The Interplay between Tunneling and Parity Violation in Chiral Molecules

In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund's paradox, with emphasis on mean-field theory and decoherence.

Chiral molecule candidates for trapped ion spectroscopy by ab initio calculations: From state preparation to parity violation

Parity non-conservation (PNC) due to the weak interaction is predicted to give rise to enantiomer dependent vibrational constants in chiral molecules, but the phenomenon has so far eluded experimental observation. The enhanced sensitivity of molecules to physics beyond the Standard Model (BSM) has led to substantial advances in molecular precision spectroscopy, and these may be applied to PNC searches as well. Specifically, trapped molecular ion experiments leverage the universality of trapping charged particles to optimize the molecular ion species studied toward BSM searches, but in searches for PNC, only a few chiral molecular ion candidates have been proposed so far. Importantly, viable candidates need to be internally cold, and their internal state populations should be detectable with high quantum efficiency. To this end, we focus on molecular ions that can be created by near threshold resonant two-photon ionization and detected via state-selective photo-dissociation. Such candidates need to be stable in both charged and neutral chiral versions to be amenable to these methods. Here, we present a collection of suitable chiral molecular ion candidates we have found, including CHDBrI+ and CHCaBrI+, that fulfill these conditions according to our ab initio calculations. We find that organo-metallic species have low ionization energy as neutrals and relatively high dissociation thresholds. Finally, we compute the magnitude of the PNC values for vibrational transitions for some of these candidates. An experimental demonstration of state preparation and readout for these candidates will be an important milestone toward measuring PNC in chiral molecules for the first time.

Microwave Three-Wave Mixing Spectroscopy of Chiral Molecules in Weakly Bound Complexes

Since the first experimental implementation in 2013, microwave three-wave mixing has emerged as a robust spectroscopic approach for analyzing and controlling chiral molecules in the gas phase. This resonant, coherent, and nonlinear technique is based on the three-dimensional light-matter interaction in the electric dipole approximation, allowing for isomer- and conformer-selective chiral analysis with high resolution. Here we demonstrate the utility of microwave three-wave mixing for analyzing a molecular complex, limonene-H2O, which serves as a compelling example of addressing its potential to improve the chiral sensitivity for only weakly polar chiral molecules. The use of molecular complexes can also extend the applicability of microwave three-wave mixing to chiral systems that are not in the C1 point group.

Pump-probe spectroscopy of chiral vibrational dynamics

A planar molecule may become chiral upon excitation of an out-of-plane vibration, changing its handedness during half a vibrational period. When exciting such a vibration in an ensemble of randomly oriented molecules with an infrared laser, half of the molecules will undergo the vibration phase-shifted by π compared to the other half, and no net chiral signal is observed. This symmetry can be broken by exciting the vibrational motion with a Raman transition in the presence of a static electric field. Subsequent ionization of the vibrating molecules by an extreme ultraviolet pulse probes the time-dependent net handedness via the photoelectron circular dichroism. Our proposal for pump-probe spectroscopy of molecular chirality, based on quantum-chemical theory and discussed for the example of the carbonyl chlorofluoride molecule, is feasible with current experimental technology.

Biological Homochirality and the Search for Extraterrestrial Biosignatures

Most amino acids and sugar molecules occur in mirror, or chiral, images of each other, knowns as enantiomers. However, life on Earth is mostly homochiral: proteins contain almost exclusively L-amino acids, while only D-sugars appear in RNA and DNA. The mechanism behind this fundamental asymmetry of life remains unknown, despite much progress in the theoretical and experimental understanding of homochirality in the past decades. We review three potential mechanisms for the emergence of biological homochirality on primal Earth and explore their implications for astrobiology: the first, that biological homochirality is a stochastic process driven by local environmental fluctuations; the second, that it is driven by circularly-polarized ultraviolet radiation in star-forming regions; and the third, that it is driven by parity violation at the elementary particle level. We argue that each of these mechanisms leads to different observational consequences for the existence of enantiomeric excesses in our solar system and in exoplanets, pointing to the possibility that the search for life elsewhere will help elucidate the origins of homochirality on Earth.

Discrimination of enantiomers for chiral molecules using analytically designed microwave pulses

We perform a theoretical exploration of quantum coherent control of enantio-selective state transfer (ESST) of chiral molecules with three rotational states connected by the a-type, b-type, and c-type components of the transition dipole moments. A pulse-area theorem based on a closed-loop three-level system is derived without applying the rotating-wave approximation and used to analytically design three linearly polarized microwave pulses with optimal amplitudes and phases. By utilizing two optimized microwaves to mix two excited rotational states into the maximal coherence, we find that the discrimination of enantiomers via ESST for chiral molecules can be achieved by controlling the delay time of the third optimized microwave pulse. We examine the robustness of such control schemes against the Rabi frequency and detuning errors and the environment effect through pure dephasing processes for practical applications. This work provides an alternative approach to analytically designing optimal control fields for quantum control of ESST by using complex pulse areas.

