiomeric excess, P 2 → 1 = ℏ[ω 1 ω 2 C L R /(2π)]( 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.