Asymmetry in photoelectron emission from chiral molecules induced by circularly polarized light

Attosecond ionic photoionization spectroscopy

Photoionization is one of the most fundamental processes in light-matter interaction. Advanced attosecond photoelectron spectroscopy provides the possibility to characterize the ultrafast photoemission process in an extremely short attosecond time scale. Following scattering symmetry rules, residual ions encode ultrafast photoionization prints at the instant of electron removal forming an alternative electron emission chronoscope. Here, we experimentally illustrate the attosecond ion reconstruction of attosecond beating by interference of two-photon transition (RABBIT)-like interferometry through the development of high-resolution ion momentum detection in atomic photoionization processes. Our ion interferometry presents identical momentum- and time-dependent scattering phase shift, as we observed in photoelectron spectroscopy, and thus demonstrates that ion interferometry can be a possible alternative attosecond approach to resolve the photoionization process, without the electron homogeneity limitation.

Optimal photoelectron circular dichroism of a model chiral system

We optimize the internuclear geometry and electronic structure of a model chiral system to achieve a maximal photoelectron circular dichroism (PECD) in its one-photon ionization by circularly polarized light. The electronic structure calculations are performed by the single center method, while the optimization is done using quantum alchemy employing a Taylor series expansion. Thereby, the effect of bond lengths and uncompensated charge distributions on the chiral response of the model is investigated theoretically in some detail. It is demonstrated that manipulating a chiral asymmetry of the ionic potential may enhance the dichroic parameter (i.e., the PECD) of the randomly oriented model system well beyond β1 = 25%. Furthermore, we demonstrate that quantum alchemy is applicable to PECD despite the unusually strong coupling of spatial and electronic degrees of freedom and discuss the relative impact of the individual degrees of freedom in this model system. We define the necessary conditions for the computational design of PECD for real (non-model) chiral molecules using our approach.

Chirality-Driven Orbital Angular Momentum and Circular Dichroism in CoSi

Chiral crystals and molecules were recently predicted to form an intriguing platform for unconventional orbital physics. Here, we report the observation of chirality-driven orbital textures in the bulk electronic structure of CoSi, a prototype member of the cubic B20 family of chiral crystals. Using circular dichroism in soft x-ray angle-resolved photoemission, we demonstrate the formation of a bulk orbital-angular-momentum texture and monopolelike orbital-momentum locking that depends on crystal handedness. We introduce the intrinsic chiral circular dichroism, icCD, as a differential photoemission observable and a natural probe of chiral electron states. Our findings render chiral crystals promising for spin-orbitronics applications.

Photoelectron Circular Dichroism in the Spin-Polarized Spectra of Chiral Molecules

We studied strong-field multiphoton ionization of 1-iodo-2-methylbutane enantiomers with 395 nm circularly polarized laser pulses experimentally and theoretically. For randomly oriented molecules, we observe spin polarization up to about 15%, which is independent of the molecular enantiomer. Our experimental findings are explained theoretically as an intricate interplay between three contributions from HOMO, HOMO-1, and HOMO-2, which are formed of 5p-electrons of the iodine atom. For uniaxially oriented molecules, our theory demonstrates even larger spin polarization. Moreover, we predict a sizable enantiosensitive photoelectron circular dichroism of about 10%, which is different for different spin states of photoelectrons.

The importance of molecular axis alignment and symmetry-breaking in photoelectron elliptical dichroism

Photoelectron angular distributions (PADs) produced from the photoionization of chiral molecules using elliptically polarized light exhibit a forward/backward asymmetry with respect to the optical propagation direction. By recording these distributions using the velocity-map imaging (VMI) technique, the resulting photoelectron elliptical dichroism (PEELD) has previously been demonstrated as a promising spectroscopic tool for studying chiral molecules in the gas phase. The use of elliptically polarized laser pulses, however, produces PADs (and consequently, PEELD distributions) that do not exhibit cylindrical symmetry about the propagation axis. This leads to significant limitations and challenges when employing conventional VMI acquisition and data processing strategies. Using novel photoelectron image analysis methods based around Hankel transform reconstruction tomography and machine learning, however, we have quantified-for the first time-significant symmetry-breaking contributions to PEELD signals that are of a comparable magnitude to the symmetric terms in the multiphoton ionization of (1R,4R)-(+)- and (1S,4S)-(-)-camphor. This contradicts any assumptions that symmetry-breaking can be ignored when reconstructing VMI data. Furthermore, these same symmetry-breaking terms are expected to appear in any experiment where circular and linear laser fields are used together. This ionization scheme is particularly relevant for investigating dynamics in chiral molecules, but it is not limited to them. Developing a full understanding of these terms and the role they play in the photoionization of chiral molecules is of clear importance if the potential of PEELD and related effects for future practical applications is to be fully realized.

