Single-loop cyclic three-level (∆-type) configuration of chiral molecules was used for enantioseparation in many theoretical works. Considering the effect of molecular rotation, this simple single-loop configuration is generally replaced by a complicated multiple-loop configuration containing multiple degenerate magnetic sub-levels and the ability of the enantio-separation methods is suppressed. For chiral asymmetric top molecules, we propose a scheme to construct a real singleloop ∆-type configuration with no connections to other states by applying three microwave fields with appropriate polarization vectors and frequencies. With our scheme, the previous theoretical proposals for enantio-separation based on single-loop ∆-type configurations can be experimentally realized when the molecular rotation is considered.

Determination of enantiomeric excess is important and remains challenges. We theoretically propose a new spectroscopic method for this issue based on the chirality-dependent AC Stark effects in cyclic three-level models under the three-photon resonance condition. The enantiomeric excess of the chiral mixture is determined by comparing the amplitudes of the two chosen AC Stark peaks in the Fourier transform spectrum of the induced polarizations, which are (approximately) proportional to the molecule numbers of the two enantiomers, respectively. Comparing with current spectroscopic methods based on the interference between the electric-and (usually weak) magneticdipole transition moments and/or with the need for enantio-pure samples, our method only involves electric-dipole transitions and does not require the enantio-pure samples. Therefore, it will give strong chiral signals and can be applied to the determinations of enantiomeric excess for chiral molecules whose enantio-pure samples are still challenging to achieve.

Based on cyclic three-level systems of chiral molecules, we propose two methods to realize highly efficient inner-state enantio-separations of a chiral mixture with the two enantiomers initially prepared in their ground states. Our methods work in the region where the evolutions of the two enantiomers can be described by their corresponding effective two-level models, simultaneously. The approximately 100%-efficiency inner-state enantio-separations can be realized when the probability occupying the ground state of one enantiomer becomes 0 by experiencing half-integer periods of its corresponding on-resonance Rabi oscillation and in the meanwhile the other one still stays approximately in the ground state, under the conditions that the two enantiomers are governed by the effective on-resonance and large-detuning two-level models, respectively. Alternatively, the exactly 100%-efficiency inner-state enantio-separation can be obtained when the probabilities occupying the ground states of the two enantiomers simultaneously experience half-integer and integer periods of their corresponding on-resonance and detuned (instead of largely-detuned) Rabi oscillations with final 0 and 1 probabilities occupying the ground state, respectively.

Based on the four-level double-model composed of two degenerated (left-and right-handed) chiral ground states and two achiral excited states, we propose a purely coherent-operation method for enantioconversion of chiral mixtures. By choosing appropriate parameters, the original four-level model will be simplified to two effective two-level subsystems with each of them involving one chiral ground state. Then, with the help of welldesigned coherent operations, the initial unwanted and wanted chiral ground states are converted, respectively, to the wanted chiral ground state and an auxiliary chiral excited state with the wanted chirality, i.e., achieving the enantioconversion of chiral mixtures. Comparing with the original works of enantioconversion based on the four-level double-model with the requirement of the time-consuming relaxation step and repeated operations, our method can be three orders of magnitude faster since we use only purely coherent operations. Thus our method offers a promising candidate for fast enantioconversion of chiral molecules with short enantiomeric lifetime or in the experimental conditions where the operation time is limited.

Optical methods of enantiomeric-specific state transfer had been proposed theoretically based on a cyclic three-level system of chiral molecules. According to these theoretical methods, recently the breakthrough progress has been reported in experiments (Eibenberger et al 2017 Phys. Rev. Lett. 118 123002; Pérez et al 2017 Angew. Chem. Int. Ed. 56 12512) for cold gaseous chiral molecules but with achieving low state-specific enantiomeric enrichment. One of the limiting factors is the influence of the thermal population in the selected cyclic three-level system based on purely rotational transitions in the experiments. Here, we theoretically explore the improvement of the enantiomeric-specific state transfer at finite temperature by introducing ro-vibrational transitions for the cyclic three-level system of chiral molecules. Then, at the typical experimental temperature, approximately only the lowest state in the desired cyclic three-level system is thermally occupied and the optical method of enantiomeric-specific state transfer works well. Comparing with the case of purely rotational transitions where all the three states are thermally occupied, this modification will remarkably increase the obtained state-specific enantiomeric enrichment with enantiomeric excess being approximately 100%.