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Advanced Quantum Technologies

Hamiltonian Inverse Engineering for Chiral Resolution in Four‐Level Systems

Guang-Hui Zhang, Xue‐Ke Song, Liu Ye, Dong Wang

Published May 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We propose a universal scheme applicable to various multistate chiral molecular configurations, achieving 100 chiral resolution with the advantages of simple procedures and high precision. By reversely designing Hamiltonians with 4D rotation, we can determine the parameters of the different four‐level Hamiltonians to realize the desired quantum state control. For the four‐level quantum systems with anti‐Y configuration and double‐ configuration, we can transfer the population of the bi‐chiral system completely from the different initial state to the target state for the left‐handed molecules and to the target state for right‐handed molecules. More importantly, we can accurately change the chirality of the N‐type four‐level quantum system by transferring the populations between states and . Furthermore, the inverse engineering method demonstrates that the fidelity of the final state remains above 95 over a wide range of parameters in the presence of Rabi and detuning errors, and energy relaxation. The result offers an effective, precise, and reliable method for rapid enantiomer conversion in different four‐level chiral systems, which may shed light on the further application of exploring quantum information techniques to achieve the effective enantioselective control of short‐lived enantiomers.

DOI
10.1002/qute.70308

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ABSTRACT We propose a universal scheme applicable to various multistate chiral molecular configurations, achieving 100 chiral resolution with the advantages of simple procedures and high precision. By reversely designing Hamiltonians with 4D rotation, we can determine the parameters of the different four‐level Hamiltonians to realize the desired quantum state control. For the four‐level quantum systems with anti‐Y configuration and double‐ configuration, we can transfer the population of the bi‐chiral system completely from the different initial state to the target state for the left‐handed molecules and to the target state for right‐handed molecules. More importantly, we can accurately change the chirality of the N‐type four‐level quantum system by transferring the populations between states and . Furthermore, the inverse engineering method demonstrates that the fidelity of the final state remains above 95 over a wide range of parameters in the presence of Rabi and detuning errors, and energy relaxation. The result offers an effective, precise, and reliable method for rapid enantiomer conversion in different four‐level chiral systems, which may shed light on the further application of exploring quantum information techniques to achieve the effective enantioselective control of short‐lived enantiomers.
We propose an accurate and convenient method to achieve 100% discrimination of chiral molecules with Lewis-Riesenfeld invariance. By reversely designing the pulse scheme of handed resolution, we obtain the parameters of the three-level Hamiltonians to achieve this goal. For the same initial state, we can completely transfer its population to one energy level for left-handed molecules, while transferring it to another energy level for right-handed molecules. Moreover, this method can be further optimized when errors exist, and it shows that the optimal method is more robust against these errors than the counterdiabatic and original invariant-based shortcut schemes. This provides an effective, accurate, and robust method to distinguish the handedness of molecules.
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.
Controlling the internal quantum states of chiral molecules for a selected enantiomer has a wide range of fundamental applications. Using tailored microwave fields, a chosen rotational state can be enriched for a selected enantiomer, even starting from a racemic mixture. This enables rapid switching between samples of different enantiomers in a given state, holding great promise, for instance, for measuring parity violation in chiral molecules. Achieving full enantiomer-specific state transfer is a key requirement for this and many other applications. Although theoretically feasible, achieving the required experimental conditions seemed unrealistic. Here, we realize near-ideal conditions, overcoming both the limitations of thermal population and spatial degeneracy in rotational states. Our results show that 96% state-specific enantiomeric purity can be obtained from a racemic mixture, in an approach that is universally applicable to all chiral molecules of C1 symmetry.
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.
Abstract A protocol to distinguish chiral molecules with the help of a cyclic three‐level structure is proposed. Non‐resonant microwave pules are applied to drive the transition of chiral molecules from their ground states to dressed‐states with different eigenenergies, which induce a large energy split in the levels of left‐handed molecules. This dynamics helps to realize a chirality‐selective transition, where only the right‐handed molecules can be excited to the higher levels. By utilizing the SU(2)‐transformation‐based shortcuts to adiabaticity method and the systematic‐error‐sensitivity nullified optimal control method, systematic‐error‐resistant control pulses to realize maximal population difference between molecules with different chirality are designed. Numerical simulations show that the protocol is also insensitive to random noise and energy relaxation. Therefore, the protocol may provide a promising approach for rapid and robust chiral discrimination.
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.