Vacuum-Induced Symmetry Breaking of Chiral Enantiomer Formation in Chemical Reactions

A material with symmetry breaking inside can transmit the symmetry breaking to its vicinity by vacuum electromagnetic fluctuations. Here, we show that vacuum quantum fluctuations proximate to a parity-symmetry-broken material can induce a chirality-dependent spectral shift of chiral molecules, resulting in a chemical reaction process that favors producing one chirality over the other. We calculate concrete examples and evaluate the chirality production rate with experimentally realizable parameters, showing the promise of selecting chirality with symmetry-broken vacuum quantum fluctuations.

Theoretical study of time-resolved photoelectron circular dichroism in the photodissociation of a chiral molecule

Photoelectron circular dichroism (PECD), the forward-backward asymmetry of the photoelectron angular distribution when ionizing randomly oriented chiral molecules with circularly polarized light, is an established method to investigate chiral properties of molecules in their electronic ground state. Here, we develop a computational strategy for predicting time-resolved PECD (TRPECD) of chemical reactions and demonstrate the method on the photodissociation of 1-iodo-2-methylbutane. Our approach combines multi-configurational quantum-chemical calculations of the relevant potential-energy surfaces of the neutral and singly ionized molecule with ab initio molecular-dynamics (AIMD) calculations. The PECD parameters along the AIMD trajectories are calculated with the aid of electron-molecule scattering calculations based on the Schwinger variational principle implemented in ePolyScat. Our calculations have been performed for two probe wavelengths (133 and 160 nm) accessible through low-order harmonic generation in gases. Our results show that the TRPECD is a highly sensitive probe of photochemical reaction dynamics. Most interestingly, the TRPECD is found to change sign multiple times along the photodissociation coordinate, in agreement with recent experiments on CHBrFI [Svoboda et al., "Femtosecond photoelectron circular dichroism of chemical reactions," Sci. Adv. 8, eabq2811 (2022)]. The computational protocol introduced in the present work is general and readily applicable to other chiral photochemical processes.

High-order harmonic generation by aligned homonuclear diatomic cations

We introduce the theory of high-order harmonic generation by aligned homonuclear diatomic cations using a strong-field approximation. The target cation is represented as a system which consists of two atomic (ionic) centres and one active electron, while the driving field is either a monochromatic or bichromatic field. For a linearly polarised driving field, we investigate the differences between the harmonic spectra obtained with a neutral molecule and the corresponding molecular cation. Due to the larger ionisation potential, the molecular cations can withstand much higher laser-field intensity than the corresponding neutral molecule before the saturation effects become significant. This allows one to produce high-order harmonics with energy in the water-window interval or beyond. Also, the harmonic spectrum provides information about the structure of the highest-occupied molecular orbital. In order to obtain elliptically polarised harmonics, we suggest that an orthogonally polarised two-colour field is employed as a driving field. In this case, we analyse the harmonic ellipticity as a function of the relative orientation of the cation in the laser field. We show that the regions with large harmonic ellipticity in the harmonic energy-orientation angle plane are the broadest for cations whose molecular orbital does not have a nodal plane. Finally, we show that the molecular cations exposed to an orthogonally polarised two-colour field represent an excellent setup for the production of elliptically polarised attosecond pulses with a duration shorter than 100 as.

Time-resolved enantiomer-exchange probed by using the orbital angular momentum of X-ray light

Molecular chirality, a geometric property of utmost importance in biochemistry, is now being investigated in the time-domain. Ultrafast chiral techniques can probe the formation or disappearance of stereogenic centers in molecules. The element-sensitivity of X-rays adds the capability to probe chiral nuclear dynamics locally within the molecular system. However, the implementation of ultrafast techniques for measuring transient chirality remains a challenge because of the intrinsic weakness of chiral-sensitive signals based on circularly polarized light. We propose a novel approach for probing the enantiomeric dynamics by using the orbital angular momentum (OAM) of X-ray light, which can directly monitor the real-time chirality of molecules. Our simulations probe the oscillations in excited chiral formamide on different potential energy surfaces and demonstrate that using the X-ray OAM can increase the measured asymmetry ratio. Moreover, combining the OAM and SAM (spin angular momentum) provides stronger dichroic signals than linearly polarized light, and offers a powerful scheme for chiral discrimination.