Quantitative Study of Enantiomer-Specific State Transfer

We here report on a quantitative study of enantiomer-specific state transfer, performed in a pulsed, supersonic molecular beam. The chiral molecule 1-indanol is cooled to low rotational temperatures (1-2 K) and a selected rotational level in the electronic and vibrational ground state of the most abundant conformer is depleted via optical pumping on the S_{1}←S_{0} transition. Further downstream, three consecutive microwave pulses with mutually perpendicular polarizations and with a well-defined duration and phase are applied. The population in the originally depleted rotational level is subsequently monitored via laser-induced fluorescence detection. This scheme enables a quantitative comparison of experiment and theory for the transfer efficiency in what is the simplest enantiomer-specific state transfer triangle for any chiral molecule, that is, the one involving the absolute ground state level, |J_{K_{a}K_{c}}⟩=|0_{00}⟩. Moreover, this scheme improves the enantiomer enrichment by over an order of magnitude compared to previous works. Starting with a racemic mixture, a straightforward extension of this scheme allows one to create a molecular beam with an enantiomer-pure rotational level, holding great prospects for future spectroscopic and scattering studies.

Enantioselective Topological Frequency Conversion

Two molecules are enantiomers if they are nonsuperimposable mirror images of each other. Electric dipole-allowed cyclic transitions |1⟩ → |2⟩ → |3⟩ → |1⟩ obey the symmetry relation OR=-OS, where OR,S = (μ₂₁^R,SE₂₁)(μ₁₃^R,SE₁₃)(μ₃₂^R,SE₃₂) and R and S label the two enantiomers. Herein, we generalize the concept of topological frequency conversion to an ensemble of enantiomers. We show that, within a rotating-frame, the pumping power between fields of frequency ω₁ and ω₂ is sensitive to enantiomeric excess, P2→1 = ℏ[ω₁ω₂C_L^R/(2π)](N_R - N_S), where N_i is the number of enantiomers i and C_L^R is an enantiomer-dependent Chern number. Connections with chiroptical microwave spectroscopy are made. Our work provides an underexplored and fertile connection between topological physics and molecular chirality.

Perspectives on parity violation in chiral molecules: theory, spectroscopic experiment and biomolecular homochirality

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number parity and a fundamental ‘non-observable’ property of space (as defined by an absolute ‘left-handed’ or ‘right-handed’ coordinate system). The discovery of the violation of this symmetry – the non-conservation of parity or ‘parity violation’ – in 1956/1957 had an important influence on the further development of physics. In chemistry the mirror symmetry of space is connected to the existence of enantiomers as isomers of chiral (‘handed’) molecules. These isomers would relate to each other as idealized left or right hand or as image and mirror image and would be energetically exactly equivalent with perfect space inversion symmetry. Parity violation results in an extremely small ‘parity violating’ energy difference between the ground states of the enantiomers which can be theoretically calculated to be about 100 aeV to 1 feV (equivalent to 10⁻¹¹ to 10⁻¹⁰ J mol⁻¹), depending on the molecule, but which has not yet been detected experimentally. Its detection remains one of the great challenges of current physical–chemical stereochemistry, with implications also for fundamental problems in physics. In biochemistry and molecular biology one finds a related fundamental question unanswered for more than 100 years: the evolution of ‘homochirality’, which is the practically exclusive preference of one chiral, enantiomeric form as building blocks in the biopolymers of all known forms of life (the l-amino acids in proteins and d-sugars in DNA, not the reverse d-amino acids or l-sugars). In astrobiology the spectroscopic detection of homochirality could be used as strong evidence for the existence of extraterrestrial life, if any. After a brief conceptual and historical introduction we review the development, current status, and progress along these three lines of research: theory, spectroscopic experiment and the outlook towards an understanding of the evolution of biomolecular homochirality.

The reflection (or ‘mirror’) symmetry of space is among the fundamental symmetries of physics. It is connected to the conservation law for the quantum number purity and its violation and has a fundamental relation to stereochemistry and molecular chirality.

Sub-Hz Differential Rotational Spectroscopy of Enantiomers

We demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry–Perot cavity. We report statistically limited sub-Hz precision of (0.08 ± 0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

High-Resolution "Magic"-Field Spectroscopy on Trapped Polyatomic Molecules

Rapid progress in cooling and trapping of molecules has enabled first experiments on high-resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a"magic" offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We thereby reduce Stark broadening on the J=5←4 (K=3) transition of formaldehyde at 364 GHz to well below 1 kHz, observe Doppler-limited linewidths down to 3.8 kHz, and determine the magic-field line position with an uncertainty below 100 Hz. Our approach opens a multitude of possibilities for investigating diverse polyatomic molecule species.

