Theoretical description of circular dichroism in photoelectron angular distributions of randomly oriented chiral molecules after multi-photon photoionization
R. E. Goetz, T. A. Isaev, B. Nikoobakht, R. Berger, C. P. Koch
Photoelectron circular dichroism refers to the forward/backward asymmetry in the photoelectron angular distribution with respect to the propagation axis of circularly polarized light. It has recently been demonstrated in femtosecond multi-photon photoionization experiments with randomly oriented camphor and fenchone molecules [C. Lux et al., Angew. Chem. Int. Ed. 51, 5001 (2012);C. S. Lehmann et al., J. Chem. Phys. 139, 234307 (2013)]. A theoretical framework describing this process as (2+1) resonantly enhanced multi-photon ionization is constructed, which consists of two-photon photoselection from randomly oriented molecules and successive one-photon ionisation of the photoselected molecules. It combines perturbation theory for the light-matter interaction with ab initio calculations for the two-photon absorption and a single-center expansion of the photoelectron wavefunction in terms of hydrogenic continuum functions. It is verified that the model correctly reproduces the basic symmetry behavior expected under exchange of handedness and light helicity. When applied it to fenchone and camphor, semi-quantitative agreement with the experimental data is found, for which a sufficient d wave character of the electronically excited intermediate state is crucial.
We demonstrate coherent control over the photoelectron circular dichroism in randomly oriented chiral molecules, based on quantum interference between multiple photoionization pathways. To significantly enhance the chiral signature, we use a finite manifold of indistinguishable $(1+1^\prime)$ REMPI pathways interfering at a common photoelectron energy but probing different intermediate states. We show that this coherent control mechanism maximizes the number of molecular states that constructively contribute to the dichroism at an optimal photoelectron energy and thus outperforms other schemes…
Continuum-electron interferometry for enhancement of photoelectron circular dichroism and measurement of bound, free, and mixed contributions to chiral response
Angular distribution of photoelectrons released by the ionization of randomly-oriented molecules with two laser fields of carrier frequencies $ω$ and $2ω$, which are linearly polarized in two mutually-orthogonal directions, is analyzed in the perturbation limit for the case of one- vs two-photon ionization process. In particular, we focus on the recently predicted [Ph.V. Demekhin {\it et al.}, Phys. Rev. Lett. \textbf{121}, 253201 (2018)] forward-backward asymmetry in the photoelectron emission, which is induced by the interference of two fields and depends on the external relative phase betwe…
Photoelectron circular dichroism results from one-photon ionization of chiral molecules by circularly polarized light and manifests itself in forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane. To expose the physical mechanism responsible for asymmetric electron ejection, we first establish a rigorous relation between the responses of unaligned and partially or perfectly aligned molecules. Next, we identify a propensity field, which is responsible for the chiral response in the electric-dipole approximation, i.e. a chiral response withou…
Photoelectron circular dichroism results from one-photon ionization of chiral molecules by circularly polarized light and manifests itself in forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane. What is the physical mechanism underlying asymmetric electron ejection? How "which way" information builds up in a chiral molecule and maps into forward-backward asymmetry? We introduce instances of bound chiral wave functions resulting from stationary superpositions of states in a hydrogen atom and use them to show that the chiral response in one…
The application of a matrix-based reconstruction protocol for obtaining Molecular Frame (MF) photoelectron angular distributions (MFPADs) from laboratory frame (LF) measurements (LFPADs) is explored. Similarly to other recent works on the topic of MF reconstruction, this protocol makes use of time-resolved LF measurements, in which a rotational wavepacket is prepared and probed via photoionization, followed by a numerical reconstruction routine; however, in contrast to other methodologies, the protocol developed herein does not require determination of photoionization matrix elements, and cons…
Entanglement and photoelectron holography in dissociative photoionization: molecular quantum eraser
Friedrich Schiller University（弗里德里希·席勒大学）；Institute for Optics and Quantum Electronics, Friedrich Schiller University（弗里德里希·席勒大学光学与量子电子学研究所）；Leibniz University Hannover（汉诺威莱布尼茨大学）；Institute of Theoretical Physics, Leibniz University Hannover（汉诺威莱布尼茨大学理论物理研究所）；Institute of Condensed Matter Theory and Optics, Friedrich Schiller University（弗里德里希·席勒大学凝聚态理论与光学研究所）；University of Sarajevo, Faculty of Science（萨拉热窝大学理学院）；Academy of Sciences and Arts of Bosnia and Herzegovina（波斯尼亚和黑塞哥维那科学与艺术学院）；Helmholtz Institute Jena（耶拿赫尔姆霍兹研究所）