Induced photoelectron circular dichroism onto an achiral chromophore

An achiral chromophore can acquire a chiral spectroscopic signature when interacting with a chiral environment. This so-called induced chirality is documented in electronic or vibrational circular dichroism, which arises from the coupling between electric and magnetic transition dipoles. Here, we demonstrate that a chiroptical response is also induced within the electric dipole approximation by observing the asymmetric scattering of a photoelectron ejected from an achiral chromophore in interaction with a chiral host. In a phenol-methyloxirane complex, removing an electron from an achiral aromatic π orbital localised on the phenol moiety results in an intense and opposite photoelectron circular dichroism (PECD) for the two enantiomeric complexes with (R) and (S) methyloxirane, evidencing the long-range effect (~5 Å) of the scattering chiral potential. This induced chirality has important structural and analytical implications, discussed here in the context of growing interest in laser-based PECD, for in situ, real time enantiomer determination.

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

Ultrafast control over chiral sum-frequency generation

We introduce an ultrafast all-optical approach for efficient chiral recognition that relies on the interference between two low-order nonlinear processes that are ubiquitous in nonlinear optics: sum-frequency generation and third-harmonic generation. In contrast to traditional sum-frequency generation, our approach encodes the medium's handedness in the intensity of the emitted harmonic signal, rather than in its phase, and it enables full control over the enantiosensitive response. We show how, by sculpting the sub-optical-cycle oscillations of the driving laser field, we can force one molecular enantiomer to emit bright light while its mirror twin remains dark, thus reaching the ultimate efficiency limit of chiral sensitivity via low-order nonlinear light-matter interactions. Our work paves the way for ultrafast and highly efficient imaging and control of the chiral electronic clouds of chiral molecules using lasers with moderate intensities, in all states of matter: from gases to liquids to solids, with molecular specificity and on ultrafast time scales.

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.

Carrier envelope phase sensitivity of photoelectron circular dichroism

We report on a combined experimental and numerical study of photoelectron circular dichroism (PECD) induced by intense few-cycle laser pulses, using methyloxirane as the molecular example. Our experiments reveal a remarkably pronounced sensitivity of the PECD strength of double-ionization on the carrier-envelope phase (CEP) of the laser pulses. By comparison to the simulations, which reproduce the measured CEP-dependence for specific orientations of the molecules in the lab frame, we attribute the origin of the observed CEP-dependence of PECD to the CEP-induced modulation of ionization from different areas of the wave functions of three dominant orbitals.

Imaging Photoelectron Circular Dichroism in the Detachment of Mass-Selected Chiral Anions

Photoelectron Circular Dichroism (PECD) is a forward-backward asymmetry in the photoemission from a non-racemic sample induced by circularly polarized light. PECD spectroscopy has potential analytical advantages for chiral discrimination over other chiroptical methods due to its increased sensitivity to the chiral potential of the molecule. The use of anions for PECD spectroscopy allows for mass-selectivity and provides a path to simple experimental schemes that employ table-top light sources. Evidence of PECD for anions is limited, and insight into the forces that govern PECD electron dynamics in photodetachment is absent. Here, we demonstrate a PECD effect in the photodetachment of mass-selected deprotonated 1-indanol anions. By utilizing velocity map imaging photoelectron spectroscopy with a tunable light source, we determine the energy-resolved PECD over a wide range of photon energies. The observed PECD reaches up to 11 %, similar to what has been measured for neutral species.

Imprinting Chirality on Atoms Using Synthetic Chiral Light Fields

Atoms are usually thought of as achiral objects. However, one can construct superpositions of atomic states that are chiral [1]. Here, we show how to excite such superpositions with tailored light fields both in the weak-field and strong-field regimes, using realistic laser parameters. First, we use time-dependent Schrödinger equation simulations to demonstrate the creation of a time-dependent bound chiral wave packet in sodium atoms. Second, we show how the time-dependent handedness of this wave packet can be probed by photoelectron circular dichroism, in spite of the central symmetry of the core potential. Third, we use time-dependent Schrödinger equation simulations to show how chirality can be directly imprinted on a photoelectron wave packet created by strong-field ionization and introduce an unambiguous chiral measure that allows us to characterize its handedness.

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.

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.