Entanglement-Assisted Quantum Chiral Spectroscopy

The most important problem of spectroscopic chiral analysis is the enantioselective effects of the light-molecule interactions are inherently weak and severely reduced by the environment noises. Enormous efforts had been spent to overcome this problem by enhancing the symmetry break in the light-molecule interactions or reducing the environment noises. Here, we propose an alternative way to solve this problem by using frequency-entangled two-photon pairs as probe signals and detecting them in coincidence, i.e., using quantum chiral spectroscopy. For this purpose, we develop the theory of entanglement-assisted quantum chiral spectroscopy. Our results show that the quantum spectra of the left- and right-handed molecules are always distinguishable by suitably configuring the frequency-entangled two-photon pairs. In contrast, the classical spectra of the two enantiomers, where the broadband signal photon is frequency-uncorrelated with the idle one, become indistinguishable in the strong dissipation region. This offers our quantum chiral spectroscopy a great advantage over the classical chiral spectroscopy. Our work opens up an exciting area that exploring profound advantages of the quantum spectroscopy in chiral analysis.

Conformer-dependent vacuum ultraviolet photodynamics and chiral asymmetries in pure enantiomers of gas phase proline

Proline is a unique amino-acid, with a secondary amine fixed within a pyrrolidine ring providing specific structural properties to proline-rich biopolymers. Gas-phase proline possesses four main H-bond stabilized conformers differing by the ring puckering and carboxylic acid orientation. The latter defines two classes of conformation, whose large ionization energy difference allows a unique conformer-class tagging via electron spectroscopy. Photoelectron circular dichroism (PECD) is an intense chiroptical effect sensitive to molecular structures, hence theorized to be highly conformation-dependent. Here, we present experimental evidence of an intense and striking conformer-specific PECD, measured in the vacuum ultraviolet (VUV) photoionization of proline, as well as a conformer-dependent cation fragmentation behavior. This finding, combined with theoretical modeling, allows a refinement of the conformational landscape and energetic ordering, that proves inaccessible to current molecular electronic structure calculations. Additionally, astrochemical implications regarding a possible link of PECD to the origin of life's homochirality are considered in terms of plausible temperature constraints.

Precisely spun super rotors

Improved optical control of molecular quantum states promises new applications including chemistry in the quantum regime, precision tests of fundamental physics, and quantum information processing. While much work has sought to prepare ground state molecules, excited states are also of interest. Here, we demonstrate a broadband optical approach to pump trapped SiO⁺ molecules into pure super rotor ensembles maintained for many minutes. Super rotor ensembles pumped up to rotational state N = 67, corresponding to the peak of a 9400 K distribution, had a narrow N spread comparable to that of a few-kelvin sample, and were used for spectroscopy of the previously unobserved C²Π state. Significant centrifugal distortion of super rotors pumped up to N = 230 allowed probing electronic structure of SiO⁺ stretched far from its equilibrium bond length.

Optical pulses can be useful to create and control molecules in higher quantum states. Here the authors use optical pumping to create rotationally excited states of SiO⁺ molecular ion into super rotor ensemble.

Synchronization in Non-Mirror-Symmetrical Chirogenesis: Non-Helical π–Conjugated Polymers with Helical Polysilane Copolymers in Co-Colloids

A curious question is whether two types of chiroptical amplifications, called sergeants-and-soldiers (Ser-Sol) and majority-rule (Maj) effects, between non-charged helical copolymers and non-charged, non-helical homopolymers occur when copolymer encounter homopolymer in co-colloids. To address these topics, the present study chose (i) two helical polysilane copolymers (HCPSs) carrying (S)- or (R)-2-methylbutyl with isobutyl groups as chiral/achiral co-pendants (type I) and (S)- and (R)-2-methylbutyl groups as chiral/chiral co-pendants (type II) and (ii) two blue luminescent π-conjugated polymers, poly[(dioctylfluorene)-alt-(trans-vinylene)] (PFV8) and poly(dioctylfluorene) (PF8). Analyses of circular dichroism (CD) and circularly polarized luminescence (CPL) spectral datasets of the co-colloids indicated noticeable, chiroptical inversion in the Ser-Sol effect of PFV8/PF8 with type I HCPS. PF8 with type IIHCPS showed the anomalous Maj rule with chiroptical inversion though PFV8 with type IIHCPS was the normal Maj effect. The noticeable non-mirror-symmetric CD-and-CPL characteristics and marked differences in hydrodynamic sizes of these colloids were assumed to originate from non-mirror-symmetrical main-chain stiffness of HCPSs in dilute toluene solution. The present chirality/helicity transfer experiments alongside of previous/recent publications reported by other workers and us allowed to raise the fundamental question; is mirror symmetry on macroscopic levels in the ground and photoexcited states rigorously conserved?

