Complete description of two‐photon (1+1’) ionization of NO deduced from rotationally resolved photoelectron angular distributions

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.

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).

Molecular Frame Reconstruction Using Time-Domain Photoionization Interferometry

Photoionization of molecular species is, essentially, a multipath interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N_{2}) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wave packet controls the geometric part of the photoionization interferometer. The data obtained is sufficient to determine the magnitudes and phases of the ionization matrix elements for all observed channels, and to reconstruct molecular frame interferograms from lab frame measurements. In principle, this methodology provides a time-domain route to complete photoionization experiments and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.

Relative detection sensitivity in ultrafast spectroscopy: state lifetime and laser pulse duration effects

Excited state lifetime and laser pulse duration have important implications for effective relative detection sensitivity in time-resolved spectroscopy.

Fine- and hyperfine-structure effects in molecular photoionization. II. Resonance-enhanced multiphoton ionization and hyperfine-selective generation of molecular cations

Resonance-enhanced multiphoton ionization (REMPI) is a widely used technique for studying molecular photoionization and producing molecular cations for spectroscopy and dynamics studies. Here, we present a model for describing hyperfine-structure effects in the REMPI process and for predicting hyperfine populations in molecular ions produced by this method. This model is a generalization of our model for fine- and hyperfine-structure effects in one-photon ionization of molecules presented in Paper I [M. Germann and S. Willitsch, J. Chem. Phys. 145, 044314 (2016)]. This generalization is achieved by covering two main aspects: (1) treatment of the neutral bound-bound transition including the hyperfine structure that makes up the first step of the REMPI process and (2) modification of our ionization model to account for anisotropic populations resulting from this first excitation step. Our findings may be used for analyzing results from experiments with molecular ions produced by REMPI and may serve as a theoretical background for hyperfine-selective ionization experiments.

Vibrational State-Selective Resonant Two-Photon Photoelectron Spectroscopy of AuS(-) via a Spin-Forbidden Excited State

Vibrational state-selective resonant two-photon photoelectron spectra have been obtained via a triplet intermediate state ((3)Σ(-)) of AuS(-) near its detachment threshold using high-resolution photoelectron imaging of cryogenically cooled AuS(-) anions. Four vibrational levels of the (3)Σ(-) excited state are observed to be below the detachment threshold. Resonant two-photon absorptions through these levels yield vibrational state-selective photoelectron spectra to the (2)Σ final state of neutral AuS with broad and drastically different Franck-Condon distributions, reflecting the symmetries of the vibrational wave functions of the (3)Σ(-) intermediate state. The (3)Σ(-) excited state is spin-forbidden from the (1)Σ(+) ground state of AuS(-) and is accessed due to strong relativistic effects. The nature of the (3)Σ(-) excited state is confirmed by angular distributions of the photoelectron images and quantum calculations.

Complete photoionization experiments via ultrafast coherent control with polarization multiplexing

Photoelectron angular distributions (PADs) obtained from ionization of potassium atoms using moderately intense femtosecond IR fields (∼10^{12}  W cm^{-2}) of various polarization states are shown to provide a route to "complete" photoionization experiments. Ionization occurs by a net three-photon absorption process, driven via the 4s→4p resonance at the one-photon level. A theoretical treatment incorporating the intrapulse electronic dynamics allows for a full set of ionization matrix elements to be extracted from 2D imaging data. 3D PADs generated from the extracted matrix elements are also compared to experimental, tomographically reconstructed, 3D photoelectron distributions, providing a sensitive test of their validity. Finally, application of the determined matrix elements to ionization via more complex, polarization-shaped, pulses is demonstrated, illustrating the utility of this methodology towards detailed understanding of complex ionization control schemes and suggesting the utility of such "multiplexed" intrapulse processes as powerful tools for measurement.

Rotationally resolved photoelectron angular distributions from a nonlinear polyatomic molecule

We present, for the first time, rotationally resolved photoelectron images resulting from the ionization of a polyatomic molecule. Photoelectron angular distributions pertaining to the formation of individual rotational levels of NH3+ have been extracted from the images and analyzed to enable a complete determination of the radial dipole matrix elements and relative phases that describe the ionization dynamics. This determination leads to the deduction of significantly different dynamics from those extracted in previous studies which lacked either angular information or rotational resolution.

Direct measurement of the angular dependence of the single-photon ionization of aligned N2 and CO2

By combining a state-of-the-art high-harmonic ultrafast soft X-ray source with field-free dynamic alignment, we map the angular dependence of molecular photoionization yields for the first time for a nondissociative molecule. The observed modulation in ion yield as a function of molecular alignment is attributed to the molecular frame transition dipole moment of single-photon ionization to the X, A and B states of N2(+) and CO2(+). Our data show that the transition dipoles for single-photon ionization of N2 and CO2 at 43 eV have larger perpendicular components than parallel ones. A direct comparison with published theoretical partial wave ionization cross-sections confirms these experimental observations, which are the first results to allow such comparison with theory for bound cation states. The results provide the first step toward a novel method for measuring molecular frame transition dipole matrix elements.

