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.
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.
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.
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.
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.