Handed Mirror Symmetry Breaking at the Photo-Excited State of π-Conjugated Rotamers in Solutions

The quest to decode the evolution of homochirality of life on earth has stimulated research at the molecular level. In this study, handed mirror symmetry breaking, and molecular parity violation hypotheses of systematically designed π-conjugated rotamers possessing anthracene and bianthracene core were evinced via circularly polarized luminescence (CPL) and circular dichroism (CD). The CPL signals were found to exhibit a (−)-sign, and a handed dissymmetry ratio, which increased with viscosity of achiral solvents depending on the rotation barrier of rotamers. The time-resolved photoluminescence spectroscopy and quantum efficiency measurement of these luminophores in selected solvents reinforced the hypothesis of a viscosity-induced consistent increase of the (−)-sign handed CPL signals.

Resonance in Chirogenesis and Photochirogenesis: Colloidal Polymers Meet Chiral Optofluidics

Metastable colloids made of crystalline and/or non-crystalline matters render abilities of photonic resonators susceptible to chiral chemical and circularly polarized light sources. By assuming that μm-size colloids and co-colloids consisting of π- and/or σ-conjugated polymers dispersed into an optofluidic medium are artificial models of open-flow, non-equilibrium coacervates, we showcase experimentally resonance effects in chirogenesis and photochirogenesis, revealed by gigantic boosted chiroptical signals as circular dichroism (CD), optical rotation dispersion, circularly polarized luminescence (CPL), and CPL excitation (CPLE) spectral datasets. The resonance in chirogenesis occurs at very specific refractive indices (RIs) of the surrounding medium. The chirogenesis is susceptible to the nature of the optically active optofluidic medium. Moreover, upon an excitation-wavelength-dependent circularly polarized (CP) light source, a fully controlled absolute photochirogenesis, which includes all chiroptical generation, inversion, erase, switching, and short-/long-lived memories, is possible when the colloidal non-photochromic and photochromic polymers are dispersed in an achiral optofluidic medium with a tuned RI. The hand of the CP light source is not a determining factor for the product chirality. These results are associated with my experience concerning amphiphilic polymerizable colloids, in which, four decades ago, allowed proposing a perspective that colloids are connectable to light, polymers, helix, coacervates, and panspermia hypotheses, nuclear physics, biology, radioisotopes, homochirality question, first life, and cosmology.

The effect of the electric trapping field on state-selective loading of molecules into rf ion traps

Trapped molecular ions in pure rovibronic states are desirable in experiments ranging from cold chemistry to searches for physics beyond the Standard Model. Resonance-enhanced multiphoton ionisation (REMPI) can be used to prepare molecular ions in specific internal states with high fidelities. However, in the presence of electric fields, ionisation spectra exhibit frequency shifts and the ionisation thresholds are broadened. For this reason, REMPI studies are normally conducted in low and highly homogeneous electric fields, whereas the operating principle of rf ion traps requires electric fields that vary in space and time. In order to investigate the impact of this on the state-selectivity of REMPI in ion traps, we have simulated the expected broadening of the ionisation threshold under various operating conditions of a typical linear Paul trap. In many cases, the width of the ionisation threshold exceeds the separation between rotational energy levels, preventing state-selective ionisation. Careful choice of the trapping and laser parameters during loading can reduce this broadening, enabling state-selective ionisation in some instances. Where this strategy is not sufficient, the broadening can be reduced further by rapidly switching the trapping voltages off and on again during loading. This has been demonstrated experimentally for a Coulomb crystal of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{40}\hbox {Ca}^+$$\end{document}40Ca+ ions without descrystallising it.

Understanding laser desorption with circularly polarized light

We present aspects of emerging optical activity in thin racemic 1,1'-Bi-2-naphthol films upon irradiation with circularly polarized light and subsequent resonant two-photon absorption in the sample. Thorough analysis of the sample morphology is conducted by means of (polarization-resolved) optical microscopy and scanning electron microscopy (SEM). The influence of crystallization on the nonlinear probing technique (second harmonic generation circular dichroism [SHG-CD]) is investigated. Optical activity and crystallization are brought together by a systematic investigation in different crystallization regimes. We find crystallization to be responsible for two counter-acting effects, which arise for different states of crystallization. Measuring crystallized samples offers the best signal-to-noise ratio, but it limits generation of optical activity due to self-assembly effects. For suppression of crystallization on the other hand, there is a clear indication that enantiomeric selective desorption is responsible for the generation of optical activity in the sample. We reach the current resolution limit of probing with SHG-CD, as we suppress the crystallization in the racemic sample during desorption. In addition, intensity-dependent measurements on the induced optical activity reveal an onset threshold (≈0.7 TW cm-2), above which higher order nonlinear processes impair the generation of optical activity by desorption with CPL.

