Detecting Chirality in Molecules by Linearly Polarized Laser Fields

Machine-Learning Enhanced Enantioselective Single-Shot-Single-Molecule ac Stark Spectroscopy

Enantiodiscrimination with single-molecule and single-shot resolution is fundamental for the understanding of the fate and behavior of two enantiomers in chemical reactions, biological activity, and the function of drugs. However, molecular decoherence gives rise to spectral broadening and random errors, offering major problems for most chiroptical methods in arriving at single-shot-single-molecule resolution. Here, we introduce a machine-learning strategy to solve these problems. Specifically, we focus on the task of single-shot measurement of single-molecule chirality based on enantioselective ac Stark spectroscopy. We find that, in the large-decoherence region, where the ac Stark spectroscopy without machine learning fails to distinguish molecular chirality, in contrast, the machine-learning-assisted strategy still holds a high correct rate of up to about 90%. Beyond this overwhelming superiority, the machine-learning strategy also has considerable robustness against variation of the decoherence rates between the training and testing sets.

Improved Chiral Photoelectron Spectroscopy via Selection of Chirality-Selective Molecular Axis Orientations: A Theoretical Analysis of Non-Negative Smooth Functions

Photoelectron spectroscopy for chiral discrimination is routinely performed for low photoelectron kinetic energies (PKEs), whereas it is considered impossible for high PKEs. We demonstrate theoretically that chiral photoelectron spectroscopy for high PKEs is possible using chirality-selective molecular orientation. The photoelectron angular distribution associated with one-photon ionization by unpolarized light can be characterized by a single parameter, β. We show that most other anisotropy parameters are zero when β is 2, as is often the case in the high PKEs. Exceptionally, odd-order anisotropy parameters are increased by a factor of 20 by orientation, even for high PKEs.

Ultrafast chirality: the road to efficient chiral measurements

Today we are witnessing the electric-dipole revolution in chiral measurements. Here we reflect on its lessons and outcomes, such as the perspective on chiral measurements using the complementary principles of "chiral reagent" and "chiral observer", the hierarchy of scalar, vectorial and tensorial enantio-sensitive observables, the new properties of the chiro-optical response in the ultrafast and non-linear domains, and the geometrical magnetism associated with the chiral response in photoionization. The electric-dipole revolution is a landmark event. It has opened routes to extremely efficient enantio-discrimination with a family of new methods. These methods are governed by the same principles but work in vastly different regimes - from microwaves to optical light; they address all molecular degrees of freedom - electronic, vibrational and rotational, and use flexible detection schemes, i.e. detecting photons or electrons, making them applicable to different chiral phases, from gases to liquids to amorphous solids. The electric-dipole revolution has also enabled enantio-sensitive manipulation of chiral molecules with light. This manipulation includes exciting and controlling ultrafast helical currents in vibronic states of chiral molecules, enantio-sensitive control of populations in electronic, vibronic and rotational molecular states, and opens the way to efficient enantio-separation and enantio-sensitive trapping of chiral molecules. The word "perspective" has two meanings: an "outlook" and a "point of view". In this perspective article, we have tried to cover both meanings.

Enantiodiscrimination of chiral molecules via quantum correlation function

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.

Optimization of the double-laser-pulse scheme for enantioselective orientation of chiral molecules

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses' parameters, a significant (~ 10%) degree of enantioselective orientation can be achieved at zero and at five kelvin rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers.

Enantio-sensitive unidirectional light bending

Structured light, which exhibits nontrivial intensity, phase, and polarization patterns in space, has key applications ranging from imaging and 3D micromanipulation to classical and quantum communication. However, to date, its application to molecular chirality has been limited by the weakness of magnetic interactions. Here we structure light's local handedness in space to introduce and realize an enantio-sensitive interferometer for efficient chiral recognition without magnetic interactions, which can be seen as an enantio-sensitive version of Young's double slit experiment. Upon interaction with isotropic chiral media, such chirality-structured light effectively creates chiral emitters of opposite handedness, located at different positions in space. We show that if the distribution of light's handedness breaks left-right symmetry, the interference of these chiral emitters leads to unidirectional bending of the emitted light, in opposite directions in media of opposite handedness, even if the number of the left-handed and right-handed emitters excited in the medium is exactly the same. Our work introduces the concepts of polarization of chirality and chirality-polarized light, exposes the immense potential of sculpting light's local chirality, and offers novel opportunities for efficient chiral discrimination, enantio-sensitive optical molecular fingerprinting and imaging on ultrafast time scales.