Atomic partial wave meter by attosecond coincidence metrology

Attosecond chronoscopy is central to the understanding of ultrafast electron dynamics in matter from gas to the condensed phase with attosecond temporal resolution. It has, however, not yet been possible to determine the timing of individual partial waves, and steering their contribution has been a substantial challenge. Here, we develop a polarization-skewed attosecond chronoscopy serving as a partial wave meter to reveal the role of each partial wave from the angle-resolved photoionization phase shifts in rare gas atoms. We steer the relative ratio between different partial waves and realize a magnetic-sublevel-resolved atomic phase shift measurement. Our experimental observations are well supported by time-dependent R-matrix numerical simulations and analytical soft-photon approximation analysis. The symmetry-resolved, partial-wave analysis identifies the transition rate and phase shift property in the attosecond photoelectron emission dynamics. Our findings provide critical insights into the ubiquitous attosecond optical timer and the underlying attosecond photoionization dynamics.

Understanding the photoelectron emission time after the interaction of photon with atoms and molecules is of fundamental interest. Here the authors examine the role of partial waves to the photoionization phase shift of atoms using an attosecond clock and electron-ion coincidence spectroscopy.

Ground-state Photoelectron Circular Dichroism of Methyl p-Tolyl Sulfoxide by Single-photon Ionisation from a Table-top Source

Single-photon ionisation of enantiopure methyl p -tolyl sulfoxide by circularly polarised light at 133nm shows remarkably strong photoelectron circular dichroism (PECD), which has been measured in a velocity-map-imaging spectrometer. Both enantiomers were measured, each showing a PECD of a similar magnitude (ca. 25%). These experiments were carried out with a tabletop high-harmonic source with a photon energy of 9.3eV, capable of ionising the electronic ground state of most organic and inorganic molecules. Ab-initio scattering calculations provide a theoretical value of the expected chiral asymmetry parameter, and agree very well with the measured values once orbital mixing via configuration interaction in the cation is taken into account. This study demonstrates a simple photoionisation scheme that can be readily applied to study the time-resolved PECD of photochemical reactions and suggests a pronounced sensitivity of PECD to electronic configuration interaction in the cation.

Femtosecond photoelectron circular dichroism of chemical reactions

Understanding the chirality of molecular reaction pathways is essential for a broad range of fundamental and applied sciences. However, the current ability to probe chirality on the time scale of primary processes underlying chemical reactions remains very limited. Here, we demonstrate time-resolved photoelectron circular dichroism (TRPECD) with ultrashort circularly polarized vacuum-ultraviolet (VUV) pulses from a tabletop source. We demonstrate the capabilities of VUV-TRPECD by resolving the chirality changes in time during the photodissociation of atomic iodine from two chiral molecules. We identify several general key features of TRPECD, which include the ability to probe dynamical chirality along the complete photochemical reaction path, the sensitivity to the local chirality of the evolving scattering potential, and the influence of electron scattering off dissociating photofragments. Our results are interpreted by comparison with high-level ab-initio calculations of transient PECDs from molecular photoionization calculations. Our experimental and theoretical techniques define a general approach to femtochirality.

Photoelectron Circular Dichroism of Electrosprayed Gramicidin Anions

Many sophisticated approaches for analyzing properties of chiral matter have been developed in recent years. But in general, the available chiroptical methods are limited to either solvated or small gaseous molecules. Studying the chirality of large biopolymers in the gas phase, including aspects of the secondary structure, becomes accessible by combining the electrospray ionization technique with chiroptical detection protocols. Here, laser-induced photodetachment from gramicidin anions, a peptide consisting of 15 amino acids has been investigated. The angular distribution of photoelectrons is demonstrated to be sensitive to the substitution of protons by cesium ions, which is accompanied by a conformational change. The photoelectron circular dichroism (PECD) is -0.5% for bare gramicidin, whereas gramicidin with several Cs⁺ ions attached exhibits a PECD of +0.5%. The results are complemented and supported by ion mobility studies. The presented approach offers the prospect of studying chirality and the secondary structure of various biopolymers.

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.

Influence of the emission site on the photoelectron circular dichroism in trifluoromethyloxirane

We report a joint experimental and theoretical study of the differential photoelectron circular dichroism (PECD) in inner-shell photoionization of uniaxially oriented trifluoromethyloxirane. By adjusting the photon energy of the circularly polarized synchrotron radiation, we address 1s-photoionization of the oxygen, different carbon, and all fluorine atoms. The photon energies were chosen such that in all cases electrons with a similar kinetic energy of about 11 eV are emitted. Employing coincident detection of electrons and fragment ions, we concentrate on identical molecular fragmentation channels for all of the electron-emitter scenarios. Thereby, we systematically examine the influence of the emission site of the photoelectron wave on the differential PECD. We observe large differences in the PECD signals. The present experimental results are supported by corresponding relaxed-core Hartree-Fock calculations.

