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The Journal of Physical Chemistry Letters

Enantioselective Topological Frequency Conversion

Kai Schwennicke, Joel Y. Yuen-Zhou

Published Mar 8, 2022• 22 citations
Publisher

Abstract

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.

DOI
10.1021/acs.jpclett.1c04161

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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.
Enantiodetection is an important and challenging task across natural sciences. The cyclic three-level models of chiral molecules provided possibilities to obtain the ultimate limit of the enantioselectivities in purely electric dipole effects, yielding an emerging frontier in enantiodetection. However, the generated enantioselectivities were usually severely reduced in the strong decoherence region, failing most of the related chiroptical methods. Here, we propose enantioselective switches of molecular responses by well designing the electromagnetic fields based on the dissipative cyclic three-level model of chiral molecules and provide a chiroptical method of enantiodetection. In our switches, the steady-state responses are turned on for the selected enantiomer and simultaneously turned off for its mirror image, which corresponds to the ultimate limit of enantioselectivities. The switches can survive in the strong decoherence regions, and so does the suggested chiroptical method of enantiodetection. Our results give more insight into answering whether the enantioselective responses of light based on the cyclic three-level model can survive in the strong decoherence region and thus have a potential impact on further research.
Determination of enantiomeric excess is important and remains challenging. We propose theoretically a 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 ac Stark peaks chosen in the Fourier transform spectrum of the induced polarizations, which are (approximately) proportional to the number of molecules of the two enantiomers, respectively. In contrast to current spectroscopic methods based on the interference between the electric and (usually weak) magnetic dipole transition moments and/or with the need for enantiopure samples, our method involves only electric dipole transitions and does not require the enantiopure samples. Therefore, it will give strong chiral signals and can be applied to the determination of enantiomeric excess for chiral molecules whose enantiopure samples are still challenging to achieve.
Enantiomer-specific pumping of chiral molecules in high-JJJ rotational states
Enantiomer-specific state transfer (ESST) based on electric-dipole transitions has attracted considerable interest in the studies of manipulating molecules with electromagnetic fields. It also holds promise as a powerful tool for enantiomer detection and separation. To date, experimental demonstrations of ESST have focused mainly on molecules in the lowest rotational angular-momentum states, namely, J=0J=0J=0 and J=1J=1J=1. Realistic molecular samples, however, may contain appreciable populations in higher-JJJ rotational states, making it desirable to develop ESST schemes applicable to such states. Nevertheless, one cannot derive such schemes via a simple and straightforward extension of existing low-JJJ schemes, because higher-JJJ manifolds contain more magnetic sub-levels and involve more complicated networks of electric-dipole transitions. Here, we propose an ESST scheme for chiral molecules involving the J=1J=1J=1 and J=2J=2J=2 rotational states. Specifically, our scheme is based on enantiomer-specific pumping driven by three linearly polarized microwave fields and one laser beam. Under this scheme, one enantiomer is pumped into an enantiomer-specific dark state within a sub manifold with J=1,2J=1,2J=1,2, whereas the other enantiomer is dissipatively pumped out of this manifold. Our strategy can be extended to systems involving rotational states with even higher angular momenta.
Achiral molecules can be prepared in superposition states that are chiral. Here, we propose angular momentum orientation in the molecular frame to achieve the required symmetry breaking, exerting rotational control without the need for laboratory frame orientation. We derive the conditions for chiral rotational dynamics from the requirement to simultaneously break the continuous spatial rotational symmetry and the molecular point group symmetry. This can be achieved by three microwave pulses as well as two non-resonant optical pulses in combination with a THz pulse or three THz pulses, all with mutually orthogonal polarization directions, and the ensuing dynamics can be probed by photoelectron circular dichroism. Our results open the way for distinguishing structural from dynamical enantioselectivity and investigating time-odd chiroptical phenomena in randomly oriented molecules.
Molecular chirality plays a crucial role in physics, chemistry, life sciences and pharmacology. Nowadays, the chiral discrimination and control at the single-molecule level is urgently needed to reveal the origin of the chirality-relevant phenomena by recovering the information disturbed by the ensemble averaging. The method of magnetic resonance (MR), as one of powerful tools for structure analysis, is blind to the molecular chirality in the absence of a chiral reagent. Here we propose and experimentally demonstrate a direct MR-based method for determining the chirality at the single-molecule level through constructing the symmetry-breaking dynamics of nearby nuclear spins. In principle, the mirror asymmetry of two enantiomers in real space is manifested by breaking the joint symmetry of the mirror reflection and time reversal in spin space under spin dynamics. Experimentally, two enantiomers are indistinguishable from the dynamics of strongly-coupled but unpolarized nuclear spins, but diverge evidently in the dynamical results that break the field-inversion symmetry after spins are polarized. Our method and results will benefit the study of chirality-induced properties in the fields of chemistry and biology.
Enantiodetection is an important and challenging task across natural science. Nowadays, some chiroptical methods of enantiodetection based on decoherence-free cyclic three-level models of chiral molecules can reach the ultimate limit of the enantioselectivities in the molecular responses. They are thus more efficient than traditional chiroptical methods. However, decoherence is inevitable and can severely reduce enantioselectivities in these advanced chiroptical methods, so they only work well in the weak decoherence region. Here, we propose an enantioselective switch on the radiation of dissipative chiral molecules and develop a novel chiroptical method of enantiodetection working well in all decoherence regions. In our scheme, radiation is turned on for the selected enantiomer and simultaneously turned off for its mirror image by designing the electromagnetic fields well based on dissipative cyclic three-level models. The enantiomeric excess of a chiral mixture is determined by comparing its emissions in two cases, where the radiations of two enantiomers are turned off respectively. The corresponding enantioselectivities reach the ultimate limit in all decoherence regions, offering our scheme advantages over other chiroptical methods in enantiodetection. Our work potentially constitutes the starting point for developing more efficient chiroptical techniques for enantiodection in all decoherence regions.