Detecting handedness of spatially oriented molecules by Coulomb explosion imaging

We present a new technique for detecting chirality in the gas phase: Chiral molecules are spatially aligned in three dimensions by a moderately strong elliptically polarized laser field. The momentum distributions of the charged fragments, produced by laser-induced Coulomb explosion, show distinct three-dimensional orientation of the enantiomers when the laser polarization ellipse is rotated by a non-right angle with respect to the norm vector of the detector plane. The resulting velocity-map-image asymmetry is directly connected to the enantiomeric excess and to the absolute handedness of molecules. We demonstrated our scheme computationally for camphor (C₁₀H₁₆O), with its methyl groups as marker fragments, using quantum-mechanical simulations geared toward experimentally feasible conditions. Computed sensitivity to enantiomeric excess is comparable to other modern chiroptical approaches. The present method can be readily optimized for any chiral molecule with an anisotropic polarizability tensor by adjusting the polarization state and intensity profile of the laser field.

Field-Induced Diastereomers for Chiral Separation

A novel approach for the state-specific enantiomeric enrichment and the spatial separation of enantiomers is presented. Our scheme utilizes techniques from strong-field laser physics-specifically an optical centrifuge in conjunction with a static electric field-to create a chiral field with defined handedness. Molecular enantiomers experience unique rotational excitation dynamics, and this can be exploited to spatially separate the enantiomers using electrostatic deflection. Notably, the rotational-state-specific enantiomeric enhancement and its handedness are fully controllable. To explain these effects, the conceptual framework of field-induced diastereomers of a chiral molecule is introduced and computationally demonstrated through robust quantum-mechanical simulations on the prototypical chiral molecule propylene oxide (C_{3}H_{6}O), for which ensembles with an enantiomeric excess of up to 30% were obtained.

Controlled Enantioselective Orientation of Chiral Molecules with an Optical Centrifuge

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation, and purification of chiral mixtures.

All-optical field-free three-dimensional orientation of asymmetric-top molecules

Orientation and alignment of molecules by ultrashort laser pulses is crucial for a variety of applications and has long been of interest in physics and chemistry, with the special emphasis on stereodynamics in chemical reactions and molecular orbitals imaging. As compared to the laser-induced molecular alignment, which has been extensively studied and demonstrated, achieving molecular orientation is a much more challenging task, especially in the case of asymmetric-top molecules. Here, we report the experimental demonstration of all-optical field-free three-dimensional orientation of asymmetric-top molecules by means of phase-locked cross-polarized two-color laser pulse. This approach is based on nonlinear optical mixing process caused by the off-diagonal elements of the molecular hyperpolarizability tensor. It is demonstrated on SO2 molecules and is applicable to a variety of complex nonlinear molecules.

Climbing the Rotational Ladder to Chirality

Molecular chirality is conventionally understood as space-inversion-symmetry breaking in the equilibrium structure of molecules. Less well known is that achiral molecules can be made chiral through extreme rotational excitation. Here, we theoretically demonstrate a clear strategy for generating rotationally induced chirality: An optical centrifuge rotationally excites the phosphine molecule (PH_{3}) into chiral cluster states that correspond to clockwise (R enantiomer) or anticlockwise (L enantiomer) rotation about axes almost coinciding with single P─H bonds. The application of a strong dc electric field during the centrifuge pulse favors the production of one rotating enantiomeric form over the other, creating dynamically chiral molecules with permanently oriented rotational angular momentum. This essential step toward characterizing rotationally induced chirality promises a fresh perspective on chirality as a fundamental aspect of nature.

Optically reconfigurable polarized emission in Germanium

Light polarization can conveniently encode information. Yet, the ability to tailor polarized optical fields is notably demanding but crucial to develop practical methods for data encryption and to gather fundamental insights into light-matter interactions. Here we demonstrate the dynamic manipulation of the chirality of light at telecom wavelengths. This unique possibility is enrooted in the multivalley nature of the conduction band of a conventional semiconductor, namely Ge. In particular, we demonstrate that optical pumping suffices to govern the kinetics of spin-polarized carriers and eventually the chirality of the radiative recombination. We found that the polarized component of the emission can be remarkably swept through orthogonal eigenstates without magnetic field control or phase shifter coupling. Our results provide insights into spin-dependent phenomena and offer guiding information for the future selection and design of spin-enhanced photonic functionalities of group IV semiconductors.