A geometric approach to decoding molecular structure and dynamics from photoionization of isotropic samples

We propose a geometric approach to the description and analysis of photoelectron angular distributions resulting from isotropic samples in the case of few-photon ionization by electric fields of arbitrary polarization. This approach formulates the standard photoionization observables - the b_l,m expansion coefficients of the photoelectron angular distribution, in terms of geometrical properties of the vector field D⃑(k⃑) ≡ 〈k⃑|d⃑|0〉 describing the electronic transition from a bound state |0〉 into a scattering state |k⃑〉 - the photoionization transition dipole. Besides revealing selection rules for the enantio-sensitivity of b_l,m coefficients in multiphoton ionization, our approach yields very compact expressions for both chiral and achiral molecules revealing how the molecular rotational invariants couple to the rotational invariants of the setup defined by the electric field polarization and the arrangement of photoelectron detectors. We apply this approach to one-photon ionization and find that the forward-backward asymmetry parameter b_1,0, emerging exclusively in chiral molecules and encoded in the field B⃑(k⃑) ≡ iD⃑*(k⃑) × D⃑(k⃑), is sensitive only to the components of D⃑(k⃑) perpendicular to k⃑, while the regular asymmetry parameter b_2,0 emerging in chiral and achiral molecules is sensitive only to the component of D⃑(k⃑) parallel to k⃑. Next, we analyze resonantly enhanced two-photon ionization and show that b_0,0 and b_1,0 can be written in terms of an effectively stretched D⃑(k⃑), and how b_1,0 and b_3,0 can be used to probe B⃑(k⃑).

New opportunities for ultrafast and highly enantio-sensitive imaging of chiral nuclear dynamics enabled by synthetic chiral light

Synthetic chiral light [D. Ayuso et al., Nat. Photon., 2019, 13, 866-871] has opened up new opportunities for ultrafast and highly efficient imaging and control of chiral matter. Here we show that the giant enantio-sensitivity enabled by such light could be exploited to probe chiral nuclear rearrangements during chemical reactions in a highly enantio-sensitive manner. Using a state-of-the-art implementation of real-time time-dependent density functional theory, we explore how the nonlinear response of the prototypical chiral molecule H₂O₂ changes as a function of its dihedral angle, which defines its handedness. The macroscopic intensity emitted from randomly oriented molecules at even harmonic frequencies (of the fundamental) depends strongly on this nuclear coordinate. Because of the ultrafast nature of such nonlinear interactions, the direct mapping between the dissymmetry factor and the nuclear geometry provides a way to probe chiral nuclear dynamics at their natural time scales. Our work paves the way for ultrafast and highly efficient imaging of enantio-sensitive dynamics in more complex chiral systems, including biologically relevant molecules.

Generation and complete polarimetry of ultrashort circularly polarized extreme-ultraviolet pulses

The generation of ultrashort circularly polarized pulses in the extreme-ultraviolet spectral range has recently attracted considerable interest for applications in time-resolved circular-dichroism experiments. Here, we demonstrate a simple approach to generate near-circularly polarized femtosecond pulses in the vacuum-ultraviolet. The ellipticity of the generated light can be continuously tuned from linear to near-circular, as demonstrated by detailed polarimetry measurements. Combining optical polarimetry with photoelectron circular-dichroism (PECD) measurements, we demonstrate a novel approach to characterizing the polarization state of light in terms of all four Stokes parameters. For photon energies of 9.3 eV, we obtained S₃ = 0.96 ± 0.02 and a degree of polarization of 97±2%, i.e. the highest values reported from any harmonic-generation source so far. This source is directly applicable to circular-dichroism experiments, also enabling time-resolved PECD in the extreme-ultraviolet, a general approach to probing time-dependent chirality during chemical processes on (sub)-femtosecond time scales.

Amplification of elliptically polarized sub-femtosecond pulses in neon-like X-ray laser modulated by an IR field

Amplification of attosecond pulses produced via high harmonic generation is a formidable problem since none of the amplifiers can support the corresponding PHz bandwidth. Producing the well defined polarization state common for a set of harmonics required for formation of the circularly/elliptically polarized attosecond pulses (which are on demand for dynamical imaging and coherent control of the spin flip processes) is another big challenge. In this work we show how both problems can be tackled simultaneously on the basis of the same platform, namely, the plasma-based X-ray amplifier whose resonant transition frequency is modulated by an infrared field.

