Cyclic three-level-pulse-area theorem for enantioselective state transfer of chiral molecules

We derive a pulse-area theorem for a cyclic three-level system, an archetypal model for exploring enantioselective state transfer (ESST) in chiral molecules driven by three linearly polarized microwave pulses. By dividing the closed-loop excitation into two separate stages, we obtain both amplitude and phase conditions of three control fields to generate high fidelity of ESST. As a proof of principle, we apply this pulse-area theorem to the cyclohexylmethanol molecules ($\text{C}_{7}\text{H}_{14}\text{O}$), for which three rotational states are connected by the $a$-type, $b$-type, and $c$-type components of the transition dipole moments in both center-frequency resonant and detuned conditions. Our results show that two enantiomers with opposite handedness can be transferred to different target states by designing three microwave pulses that satisfy the amplitude and phase conditions at the transition frequencies. The corresponding control schemes are robust against the time delays between the two stages. We suggest that the two control fields used in the second stage should be applied simultaneously for practical applications. This work contributes an alternative pulse-area theorem to the field of quantum control, which has the potential to determine the chirality of enantiomers in a mixture.