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arXiv:2001.10871 · Physical Review A

Efficient and robust chiral resolution by composite pulses

Boyan T. Torosov, Michael Drewsen, Nikolay V. Vitanov

Published Jun 1, 2020• 33 citations
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Abstract

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.

DOI
10.1103/physreva.101.063401

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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 \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 pulses and the middle pulse is a \ensuremathπ\ensuremath{\pi}\ensuremathπ pulse. In addition, one of the three pulses must have a phase shift of \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/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 \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2 and \ensuremathπ\ensuremath{\pi}\ensuremathπ 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.
A highly efficient method for optical or microwave detection and separation of left- and right-handed chiral molecules is proposed. The method utilizes a closed-loop three-state system in which the population dynamics depends on the phases of the three couplings. Because of the different signs of the coupling between two of the states for the opposite chiralities the population dynamics is chirality dependent. By using the "shortcuts to adiabaticity" concept applied to the stimulated Raman adiabatic passage technique, one can achieve 100% contrast between the two enantiomers in the population of a particular state. It can be probed by light-induced fluorescence for large ensembles or through resonantly enhanced multiphoton ionization for single molecules.
We propose a method for enantio-detection of chiral molecules based on a cavity-molecule system, where the left- and right-handed molecules are coupled with a cavity and two classical light fields to form cyclic three-level models. Via the cavity-assisted three-photon processes based on the cyclic three-level model, photons are generated continuously in the cavity even in the absence of external driving to the cavity. However, the photonic fields generated from the three-photon processes of left- and right-handed molecules differ with the phase difference π according to the inherent properties of electric-dipole transition moments of enantiomers. This provides a potential way to detect the enantiomeric excess of chiral mixture by monitoring the output field of the cavity.
Composite pulses---sequences of pulses with well-defined relative phases---are an efficient, robust, and flexible technique for coherent control of quantum systems. Composite sequences can compensate for a variety of experimental errors in the driving field (e.g., in the pulse amplitude, duration, detuning, chirp, etc.) or in the quantum system and its environment (e.g., inhomogeneous broadening, stray electric or magnetic fields, unwanted couplings, etc.). The control parameters are the relative phases between the constituent pulses in the composite sequence, an accurate control over which is required in all composite sequences reported hitherto. In this paper, we introduce two types of composite pulse sequences which, in addition to error compensation in the basic experimental parameters, compensate for systematic errors in the composite phases. In the first type of such composite sequences, which compensate for pulse area errors, relative phase errors of over 10% can be tolerated with reasonably short sequences while maintaining the fidelity above the 99.99% quantum computing benchmark. In the second type of composite sequences, which compensate for simultaneous pulse area and detuning errors, relative phase errors of over 5% can be compensated.
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.
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.