Photoelectron circular dichroism in angle-resolved photoemission from liquid fenchone

We present an experimental X-ray photoelectron circular dichroism (PECD) study of liquid fenchone at the C 1s edge. A novel setup to enable PECD measurements on a liquid microjet [Malerz et al., Rev. Sci. Instrum., 2022, 93, 015101] was used. For the C 1s line assigned to fenchone's carbonyl carbon, a non-vanishing asymmetry is found in the intensity of photoelectron spectra acquired under a fixed angle in the backward-scattering plane. This experiment paves the way towards an innovative probe of the chirality of organic/biological molecules in aqueous solution.

We present the first X-ray photoelectron circular dichroism (PECD) study from a liquid phase sample, exemplified for liquid fenchone at the C 1s edge.

Disentangling enantiosensitivity from dichroism using bichromatic fields

We discuss how tensorial observables, available in photoelectron angular distributions resulting from interaction between isotropic chiral samples and cross polarized ω-2ω bichromatic fields, allow for chiral discrimination without chiral light and within the electric-dipole approximation. We extend the concept of chiral setup [A. F. Ordonez and O. Smirnova, Phys. Rev. A, 2018, 98, 063428], which explains how chiral discrimination can be achieved in the absence of chiral light, to the case of tensorial observables. We derive selection rules for the enantiosensitivity and dichroism of the b_l,m coefficients describing the photoelectron angular distribution valid for both weak and strong fields and for arbitrary ω-2ω relative phase. Explicit expressions for simple perturbative cases are given. We find that, besides the known dichroic non-enantiosensitive [R. E. Goetz, C. P. Koch and L. Greenman, J. Chem. Phys., 2019, 151, 074106], and dichroic-and-enantiosensitive b_l,m coefficients found recently [P. V. Demekhin, Phys. Rev. A, 2019, 99, 063406], there are also enantiosensitive non-dichroic b_l,m coefficients. These reveal the molecular enantiomer independently of the relative phase between the two colors and are therefore observable even in the absence of stabilization of the ω-2ω relative phase.

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.

Time-resolved photoelectron spectroscopy: the continuing evolution of a mature technique

Time-resolved photoelectron spectroscopy (TRPES) has become one of the most widespread techniques for probing nonadiabatic dynamics in the excited electronic states of molecules. Furthermore, the complementary development of ab initio approaches for the simulation of TRPES signals has enabled the interpretation of these transient spectra in terms of underlying coupled electronic-nuclear dynamics. In this perspective, we discuss the current state-of-the-art approaches, including efforts to push femtosecond pulses into vacuum ultraviolet and soft X-ray regimes as well as the utilization of novel polarizations to use time-resolved optical activity as a probe of nonadiabatic dynamics. We close this perspective with a forward-looking prospectus on the new areas of application for this technique.

Elliptic dichroism in strong-field ionization of atoms subjected to tailored laser fields

The differential ionization rate for strong-field ionization by tailored laser fields of atomic systems averaged over the magnetic quantum number satisfies particular inversion and reflection symmetries. The symmetries of the elliptic-dichroism parameter, which is related to the change of sign of the ellipticity of the laser field, are considered in detail, with particular emphasis on high-order above-threshold ionization. The general results are illustrated by the examples of an elliptically polarized laser field and a bi-elliptical orthogonally polarized two-color (BEOTC) field. For the BEOTC field the differential ionization rate and the elliptic-dichroism parameter are investigated for the ω-2ω and ω-3ω field combinations and for various relative phases between the laser-field components. The inversion and reflection symmetries of the photoelectron momentum distribution in the polarization plane of the field depend on the parities of r and s in the rω--sω BEOTC field combination and on the relative phase between the field components. We suggest that, by analyzing the symmetry properties of the measured momentum distribution of the elliptic-dichroism parameter, one can identify the mechanism of strong-field ionization. If the rescattering mechanism is dominant one can use these distributions to obtain information about the atomic and molecular structure and dynamics.

Photoelectron elliptical dichroism spectroscopy of resonance-enhanced multiphoton ionization via the 3s, 3p and 3d Rydberg series in fenchone

The resonance-enhanced multiphoton ionization of chiral molecules by elliptically polarized laser pulses produces photoelectron angular distributions that are forward/backward asymmetric with respect to the light propagation axis. We investigate this photoelectron elliptical dichroism in the (2 + 1)-photon ionization of fenchone molecules, using wavelength tunable femtosecond UV pulses. We show that the photoelectron elliptical asymmetry is extremely sensitive to the intermediate resonant states involved in the ionization process, and enables electronic couplings to be revealed that do not show up so clearly when using circularly polarized light.