Assessing the performance of rotational spectroscopy in chiral analysis

The capabilities of rotational spectroscopy-based methods as tools to deliver accurate and precise chirality-sensitive information are still breaking ground, but their applicability in the challenging field of analytical chemistry is already clear. In this mini review, we explore the current abilities and challenges of two emergent techniques for chiral analysis based on rotational spectroscopy. For that, we will showcase the two methods (microwave 3-wave mixing and chiral tag rotational spectroscopy) while testing their performance to solve the absolute configuration and the enantiomeric excess of a blind sample containing a mixture of enantiomers of styrene oxide.

Chiral Molecules as Sensitive Probes for Direct Detection of P-Odd Cosmic Fields

Potential advantages of chiral molecules for a sensitive search for parity violating cosmic fields are highlighted. Such fields are invoked in different models for cold dark matter or in the Lorentz-invariance violating standard model extensions and thus are signatures of physics beyond the standard model. The sensitivity of a 20-year-old experiment with the molecule CHBrClF to pseudovector cosmic fields as characterized by the parameter |b_{0}^{e}| is estimated to be O(10^{-12}  GeV) employing ab initio calculations. This allows us to project the sensitivity of future experiments with favorable choices of chiral heavy-elemental molecular probes to be O(10^{-17}  GeV), which will be an improvement of the present best limits by at least two orders of magnitude.

Second-Scale Coherence Measured at the Quantum Projection Noise Limit with Hundreds of Molecular Ions

Cold molecules provide an excellent platform for quantum information, cold chemistry, and precision measurement. Certain molecules have enhanced sensitivity to beyond standard model physics, such as the electron's electric dipole moment (eEDM). Molecular ions are easily trappable and are therefore particularly attractive for precision measurements where sensitivity scales with interrogation time. Here, we demonstrate a spin precession measurement with second-scale coherence at the quantum projection noise (QPN) limit with hundreds of trapped molecular ions, chosen for their sensitivity to the eEDM rather than their amenability to state control and readout. Orientation-resolved resonant photodissociation allows us to simultaneously measure two quantum states with opposite eEDM sensitivity, reaching the QPN limit and fully exploiting the high count rate and long coherence.

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.

Infrared electric field sampled frequency comb spectroscopy

Probing matter with light in the mid-infrared provides unique insight into molecular composition, structure, and function with high sensitivity. However, laser spectroscopy in this spectral region lacks the broadband or tunable light sources and efficient detectors available in the visible or near-infrared. We overcome these challenges with an approach that unites a compact source of phase-stable, single-cycle, mid-infrared pulses with room temperature electric field-resolved detection at video rates. The ultrashort pulses correspond to laser frequency combs that span 3 to 27 μm (370 to 3333 cm-1), and are measured with dynamic range of >106 and spectral resolution as high as 0.003 cm-1. We highlight the brightness and coherence of our apparatus with gas-, liquid-, and solid-phase spectroscopy that extends over spectral bandwidths comparable to thermal or infrared synchrotron sources. This unique combination enables powerful avenues for rapid detection of biological, chemical, and physical properties of matter with molecular specificity.

Entangling non planar molecules via inversion doublet transition with negligible spontaneous emission

We analyze theoretically the entanglement between two non-planar and light identical molecules (e.g., pyramidal NH3) that present inversion doubling due to the internal spatial inversion of their nuclear conformations by tunneling. The peculiarity of this system lies in the simplicity of this type of molecular system in which two near levels can be connected by an allowed electric dipole transition with considerable value of the dipole moment transition and negligible spontaneous emission because the transition is in the microwave or far-infrared range. These properties give place to entanglement states oscillating by free evolution with frequency determined by the dipole-dipole interaction and negligible spontaneous decay, which allows consideration of an efficient quantum Zeno effect by frequent measurements of one of the entangled states. If the molecules are initially both in the upper (or lower) eigenstate, the system evolves under an external radiation field, which can induce oscillations of the generated entangled states, with frequency of the order of the Rabi frequency of the field. For a certain detuning, a symmetric entangled state, which is an eigenstate of the collective system, can be populated, and given its negligible spontaneous emission, could be maintained for a time limited only by external decoherence processes, which could be minimized. Although the data used are those of the NH3 molecule, other molecules could present the same advantageous features.