Selective Orientation of Chiral Molecules by Laser Fields with Twisted Polarization

We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH₃CHCH₂O), and ethyl oxirane (CH₃CH₂CHCH₂O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

Chirality in molecular collision dynamics

Chirality is a phenomenon that permeates the natural world, with implications for atomic and molecular physics, for fundamental forces and for the mechanisms at the origin of the early evolution of life and biomolecular homochirality. The manifestations of chirality in chemistry and biochemistry are numerous, the striking ones being chiral recognition and asymmetric synthesis with important applications in molecular sciences and in industrial and pharmaceutical chemistry. Chiral discrimination phenomena, due to the existence of two enantiomeric forms, very well known in the case of interaction with light, but still nearly disregarded in molecular collision studies. Here we review some ideas and recent advances about the role of chirality in molecular collisions, designing and illustrating molecular beam experiments for the demonstration of chiral effects and suggesting a scenario for a stereo-directional origin of chiral selection.

Chiral discrimination in nuclear magnetic resonance spectroscopy

Chirality is a fundamental property of molecules whose spatial symmetry is characterized by the absence of improper rotations, making them not superimposable to their mirror image. Chiral molecules constitute the elementary building blocks of living species and one enantiomer is favoured in general (e.g. L-aminoacids and D-sugars pervade terrestrial homochiral biochemistry) because most chemical reactions producing natural substances are enantioselective. Since the effect of chiral chemicals and drugs on living beings can be markedly different between enantiomers, the quest for practical spectroscopical methods to scrutinize chirality is an issue of great importance and interest. Nuclear magnetic resonance (NMR) is a topmost analytical technique, but spectrometers currently used are 'blind' to chirality, i.e. unable to discriminate the two mirror-image forms of a chiral molecule, because, in the absence of a chiral solvent, the spectral parameters, chemical shifts and spin-spin coupling constants are identical for enantiomers. Therefore, the development of new procedures for routine chiral recognition would offer basic support to scientists. However, in the presence of magnetic fields, a distinction between true and false chirality is mandatory. The former epitomizes natural optical activity, which is rationalized by a time-even pseudoscalar, i.e. the trace of a second-rank tensor, the mixed electric dipole/magnetic dipole polarizability. The Faraday effect, magnetic circular dichroism and magnetic optical activity are instead related to a time-odd axial vector. The present review summarizes recent theoretical and experimental efforts to discriminate enantiomers via NMR spectroscopy, with the focus on the deep connection between chirality and symmetry properties under the combined set of fundamental discrete operations, namely charge conjugation, parity (space inversion) and time (motion) reversal.

Simulating electric field interactions with polar molecules using spectroscopic databases

Ro-vibrational Stark-associated phenomena of small polyatomic molecules are modelled using extensive spectroscopic data generated as part of the ExoMol project. The external field Hamiltonian is built from the computed ro-vibrational line list of the molecule in question. The Hamiltonian we propose is general and suitable for any polar molecule in the presence of an electric field. By exploiting precomputed data, the often prohibitively expensive computations associated with high accuracy simulations of molecule-field interactions are avoided. Applications to strong terahertz field-induced ro-vibrational dynamics of PH₃ and NH₃, and spontaneous emission data for optoelectrical Sisyphus cooling of H₂CO and CH₃Cl are discussed.

Antisymmetric Couplings Enable Direct Observation of Chirality in Nuclear Magnetic Resonance Spectroscopy

Here we demonstrate that a term in the nuclear spin Hamiltonian, the antisymmetric J-coupling, is fundamentally connected to molecular chirality. We propose and simulate a nuclear magnetic resonance (NMR) experiment to observe this interaction and differentiate between enantiomers without adding any additional chiral agent to the sample. The antisymmetric J-coupling may be observed in the presence of molecular orientation by an external electric field. The opposite parity of the antisymmetric coupling tensor and the molecular electric dipole moment yields a sign change of the observed coupling between enantiomers. We show how this sign change influences the phase of the NMR spectrum and may be used to discriminate between enantiomers.

Anomalous circular dichroism in high harmonic generation of stereoisomers with two chiral centers

When a molecule has more than one chiral center, it can be either a chiral molecule or a meso isomer. High harmonic generation (HHG) of stereoisomers with two chiral centers driven by circularly polarized (CP) laser pulses is investigated. Counterintuitively, it is found that the HHG exhibits prominent circular dichroism for the meso isomer, while the harmonic spectra with left and right CP laser pulses are nearly the same for the chiral isomers. We show that the anomalous circular dichroism is attributed to the characteristic recollision dynamics of HHG. This feature makes the HHG a promising tool to discriminate the meso isomer and racemic mixture, where no optical activity can be found in both cases. Similar dichroism responses are also found by applying the counter-rotating bicircular laser pulses.