We investigate how optimal control theory can be used to improve Circular Dichroism (CD) signals for A--band of fenchone measured via the photoionization yield upon further excitation. These transitions are electric dipole forbidden to first order, which translates into low population transfer to the excited state (~8%) but also allows for a clearer interplay between electric and magnetic transition dipole moments, which are of the same order of magnitude. Using a model including the electronic ground and excited A state as well as all permanent and transition multipole moments up to the elect…
Photoionization of atoms immersed in an environment such as an ultracold gas is investigated. We show that the interference of two ionization pathways, one passing directly to the continuum and one accounting for scattering processes between the photoelectron and a neighboring atom, produces a fine structure in the photoionization cross-section over an energy range less than 1 eV above threshold. This fine structure includes all the details of the corresponding three-body system, e.g. the interatomic distance or the scattering information of the electron-atom subsystem; therefore, photoelectro…
Spin-current correlations in photoionization of chiral molecules
Max-Born-Institut（马克斯·伯恩研究所）；Humboldt University zu Berlin（柏林洪堡大学）；Technion - Israel Institute of Technology（以色列理工学院）；Imperial College London（伦敦帝国理工学院）；Freie Universität Berlin（柏林自由大学）；Technische Universität Berlin（柏林工业大学）
X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the Restricted Active Space Self-Consistent Field method including spin-orbit coupling is used to cope with this challenge and to calculate valence and core photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and t…
We present an experimental and theoretical energy- and angle-resolved study on the photoionization dynamics of non-resonant one-color two-photon single valence ionization of neutral N$_2$ molecules. Using 9.3 eV photons produced via high harmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons and ions produced from one-color two-photon ionization in coincidence. Photoionization of N$_2$ populates the X $^2Σ^+_g$, A $^2Π_u$, and B $^2Σ^+_u$ ionic states of N$_2^+$, where the photoelectron angular distributions associated with the X $^2Σ^+_g$ and A $^2Π_u$ state…
Photoelectron spectra and photoelectron angular distributions obtained in photoionization reveal important information on e.g. charge transfer or hole coherence in the parent ion. Here we show that optimal control of the underlying quantum dynamics can be used to enhance desired features in the photoelectron spectra and angular distributions. To this end, we combine Krotov's method for optimal control theory with the time-dependent configuration interaction singles formalism and a splitting approach to calculate photoelectron spectra and angular distributions. The optimization target can accou…
Photoelectron interferograms, manifested in photoelectron angular distributions (PADs), are a high-information, coherent observable. In order to obtain the maximum information from angle-resolved photoionization experiments it is desirable to record the full, 3D, photoelectron momentum distribution. Here we apply tomographic reconstruction techniques to obtain such 3D distributions from multiphoton ionization of potassium atoms, and fully analyse the energy and angular content of the 3D data. The PADs obtained as a function of energy indicate good agreement with previous 2D data and detailed a…
We present an experimental study on the photoionization dynamics of non-resonant one-color two-photon single valence ionization of neutral argon atoms. Using 9.3 eV photons produced via high harmonic generation and a 3-D momentum imaging spectrometer, we detect the photoelectrons and ions produced from non-resonant two-photon ionization in coincidence. Photoionization from the $3p$ orbital produces a photoelectron scattering wave function with $p$ and $f$ partial wave components, which interfere and result in a photoelectron angular distribution with peak amplitude perpendicular to the VUV pol…
We report measurements of energy-dependent attosecond photoionization delays between the two outer-most valence shells of N$_2$O and H$_2$O. The combination of single-shot signal referencing with the use of different metal foils to filter the attosecond pulse train enables us to extract delays from congested spectra. Remarkably large delays up to 160 as are observed in N$_2$O, whereas the delays in H$_2$O are all smaller than 50 as in the photon-energy range of 20-40 eV. These results are interpreted by developing a theory of molecular photoionization delays. The long delays measured in N$_2$O…
The present tutorial provides an overview of the time-dependent configuration interaction singles (\acs{TDCIS}) scheme applied to nonlinear ionization over a broad photon-energy range. The efficient propagation of the wave function and the calculation of photoelectron spectra within this approach are described and demonstrated in various applications. Above-threshold ionization of argon and xenon in the extreme ultraviolet energy range is investigated as an example. A particular focus is put on the xenon $4d$ giant dipole resonance and the information that nonlinear ionization can provide abou…
