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arXiv:2301.03778 · Optics Letters

Efficient and robust chiral discrimination by invariant-based inverse engineering

Hang Xu, Xue‐Ke Song, Ye Liu, Dong Wang

Published Apr 14, 2023• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/ol.484455

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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.
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 a scheme for chirality discrimination via a topological invariant. The physical model is based on a three-level subspace of a molecule. By modulating the components of the control field with proper frequencies, two different two-level effective Hamiltonians are derived for the left-handed and the right-handed molecules. We parameterize the effective Hamiltonians with two angles and demonstrate that a topological quantum phase transition can be induced by tuning the effective Rabi frequency if the molecule is right-handed. This phenomenon provides a method to discriminate the chirality of the molecule by measuring a topological invariant, i.e., the Chern number, of the parametric manifold. Since the Chern number is robust against perturbations to the system, the scheme is insensitive to the systematic errors of the control fields, the deviations of the modulation frequencies, and decoherence of the molecule. Therefore, the scheme may provide useful perspectives to construct a robust discriminator of chiral molecules.
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.
We introduce a method for the detection of chiral molecules using sequences of three pulses driving a closed-loop three-state quantum system. The left- and right-handed enantiomers have identical optical properties (transition frequencies and transition dipole moments) with the only difference being the sign of one of the couplings. We identify 12 different sequences of resonant pulses for which chiral resolution with perfect contrast occurs. In all of them, the first and third pulses are $\ensuremath{\pi}/2$ pulses and the middle pulse is a $\ensuremath{\pi}$ pulse. In addition, one of the three pulses must have a phase shift of $\ensuremath{\pi}/2$ with respect to the other two. The simplicity of the proposed chiral resolution technique allows for straightforward extensions to more efficient and more robust implementations by replacing the single $\ensuremath{\pi}/2$ and $\ensuremath{\pi}$ pulses by composite pulses. We present specific examples of chiral resolution by composite pulses which compensate errors in the pulse areas and the detuning of the driving fields.
We propose to discriminate chiral molecules by combining one- and two-photon processes in a closed-loop configuration. The one-photon-coupling intrinsic $\ensuremath{\pi}$-phase difference between two enantiomers leads to their different superposition states, which is then followed by a two-photon process through three-mode parallel paths (3MPPs), enabling the discrimination of enantiomers by inducing their entirely different population distributions. The 3MPPs are constructed by ``chosen paths,'' a method of shortcuts to adiabaticity, exhibiting a fast two-photon process. As an example, we propose to perform the scheme in 1,2-propanediol molecules, which show relatively robust and highly efficient results under considering the experimental issues concerning unwanted transitions, imperfect initial state, pulse shaping, control errors, and the effect of energy relaxations. The present work may provide help for laboratory researchers in a robust separation of chiral molecules.