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arXiv:1906.12009 · Physical Review A

Effective two-level models for highly efficient inner-state enantioseparation based on cyclic three-level systems of chiral molecules

Chong Ye, Quansheng Zhang, Yu-Yuan Chen, Yong Li

Published Oct 10, 2019• 38 citations
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Abstract

Based on cyclic three-level systems of chiral molecules, we propose two methods to realize highly efficient inner-state enantioseparations 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 enantioseparations can be realized when the probability occupying the ground state of one enantiomer becomes zero by experiencing half-integer periods of its corresponding on-resonance Rabi oscillation and the other one stays always in the ground state approximately, 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 enantioseparation can be obtained when the probability occupying the ground state of one enantiomer becomes zero by experiencing half-integer periods of its corresponding on-resonance Rabi oscillation and in the meanwhile that of the other one becomes 1 by experiencing integer periods of its corresponding detuned Rabi oscillation, respectively.

DOI
10.1103/physreva.100.043403

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Based on cyclic three-level systems of chiral molecules, we propose two methods to realize highly efficient inner-state enantioseparations 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 100100%100-efficiency inner-state enantioseparations can be realized when the probability occupying the ground state of one enantiomer becomes zero by experiencing half-integer periods of its corresponding on-resonance Rabi oscillation and the other one stays always in the ground state approximately, under the conditions that the two enantiomers are governed by the effective on-resonance and large-detuning two-level models, respectively. Alternatively, the exactly 100100%100-efficiency inner-state enantioseparation can be obtained when the probability occupying the ground state of one enantiomer becomes zero by experiencing half-integer periods of its corresponding on-resonance Rabi oscillation and in the meanwhile that of the other one becomes 1 by experiencing integer periods of its corresponding detuned Rabi oscillation, respectively.
We propose a streamlined method of fast enantiomer-specific state transfer (ESST) of chiral molecules in cyclic three-level systems. Such three-level enantiomers are chirality-dependent systems driven by one of the three Rabi frequencies differing with a sign for the left- and right-handed chiral molecules. When the Hamiltonian of the three-level chiral molecules possesses the specific SU(2) algebraic structure, the populations transferred to the two excited states are shown to be exchanged between the left- and right-handed chiral molecules if they are initially prepared in their ground states. By employing unitary SU(2) transformation and inversely engineering time-dependent Hamiltonians with designed Rabi frequencies, we can make the left- and right-handed chiral molecules evolve respectively to different excited states from their initial ground states simultaneously. Thus a fast ESST is achieved.
Enantiospecific state transfer of chiral molecules is extremely important because enantiomers coexist in many biologically active compounds and play significantly different physiological, pharmacological, and biological roles. The inherently strong electric-dipole optical approaches based on the cyclic three-level model of chiral molecules have been extensively discussed. But, for the cases of large chiral molecules and/or chiral molecules of low asymmetry, the four-level model with two sub-loops is more realistic to describe the molecules. Based on the four-level model, we propose a pump-control approach to realize the highly efficient enantiospecific state transfer. In our approach, two pump pulses are applied to generate molecular coherence between the ground state and the first excited state of our working model. According to the coherence of the molecules, we adjust the phase and pulse area of the control pulse, then we obtain the highly efficient enantiospecific state transfer in the first excited working state. In addition, we further optimize the fraction of enantiopure samples by adjusting the area of the two pump pulses.
Using a microwave-regime cyclic three-state configuration, enantiomer-selective state transfer (ESST) is carried out through two-path interference between a direct one-photon coupling and an effective two-photon coupling. A phase difference of $\ensuremath{\pi}$ in the one-photon process between the two enantiomers makes the interference constructive for one enantiomer but destructive for the other. Therefore only one enantiomer is excited into a higher rotational state, while the other remains in the ground state. The scheme allows flexibility in the pulse waveforms and the time order of the two paths. We simulate the scheme for a sample of cyclohexylmethanol (C7H14O{\mathrm{C}}_{7}{\mathrm{H}}_{14}\mathrm{O}C7​H14​O) molecules. The simulation results show that robust high-fidelity ESST can be obtained when experimental concerns are considered. Finally, we propose to employ the ESST scheme to implement enantioseparation and determine enantiomeric excesses.
We study the enantiospecific state transfer for gaseous symmetric-top chiral molecules by constructing a four-level model. This model is formed by coupling the electric dipole transitions among four appropriate rovibrational states with three electromagnetic fields. It includes two cyclic three-level substructures, where the overall phases of the coupling strengths differ by $\ensuremath{\pi}$ with enantiomers and reflect the chirality dependence of the molecules. Based on this four-level model, two dynamic ways are proposed to achieve the approximately perfect enantiospecific state transfer for gaseous symmetric-top chiral molecules when all the molecules are initially in the ground state of the system.
We explore the spatial enantioseparation of gaseous chiral molecules for the cyclic three-level systems coupled with three electromagnetic fields. Due to molecular rotations, the specific requirements of the polarization directions of the three electromagnetic fields lead to the space-dependent part of the overall phase of the coupling strengths. Thus, the overall phase of the coupling strengths, which differs with $\ensuremath{\pi}$ for the enantiomers in the cyclic three-level model of chiral molecules, varies intensely in the length scale of the typical wavelength of the applied electromagnetic fields. Under the induced gauge potentials resulting from the space-dependent part of the overall phase and the space-dependent intensities of coupling strengths, we further show spatial enantioseparation for typical parameters of gaseous chiral molecules.
An interesting method of fast enantio-specific state transfer (ESST) is proposed for cyclic three-level systems of chiral molecules. We show that the fast population transfer via shortcut to adiabaticity can be accomplished for the cyclic three-level system of a general (chiral) molecule with invariant-based inverse engineering of the coupling strengths. By choosing appropriate parameters, the two enantiomers, which are initially prepared in their ground states in the three-level systems, will evolve respectively along their enantio-selective shortcut-to-adiabaticity paths to different-energy final states simultaneously, thereby achieving the fast ESST.