We derive a pulse-area theorem for a single-loop cyclic three-level system without applying the rotating-wave approximation while explicitly taking into account the time delays of control fields. This corresponds to an archetypal model for exploring enantioselective state transfer (ESST) in chiral molecules driven by three linearly polarized microwave pulses. By dividing the closed-loop excitation into two separate stages, we obtain both amplitude and phase conditions of three control fields to generate high fidelity of ESST. As a proof of principle, we apply this pulse-area theorem to cyclohexylmethanol molecules, for which three rotational states are connected by
a-type,
b-type, and
c-type components of the transition dipole moments in both center-frequency-resonant and -detuned conditions. Our results show that two enantiomers with opposite handedness can be transferred to different target states by designing three microwave pulses that satisfy the amplitude and phase conditions at the transition frequencies. The corresponding control schemes are robust against the time delays between the two stages. We suggest that the two control fields used in the second stage should be applied simultaneously for practical applications. This work contributes an alternative pulse-area theorem to the field of quantum control, which has the potential to determine the chirality of enantiomers in a mixture.
Abstract We theoretically study enantioselective state transfer (ESST) in a reduced four-level rotational model of a chiral molecule. The cyclic three-level description is reliable only when the microwave bandwidth remains well below the detunings to nearby dipole-allowed rotational transitions. When the bandwidth becomes comparable to the detuning of the nearest relevant additional state, this state can participate in the dynamics, requiring a four-level description. Using a constrained multiobjective quantum optimal-control method, we design microwave control fields in the narrow-band three-level and broadband four-level regimes. The resulting optimized fields achieve final discrimination degrees above 0.999 under four-level propagation in both regimes, while direct four-level optimization permits shorter-duration control by explicitly accounting for transient fourth-state participation. To reveal the underlying coherent mechanism, the transition amplitudes are decomposed into even- and odd- a pathway groups. The even- a contribution is common to the two enantiomers, whereas the odd- a contribution changes sign, resulting in constructive interference for one enantiomer and destructive interference for the other. Lindblad simulations further show that the four-level optimized control fields exhibit enhanced robustness against rotational relaxation owing to their shorter control durations. These results show that broadband four-level optimization can enable faster ESST with improved robustness against dissipative relaxation while preserving the even/odd- a pathway-interference mechanism.
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) 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 propose a simple dynamical method to realize fast enantio-specific state transfer (ESST) of chiral molecules. Driven by three external electromagenetic fields, the chiral molecules are modeled as cyclic three-level systems, where the overall phase differs by π for the left- and right-handed chiral molecules. We unveil that the ESST is allowed when the amplitudes of three Rabi frequencies in the cyclic three-level systems are equal. Our method is robust and highly efficient in the sense that the external fields can have arbitrary waveforms. This thus provides the opportunity of simplifying the experimental implementations of ESST through pulse design.
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=0 and
J=1. Realistic molecular samples, however, may contain appreciable populations in higher-
J 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-
J schemes, because higher-
J 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=1 and
J=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=1,2, 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.
Enantiomer-specific state transfer (ESST), which involves transferring enantiomers with different handedness of a chiral molecule into different-energy internal states, is a challenging yet significant task. Previous ESST methods are based on dynamic processes and thus require the preparation of initial states and precise control of microwave operation times. We propose a novel ESST approach, called enantiomer-specific pumping (ESP), which is based on a dissipative process and thereby eliminates the need for these two technical requirements. This approach utilizes a special microwave-induced dark state that appears exclusively for the enantiomer with a specific handedness. Specifically, in ESP, the enantiomer lacking the dark state can be pumped out of the subspace of relevant internal states, while the enantiomer with the dark state maintains a finite probability within this subspace, offering high efficiency in ESST. Notably, ESP facilitates enantiodetection without the need for enantiopure samples as reference.