Highly Efficient Detection and Separation of Chiral Molecules through Shortcuts to Adiabaticity

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.

Questions of Mirror Symmetry at the Photoexcited and Ground States of Non-Rigid Luminophores Raised by Circularly Polarized Luminescence and Circular Dichroism Spectroscopy. Part 2: Perylenes, BODIPYs, Molecular Scintillators, Coumarins, Rhodamine B, and DCM

We investigated whether semi-rigid and non-rigid π-conjugated fluorophores in the photoexcited (S1) and ground (S0) states exhibited mirror symmetry by circularly polarized luminescence (CPL) and circular dichroism (CD) spectroscopy using a range of compounds dissolved in achiral liquids. The fluorophores tested were six perylenes, six scintillators, 11 coumarins, two pyrromethene difluoroborates (BODIPYs), rhodamine B (RhB), and 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM). All the fluorophores showed negative-sign CPL signals in the ultraviolet (UV)–visible region, suggesting energetically non-equivalent and non-mirror image structures in the S1 state. The dissymmetry ratio of the CPL (glum) increased discontinuously from approximately −0.2 × 10−3 to −2.0 × 10−3, as the viscosity of the liquids increased. Among these liquids, C2-symmetrical stilbene 420 showed glum ≈ −0.5 × 10−3 at 408 nm in H2O and D2O, while, in a viscous alkanediol, the signal was amplified to glum ≈ −2.0 × 10−3. Moreover, BODIPYs, RhB, and DCM in the S0 states revealed weak (−)-sign CD signals with dissymmetry ratios (gabs) ≈ −1.4 × 10−5 at λmax/λext. The origin of the (−)-sign CPL and the (−)-sign CD signals may arise from an electroweak charge at the polyatomic level. Our CPL and CD spectral analysis could be a possible answer to the molecular parity violation hypothesis based on a weak neutral current of Z0 boson origin that could connect to the origin of biomolecular handedness.

Frequency metrology of molecules in the near-infrared by NICE-OHMS

Noise-immune cavity enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) is extremely sensitive in detecting weak absorption. However, the use of NICE-OHMS for metrology study was also hindered by its sensitivity to influence from various experimental conditions such as the residual amplitude modulation. Here we demonstrate to use NICE-OHMS for precision measurements of Lamb-dip spectra of molecules. After a dedicated investigation of the systematic uncertainties in the NICE-OHMS measurement, the transition frequency of a ro-vibrational line of C₂H₂ near 789 nm was determined to be 379 639 280 915.3±1.2 kHz (fractional uncertainty 3.2 × 10^-12), agreeing well with, but more accurate than, the value determined from previous cavity ring-down spectroscopy measurements. The study indicates the possibility to implement the very sensitive NICE-OHMS method for frequency metrology of molecules, or a molecular clock, in the near-infrared.

The Gigahertz and Terahertz spectrum of monodeutero-oxirane (c-C2H3DO)

The rotational spectrum of monodeutero-oxirane was analysed as measured using the Zurich Gigahertz (GHz) spectrometer and our highest resolution Fourier Transform Infrared (FTIR) spectrometer system coupled to synchrotron radiation at the Swiss Light Source (SLS). 112 distinct line frequencies have been newly assigned in the GHz range (extended to 120 GHz, compared to previous work extending to only 59 GHz) including rotational states up to J = 23. We have furthermore assigned 398 lines in the far infrared or Terahertz range (0.75-2.10 THz or 25-70 cm-1) including transitions with rotational quantum numbers up to J = 59. The results are discussed in relation to the possible first astrophysical observation of an isotopically chiral molecule and in relation to molecular parity violation.

Multi-photon ionisation spectroscopy for rotational state preparation of [Formula: see text]

In this paper we investigate the 2 + 1' resonance enhanced multi-photon ionisation (REMPI) of molecular nitrogen via the a1Πg(v = 6) intermediate state and analyse its feasibility to generate molecular nitrogen ions in a well defined ro-vibrational state. This is an important tool for high precision experiments based on trapped molecular ions, and is crucial for studying the time variation of the fundamental constant mp/me using [Formula: see text]. The transition is not reported in the literature and detailed spectral analysis has been conducted to extract the molecular constants of the intermediate state. By carefully choosing the intermediate ro-vibrational state, the ionisation laser wavelength and controlling the excitation laser pulse energy, unwanted formation of rotationally excited molecular ions can be suppressed and ro-vibrational ground state ions can be generated with high purity.

