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arXiv:2103.01758 · Physical Review A

Spatial enantioseparation of gaseous chiral molecules

Бо Лю, Chong Ye, C. P. Sun, Yong Li

Published Jul 21, 2021• 22 citations
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Abstract

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.

DOI
10.1103/physreva.104.013113

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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 \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
We investigate an efficient spatial enantioseparation method of chiral molecules in cyclic three-level systems coupled with three optical fields using optically induced forces. When the overall phase differs by π between two enantiomers, significant variations in the magnitude and direction of the optically induced forces are observed. The manipulation of the center of mass of chiral molecules in optical fields can be achieved through the induced gauge force, primarily generated from the variations in the chirality-dependent scalar potentials created by the three inhomogeneous laser fields. By appropriately configuring the system, we can completely separate the slow spatial and fast inner dynamics, making instantaneous eigenstates of the inner Hamiltonian independent of the transverse profiles of the laser beams. Compared to previous methods, which required adiabatic conditions to be satisfied, the proposed method overcomes the limitations of the adiabatic approximation by utilizing a specific system configuration. This allows for increased flexibility in the transverse profiles of the laser beams and relaxes the constraints on the velocity of chiral molecules, leading to significantly greater spatial separations achievable across a broader range of parameters.
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.
Abstract In this paper, we show the possibility of spatially separating two opposite enantiomers of chiral molecules, using an optical dipole potential. Because of the broken mirror symmetry of effective potential, chiral molecules have a cyclic three-level Δ-configuration structure. Irradiation of these molecules with three femtosecond laser pulses gives rise to an enantiomer-dependent optical force. Interestingly, considerable differences in the direction of the force felt by the enantiomers have been shown to cause the chirality-dependent optical dipole potential which stably captures only one enantiomeric form. Moreover, the proposed scheme provides a complete control over what kind of molecules, the left- or right-handed ones, can be selectively trapped. Note that we have analyzed the optical force, and specifically the trapping effect, by considering the full interaction Hamiltonian, including both rotating and counter-rotating terms.
We propose a theoretical method for enantio-discrimination based on the light deflection effect in four-level models of chiral molecules. This four-level model consists of a cyclic three-level subsystem coupled by three strong driving fields and an auxiliary level connected to the cyclic three-level subsystem by a weak probe field. It is shown that the induced refractive index for the weak probe field is chirality-dependent. Thus, it will lead to chirality-dependent light deflection when the intensities of two of the three strong driving fields are spatially inhomogeneous. As a result, the deflection angle of the weak probe light can be utilized to detect the chirality of pure enantiomers and enantiomeric excess of the chiral mixture. Therefore, our method may act as a tool for enantio-discrimination.
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.
Recently, several laser schemes have been proposed to separate racemic mixtures of enantiomers by splitting a molecular beam into subbeams consisting of molecules of definite chirality [Y. Li, C. Bruder, and C. P. Sun, Phys. Rev. Lett. 99, 130403 (2007); X. Li and M. Shapiro, J. Chem. Phys. 132, 194315 (2010)]. These ideas rely on laser-induced effective gauge potentials in an adiabatic basis which lead to a chirality dependent force on the center-of-mass. However, the effect of molecular rotation has been neglected in these studies. Accounting for the full molecular quantum state we find that the potentials from the adiabatic dressed state approach cannot be recovered once the molecular orientation dynamics is included, even in the rotational ground state. This affects substantially the ability to perform enantioseparation in the above mentioned setups.