Alignment of a molecular anion via a shape resonance in near-threshold photodetachment

One-color-two-photon photodetachment of HOCO- at E hnu=1.60 eV accompanied by a measurement of the photoelectron angular distribution (PAD) is used to illustrate a novel approach to the alignment of a molecular anion. A quantitative analysis of the PAD reveals this alignment process is associated with a temporary anion formed by a p-wave shape resonance and the PAD in the two-photon signal is a result of interfering s- and d-partial waves within the atomic approximation. The extracted intensity and phase shift of the partial waves are consistent with the Wigner threshold law for photodetachment.

Femtosecond time-resolved photoelectron imaging

Femtosecond time-resolved photoelectron imaging (TRPEI) is a variant of time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential cross section provides useful information on wave-packet motions, electronic dephasing, and photoionization dynamics. This review describes fundamental issues and the most recent works involving TRPEI.

Optical-optical double resonance photoionization spectroscopy of nf Rydberg states of nitric oxide

The spectra of vibrationally excited nf Rydberg states of nitric oxide were recorded by monitoring the photoion current produced using two-photon double resonance excitation via the NO A (2)Sigma(+) state followed by photoexcitation of the Rydberg state that undergoes autoionization. The optical transition intensities from NO A state to nf Rydberg states were calculated, and the results agree closely with experiment. These results combined with circular dichroism measurements allow us to assign rotational quantum numbers to the nf Rydberg states even in a spectrum of relatively low resolution. We report the positions of these nf (upsilon,N,N(c)) Rydberg levels converging to the NO X (1)Sigma(+) upsilon(+) = 1 and 2 ionization limits where N is the total angular momentum excluding electron and nuclear spin and N(c) represents the rotational quantum number of the ion core. Our two-color optical-optical double resonance measurements cover the range of N from 15 to 28, N(c) from 14 to 29, and the principal quantum number n from 9 to 21. The electrostatic interaction between the Rydberg electron and the ion core is used to account for the rotational fine structure and a corresponding model is used to fit the energy levels to obtain the quadrupole moment and polarizability of the NO(+) core. Comparison with a multichannel quantum defect theory fit to the same data confirms that the model we use for the electrostatic interaction between the nf Rydberg electron and the ion core of NO well describes the rotational fine structure.

Time-resolved electron detachment imaging of the I[sup −] channel in I[sub 2]Br[sup −] photodissociation

The evolution of the I(-) channel in I(2)Br(-) photodissociation is examined using time-resolved negative-ion photoelectron imaging spectroscopy. The 388 nm photodetachment images obtained at variable delays following 388 nm excitation reveal the transformation of the excess electron from that belonging to an excited trihalide anion to that occupying an atomic orbital localized on the I(-) fragment. With increasing pump-probe delay, the corresponding photoelectron band narrows on a approximately 300 fs time scale. This trend is attributed to the localization of the excess-electron wave function on the atomic-anion fragment and the establishment of the fragment's electronic identity. The corresponding band position drifts towards larger electron kinetic energies on a significantly longer, approximately 1 ps, time scale. The gradual spectral shift is attributed to exit-channel interactions affecting the photodetachment energetics, as well as the photoelectron anisotropy. The time-resolved angular distributions are analyzed and found consistent with the formation of the asymptotic I(-) fragment.

Time-resolved photoelectron spectroscopy of molecules and clusters

Time-resolved photoelectron spectroscopy (TRPES) has become a powerful new tool in studying the dynamics of molecules and clusters. It has been applied to processes ranging from energy flow in electronically excited states of molecules to electron solvation dynamics in clusters. This review covers experimental and theoretical aspects of TRPES, focusing on studies of neutral and negatively charged species.

Femtosecond time-resolved photoelectron angular distributions probed during photodissociation of NO2

Femtosecond time-resolved photoelectron angular distributions (PADs) are measured for the first time in the molecular frame of a dissociating molecule. Various stages of the dissociation process, NO2-->NO(C Pi)+O(P), are probed using ionization of the NO(C Pi) fragment to NO+(X Sigma(+)). The PADs evolve from forward-backward asymmetric with respect to the dissociation axis at short time delays ( < or =500 fs) to symmetric at long time delays (> or = 1 ps). Changes in the PADs directly reflect the time-dependent separation and reorientation of the dissociating photofragments.