Two-Photon Vibrational Transitions in 16O2+ as Probes of Variation of the Proton-to-Electron Mass Ratio

Vibrational overtones in deeply-bound molecules are sensitive probes for variation of the proton-to-electron mass ratio μ . In nonpolar molecules, these overtones may be driven as two-photon transitions. Here, we present procedures for experiments with 16 O 2 + , including state-preparation through photoionization, a two-photon probe, and detection. We calculate transition dipole moments between all X 2 Π g vibrational levels and those of the A 2 Π u excited electronic state. Using these dipole moments, we calculate two-photon transition rates and AC-Stark-shift systematics for the overtones. We estimate other systematic effects and statistical precision. Two-photon vibrational transitions in 16 O 2 + provide multiple routes to improved searches for μ variation.

Questions of Mirror Symmetry at the Photoexcited and Ground States of Non-Rigid Luminophores Raised by Circularly Polarized Luminescence and Circular Dichroism Spectroscopy: Part 1. Oligofluorenes, Oligophenylenes, Binaphthyls and Fused Aromatics

We report experimental tests of whether non-rigid, π-conjugated luminophores in the photoexcited (S₁) and ground (S₀) states dissolved in achiral liquids are mirror symmetrical by means of circularly polarized luminescence (CPL) and circular dichroism (CD) spectroscopy. Herein, we chose ten oligofluorenes, eleven linear/cyclic oligo-p-arylenes, three binaphthyls and five fused aromatics, substituted with alkyl, alkoxy, phenyl and phenylethynyl groups and also with no substituents. Without exception, all these non-rigid luminophores showed negative-sign CPL signals in the UV-visible region, suggesting temporal generation of energetically non-equivalent non-mirror image structures as far-from equilibrium open-flow systems at the S₁ state. For comparison, unsubstituted naphthalene, anthracene, tetracene and pyrene, which are achiral, rigid, planar luminophores, did not obviously show CPL/CD signals. However, camphor, which is a rigid chiral luminophore, showed mirror-image CPL/CD signals. The dissymmetry ratio of CPL (glum) for the oligofluorenes increased discontinuously, ranging from ≈ -(0.2 to 2.0) × 10-3, when the viscosity of the liquids increased. When the fluorene ring number increased, the glum value extrapolated at [η] = 0 reached -0.8 × 10-3 at 420 nm, leading to (⁻)-CPL signals predicted in the vacuum state. Our comprehensive CPL and CD study should provide a possible answer to the molecular parity violation hypothesis arising due to the weak neutral current mediated by the Z⁰-boson.

Comments on 'Hydrogen bonds in crystalline d-alanine: diffraction and spectroscopic evidence for differences between enantiomers'

The recent paper by Belo, Pereira, Freire, Argyriou, Eckert & Bordallo [(2018 ▸), IUCrJ, 5, 6-12] reports observations that may lead one to think of very strong and visible consequences of the parity-violation energy difference between enantiomers of a molecule, namely alanine. If proved, this claim would have an enormous impact for research in structural chemistry. However, alternative, more realistic, explanations of their experiments have not been ruled out by the authors. Moreover, the theoretical calculations carried out to support the hypothesis are unable to differentiate between enantiomers (molecules or crystals). Therefore, the conclusions drawn by Belo et al. (2018 ▸) are deemed inappropriate as the data presented do not contain sufficient information to reach such a conclusion.

State-Specific Enrichment of Chiral Conformers with Microwave Spectroscopy

An interesting class of molecules is that in which the molecules do not possess a stereogenic center but can become chiral because of their spatial arrangement. These molecules can be seen as chiral conformers, whose two nonsuperimposable forms can interconvert from one to another by rotations about single bonds. Here, we show that an initially racemic mixture of chiral conformers, such as a sample of cyclohexylmethanol, C₇H₁₄O, can be enantiomerically enriched by performing the enantioselective process of coherent population transfer between rotational levels. By first performing a population transfer cycle, followed by a three-wave mixing experiment, we show that an enantiomeric excess in a rotational level of choice can be achieved. This represents the first experimental demonstration of such an effect in a chiral pair of conformers, and it showcases the broad applicability of three-wave mixing not only for analytical applications but also to a wide scope of experiments of fundamental interest.

Sensing Chirality with Rotational Spectroscopy

Chiroptical spectroscopy techniques for the differentiation of enantiomers in the condensed phase are based on an established paradigm that relies on symmetry breaking using circularly polarized light. We review a novel approach for the study of chiral molecules in the gas phase using broadband rotational spectroscopy, namely microwave three-wave mixing, which is a coherent, nonlinear, and resonant process. This technique can be used to generate a coherent molecular rotational signal that can be detected in a manner similar to that in conventional Fourier transform microwave spectroscopy. The structure (and thermal distribution of conformations), handedness, and enantiomeric excess of gas-phase samples can be determined unambiguously by employing tailored microwave fields. We discuss the theoretical and experimental aspects of the method, the significance of the first demonstrations of the technique for enantiomer differentiation, and the method's rapid advance into a robust choice to study molecular chirality in the gas phase. Very recently, the microwave three-wave mixing approach was extended to enantiomer-selective population transfer, an important step toward spatial enantiomer separation on the fly.

