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arXiv:1911.08804 · Physical Review A

Enantiomeric-excess determination based on nonreciprocal-transition-induced spectral-line elimination

Xun‐Wei Xu, Chong Ye, Yong Li, Aixi Chen

Published Sep 28, 2020• 16 citations
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Abstract

The spontaneous emission spectrum of a multilevel atom or molecule with nonreciprocal transition is investigated. It is shown that the nonreciprocal transition can lead to the elimination of a spectral line in the spontaneous emission spectrum. As an application, we show that nonreciprocal transition arises from the phase-related driving fields in chiral molecules with cyclic three-level transitions, and the elimination of a spectral line induced by nonreciprocal transition provides us a method to determine the enantiomeric excess for the chiral molecules without requiring the enantio-pure samples.

DOI
10.1103/physreva.102.033727

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The spontaneous emission spectrum of a multilevel atom or molecule with nonreciprocal transition is investigated. It is shown that the nonreciprocal transition can lead to the elimination of a spectral line in the spontaneous emission spectrum. As an application, we show that nonreciprocal transition arises from the phase-related driving fields in chiral molecules with cyclic three-level transitions, and the elimination of a spectral line induced by nonreciprocal transition provides us a method to determine the enantiomeric excess for the chiral molecules without requiring the enantio-pure samples.
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.
We propose a theoretical scheme to realize nonreciprocal transition in a multi-level atomic system with cyclic four-level transition. The effective transition between two indirectly coupled energy levels become nonreciprocal, when they are coupled to two auxiliary levels simultaneously, by four strong driving fields with the total phase serving as a synthetic magnetic flux and breaking the time reversal symmetry of the system. The nonreciprocal transition can lead to the elimination of a spectral line in the spontaneous emission spectrum, which provide us a simple approach to measure the phenomenon in steady state. This work provides a feasible approach to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms with parity symmetry.
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.
We propose a theoretical scheme to realize nonreciprocal transition between two energy levels that can not coupled directly. Suppose they are coupled indirectly by two auxiliary levels with a cyclic four-level configuration, and the four transitions in the cyclic configuration are controlled by external fields. The indirectly transition become nonreciprocal when the time reversal symmetry of the system is broken by the synthetic magnetic flux, i.e., the total phase of the external driving fields through the cyclic four-level configuration. The nonreciprocal transition can be identified by the elimination of a spectral line in the spontaneous emission spectrum. Our work introduces a feasible way to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms or ions with parity symmetry.
Developing effective methods to measure the enantiomeric excess of the chiral mixture is one of the major topics in chiral molecular researches, yet remains challenging. Enantiodetection method via two-dimensional (2D) spectroscopy based on a four level model, containing a cyclic three-level system (CTLS), of chiral molecules was recently proposed and demonstrated, yet with a strict condition of the one-photon resonance (where three driving fields are exactly resonantly coupled to the three electric-dipole transitions, respectively) in the CTLS and narrowband probe pulse assumption. Here, we extend the 2D spectroscopy method to more general experimental conditions, with three-photon resonance (where the sum of the two smaller frequencies among the three driving fields equals to the third one) and broadband probe pulse. Our method remains effective on enantiodetection with the help of experimental techniques, such as the chop detection method, which is used to eliminate the influence of the other redundant levels existing in the real system of chiral molecules. Under these more general conditions, the enantiomeric excess of the chiral mixture is estimated by taking an easily available standard sample (usually the racemic mixture) as the reference.
Developing effective methods to measure the enantiomeric excess of chiral mixtures is one of the major topics in chiral molecular research but remains challenging. An enantiodetection method via two-dimensional (2D) spectroscopy based on a four-level model containing a cyclic three-level system (CTLS) of chiral molecules was recently proposed and demonstrated, but with a strict condition of one-photon resonance (where three driving fields are exactly resonantly coupled to the three electric dipole transitions) in the CTLS and narrow-band probe-pulse assumption. Here, we extend the 2D spectroscopy method to more general experimental conditions, with three-photon resonance (where the sum of the two smaller frequencies among the three driving fields equals the third one) and a broadband probe pulse. Our method remains effective on enantiodetection with the help of experimental techniques such as the chop-detection method, which is used to eliminate the influence of the other redundant levels that exist in the real system of chiral molecules. Under these more general conditions, the enantiomeric excess of the chiral mixture is estimated by taking an easily available standard sample (usually the racemic mixture) as the reference.