Propensity rules for photoelectron circular dichroism in strong field ionization of chiral molecules

Chiral molecules ionized by circularly polarized fields produce a photoelectron current orthogonal to the polarization plane. This current has opposite directions for opposite enantiomers and provides an extremely sensitive probe of molecular handedness. Recently, such photoelectron currents have been measured in the strong-field ionization regime, where they may serve as an ultrafast probe of molecular chirality. Here we provide a mechanism for the emergence of such strong-field photoelectron currents in terms of two propensity rules that link the properties of the initial electronic chiral state to the direction of the photoelectron current.

Strong chiral response in non-collinear high harmonic generation driven by purely electric-dipole interactions

High harmonic generation (HHG) records the ultrafast electronic response of matter to light, encoding key properties of the interrogated quantum system, such as chirality. The first implementation of chiral HHG [Cireasa et al, Nat. Phys.11, 654 (2015)10.1038/nphys3369] relied on the weak electronic response of a medium of randomly oriented chiral molecules to the magnetic component of an elliptically polarized wave, yielding relatively weak chiro-optical signals. Here we apply state-of-the-art semi-analytical modelling to show that elliptically polarized light can drive a strong chiral response in chiral molecules via purely electric-dipole interactions - the magnetic component of the wave does not participate at all. This strong chiro-optical response, which remains hidden in standard HHG experiments, can be mapped into the macroscopic far-field signal using a non-collinear configuration, creating new opportunities for imaging chiral matter and chiral dynamics on ultrafast time scales.

Circularly polarized light-induced potentials and the demise of excited states

In the presence of strong electric fields, the excited states of single-electron molecules and molecules with large transient dipoles become unstable because of anti-alignment, the rotation of the molecular axis perpendicular to the field vector, where bond hardening is not possible. We show how to overcome this problem by using circularly polarized electromagnetic fields. Using a full quantum description of the electronic, vibrational, and rotational degrees of freedom, we characterize the excited electronic state dressed by the field and analyze its dependence on the bond length and angle and the stability of its vibro-rotational eigenstates. Although the dynamics is metastable, most of the population remains trapped in this excited state for hundreds of femtoseconds, allowing quantum control. Contrary to what happens with linearly polarized fields, the photodissociation occurs along the initial molecular axis, not perpendicular to it.

Detecting chirality in mixtures using nanosecond photoelectron circular dichroism

We report chirality detection of structural isomers in a gas phase mixture using nanosecond photoelectron circular dichroism (PECD). Combining pulsed molecular beams with high-resolution resonance enhanced multi-photon ionization (REMPI) allows specific isolated transitions belonging to distinct components in the mixture to be targeted.

Coincident measurement of photo-ion circular dichroism and photo-electron circular dichroism on 1-Phenylethylamine

Here we report the coincident measurement of the PICD and PECD effect in 1-Phenylethylamine upon multiphoton ionisation. Photo-ion circular dichroism (PICD) and photo-electron circular dichroism (PECD) are both methods to...

Pulse length dependence of photoelectron circular dichroism

We investigated photoelectron circular dichroism (PECD) using pulses with various durations. From the experiment with fenchone, we found constancy of the PECD over a wide range of pulse durations and estimated lifetimes of internal conversions.

Trends in angle-resolved molecular photoelectron spectroscopy

In this perspective article, main trends of angle-resolved molecular photoelectron spectroscopy in the laboratory up to the molecular frame, in different regimes of light-matter interactions, are highlighted with emphasis on foundations and most recent applications.

Fundamentals and applications of molecular photoelectron spectroscopy – Festschrift for Ivan Powis

This themed collection includes a collection of articles on fundamentals and applications of molecular photoelectron spectroscopy.

