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Optics Letters

Robust discriminator of chiral molecules via a topological invariant

Yi‐Hao Kang, Yu Wang, Qi-Ping Su, Guo-Qiang Zhang, Wei Feng, Chui‐Ping Yang

Published Jul 16, 2024• 2 citations
Publisher

Abstract

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.

DOI
10.1364/ol.532630

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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.
We propose a method to realize enantiodiscrimination of chiral molecules based on quantum correlation function in a driven cavity-molecule system, where the chiral molecule is coupled with a quantized cavity field and two classical light fields to form a cyclic three-level model. According to the inherent properties of electric-dipole transition moments of chiral molecules, there is a π-phase difference in the overall phase of the cyclic three-level model for the left- and right-handed chiral molecules. Thus, the correlation function depends on this overall phase and is chirality-dependent. The analytical and numerical results indicate that the left- and right-handed chiral molecules can be discriminated by detecting quantum correlation function. Our work opens up a promising route to discriminate molecular chirality, which is an extremely important task in pharmacology and biochemistry.
We propose a protocol to realize discrimination of chiral molecules based on steady states of a cavity mode. Using the closed-loop three-level structure of a molecule, an effective Hamiltonian of the molecule-cavity-coupled system is derived. The effective Hamiltonian is similar to a linear driving of the cavity mode, but the driving strength depends on the chirality of the molecule. In the presence of photon loss, the cavity behaves like a driven damped harmonic oscillator, and it will evolve to different steady coherence states according to the chirality of the molecule. By selecting proper parameters, it is possible to obtain steady coherence states with large-enough amplitudes that can be well determined by homodyne measurements on the cavity. Consequently, the chirality of the molecules can be discriminated near perfectly, according to the measurement result of the cavity. Numerical simulations show that the protocol is insensitive to the systematic errors of the control fields and the energy relaxation of the molecules. Therefore, the protocol may provide an effective approach to realize chirality discrimination with high accuracy.
Abstract For quantum systems with broken parities, a transition can appear for any two different states, and cyclic transition structures can be generated for the lowest three levels. Based on these loop transitions, we discuss how to achieve high-precision localization effects for physical objects with broken parities, i.e . chiral molecules and asymmetric quantum wells. In a Δ-type three-level system interacting simultaneously with three external fields, one of which is a standing-wave field, the absorption spectrum carries information about the position of the objects. Moreover, we can achieve 100% probability of finding the objects at certain positions by choosing appropriate parameters. In addition, we present two possible implementations of the suggested scheme in a system comprising a mixture of left- and right-handed chiral molecules and asymmetric quantum wells and show how the phase-sensitive localization effect can be used to discriminate between enantiomeric molecules.
We propose a scheme for realizing parity measurement of cat-state qubits based on a topological quantum phase transition. The cat-state qubits, formed by the bosonic modes in the Kerr-nonlinear resonators with two-photon squeezing drives, couple with a superconducting qubit in the center. We demonstrate that the resonator-qubit couplings with proper strengths can induce a topological quantum phase transition when the cat-state qubits are initial in the even-parity states. The topological quantum phase transition provides an approach to distinguish the even-parity states from the odd-parity states by measuring a topological invariant, namely the Chern number. Due to the robustness of the Chern number, the scheme shows great tolerance for multiple types of disturbing factors, including the systematic errors of the control fields and the coupling strengths, the inter-resonator crosstalk, and decoherence. Therefore, the scheme may be useful to construct an error-tolerant parity detector of cat-state qubits.
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.