Probing chirality recognition of protonated glutamic acid dimers by gas-phase vibrational spectroscopy and first-principles simulations

We characterize stereospecific aspects of homochiral and heterochiral dimers of glutamic acid by infrared spectroscopy and first-principles molecular dynamics simulations.

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.

X-ray circular dichroism signals: a unique probe of local molecular chirality

Core-resonant circular dichroism (CD) signals are induced by molecular chirality and vanish for achiral molecules and racemic mixtures. The highly localized nature of core excitations makes them ideal probes of local chirality within molecules. Simulations of the circular dichroism spectra of several molecular families illustrate how these signals vary with the electronic coupling to substitution groups, the distance between the X-ray chromophore and the chiral center, geometry, and chemical structure. Clear insight into the molecular structure is obtained through analysis of the X-ray CD spectra.

Validity Examination of the Dissipative Quantum Model of Olfaction

Despite some inconclusive experimental evidences for the vibrational model of olfaction, the validity of the model has not been examined yet and therefore it suffers from the lack of conclusive experimental support. Here, we generalize the model and propose a numerical analysis of the dissipative odorant-mediated inelastic electron tunneling mechanism of olfaction, to be used as a potential examination in experiments. Our analysis gives several predictions on the model such as efficiency of elastic and inelastic tunneling of electrons through odorants, sensitivity thresholds in terms of temperature and pressure, isotopic effect on sensitivity, and the chiral recognition for discrimination between the similar and different scents. Our predictions should yield new knowledge to design new experimental protocols for testing the validity of the model.

Phase-Modulated Nonresonant Laser Pulses Can Selectively Convert Enantiomers in a Racemic Mixture

Deracemization occurs when a racemic molecular mixture is transformed into a mixture containing an excess of a single enantiomer. Recent advances in ultrafast laser technology hint at the possibility of using shaped pulses to generate deracemization via selective enantiomeric conversion; however, experimental implementation remains a challenge and has not yet been achieved. Here we suggest a simple, yet novel approach to laser-induced enantiomeric conversion based on dynamic Stark control. We demonstrate theoretically that current laser and optical technology can be used to generate a pair of phase-modulated, nonresonant, linearly polarized Gaussian laser pulses that can selectively deracemize a racemic mixture of 3D-oriented, 3,5-difluoro-3',5'-dibromobiphenyl (F₂H₃C₆-C₆H₃Br₂) molecules, the laser-induced dynamics of which are well studied experimentally. These results strongly suggest that designing a closed-loop coherent control scheme based on this methodology may lead to the first-ever achievement of enantiomeric conversion via coherent laser light in a laboratory setting.

Sisyphus Laser Cooling of a Polyatomic Molecule

We perform magnetically assisted Sisyphus laser cooling of the triatomic free radical strontium monohydroxide (SrOH). This is achieved with principal optical cycling in the rotationally closed P(N^{''}=1) branch of either the X[over ˜]^{2}Σ^{+}(000)↔A[over ˜]^{2}Π_{1/2}(000) or the X[over ˜]^{2}Σ^{+}(000)↔B[over ˜]^{2}Σ^{+}(000) vibronic transitions. Molecules lost into the excited vibrational states during the cooling process are repumped back through the B[over ˜](000) state for both the (100) level of the Sr-O stretching mode and the (02^{0}0) level of the bending mode. The transverse temperature of a SrOH molecular beam is reduced in one dimension by 2 orders of magnitude to ∼750  μK. This approach opens a path towards creating a variety of ultracold polyatomic molecules by means of direct laser cooling.

Chiral nanoparticles in singular light fields

The studying of how twisted light interacts with chiral matter on the nanoscale is paramount for tackling the challenging task of optomechanical separation of nanoparticle enantiomers, whose solution can revolutionize the entire pharmaceutical industry. Here we calculate optical forces and torques exerted on chiral nanoparticles by Laguerre-Gaussian beams carrying a topological charge. We show that regardless of the beam polarization, the nanoparticles are exposed to both chiral and achiral forces with nonzero reactive and dissipative components. Longitudinally polarized beams are found to produce chirality densities that can be 109 times higher than those of transversely polarized beams and that are comparable to the chirality densities of beams polarized circularly. Our results and analytical expressions prove useful in designing new strategies for mechanical separation of chiral nanoobjects with the help of highly focussed beams.