Ultrafast relaxation investigated by photoelectron circular dichroism: an isomeric comparison of camphor and fenchone

We study the isomeric effects using time resolved photoelectron circular dichroism (TR-PECD). Using a (1 + 1') pump-probe ionisation scheme with photoelectrons collected by the velocity map imaging technique, we compare the relaxation dynamics from the 3s-Rydberg state in 1R,4R-(+)-camphor with the one in its chiral isomer, 1R,4S-(-)-fenchone [Comby et al., 2016, JPCL, 7, 4514]. Our measurements revealed a similar lifetime for both isomers. However, the circular dichroism in the photoelectron angular distribution decays exponentially in ∼730 fs from a +9% forward amplitude during the first hundreds of femtoseconds to reach an asymptotic -2% backward amplitude. This time-scale is drastically shorter than in fenchone. Our analysis allows us to evaluate the impact of the anisotropy of excitation; the relaxation dynamics, following photoexcitation by the linearly polarized pump, is then compared to that induced by a circularly polarized pump pulse (CPL). With such a CPL pump, we then retrieve time constants of our chiral observables similar to the ones recorded in fenchone. Quantum and classical simulations are developed and used to decipher the dependence of the PECD on the anisotropy of excitation and the spatial distribution of the 3s-Rydberg electron wavefunction. Our experimental investigations, supported by our simulations, suggest that varying the pump ellipticity enables us to reveal the breakdown of the Franck-Condon approximation.

Valence-shell photoelectron circular dichroism of ruthenium(III)-tris-(acetylacetonato) gas-phase enantiomers

Chiral transition-metal complexes are of interest in many fields ranging from asymmetric catalysis and molecular materials science to optoelectronic applications or fundamental physics including parity violation effects. We present here a combined theoretical and experimental investigation of gas-phase valence-shell photoelectron circular dichroism (PECD) on the challenging open-shell ruthenium(III)-tris-(acetylacetonato) complex, Ru(acac)₃. Enantiomerically pure Δ- or Λ-Ru(acac)₃, characterized by electronic circular dichroism (ECD), were vaporized and adiabatically expanded to produce a supersonic beam and photoionized by circularly-polarized VUV light from the DESIRS beamline at Synchrotron SOLEIL. Photoelectron spectroscopy (PES) and PECD experiments were conducted using a double imaging electron/ion coincidence spectrometer, and compared to density functional theory (DFT) and time-dependent DFT (TDDFT) calculations. The open-shell character of Ru(acac)₃, which is not taken into account in our DFT approach, is expected to give rise to a wide multiplet structure, which is not resolved in our PES signals but whose presence might be inferred from the additional striking features observed in the PECD curves. Nevertheless, the DFT-based assignment of the electronic bands leads to the characterisation of the ionized orbitals. In line with other recent works, the results confirm that PECD persists independently on the localization and/or on the achiral or chiral nature of the initial orbital, but is rather a probe of the molecular potential as a whole. Overall, the measured PECD signals on Ru(acac)₃, a system exhibiting D₃ propeller-type chirality, are of similar magnitude compared to those on asymmetric-carbon-based chiral organic molecules which constitute the vast majority of species investigated so far, thus suggesting that PECD is a universal mechanism, inherent to any type of chirality.

Bayesian optimal control of the ultrashort circularly polarized attosecond pulse generation by two-color polarization gating

We present ab initio simulations of optimal control of high-order-harmonic generation spectra that enable the synthesis of a circularly polarized 53-attosecond pulse in a single Helium atom response. The Bayesian optimization is used to achieve control of a two-color polarization gating laser waveform such that a series of harmonics in the plateau region are phase-matched, which can be used for attosecond pulse synthesis. To find the underlying mechanisms for generating these harmonics, we perform a wavelet analysis for the induced dipole moment in acceleration form, and compare the time-energy representation with the quantum paths extracted from the semiclassical calculation. We found that these coherent harmonics are excited along the short trajectories. The proposed method has the potential to migrate to laboratories for generation of isolated circularly polarized ultrashort attosecond pulses.

Fourfold Differential Photoelectron Circular Dichroism

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s photoelectrons in coincidence with fragment ions, we deduce the molecule's orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase.

Photoelectron Circular Dichroism in the Photodetachment of Amino Acid Anions

The chirality of chemical compounds is of undisputed importance in science and technology. In particular with respect to pharmacological application most molecules of interest cannot be accessed by the powerful techniques developed in recent years for gas phase analytes. Here, we demonstrate that the combination of electrospray ionization (ESI) with the detection of photoelectron circular dichroism (PECD) provides access to chirality information applicable to molecular materials with negligible vapor pressure, for example, amino acids. To this end, glutamic acid and 3,4‐dihydroxyphenylalanine (DOPA) have been electrosprayed into the source of a chirality spectrometer, where photodetachment is enforced and the PECD is detected. The technique can be expected to be conceptually applicable to all chemical systems with chirality based on molecular properties.