Molecular Frame Reconstruction Using Time-Domain Photoionization Interferometry

Abstract

Photoionization of molecular species is, essentially, a multi-path interferometer with both experimentally controllable and intrinsic molecular characteristics. In this work, XUV photoionization of impulsively aligned molecular targets (N2) is used to provide a time-domain route to "complete" photoionization experiments, in which the rotational wavepacket 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 timedomain route to complete photoionization experiments, and the molecular frame, which is generally applicable to any molecule (no prerequisites), for all energies and ionization channels.Photoionization is an interferometric process, in which the final observable results from a coherent sum over multiple quantum paths to a set of final continuum photoelectron states |k, l, m [1,2]. Interferences between these components are manifest in the observable energy spectra and photoelectron angular distributions (PADs) [2][3][4], the latter of which can be considered as a particularly high information content observable, extremely sensitive to the phases of the partial waves |l, m [4, 5]; consequently, PADs have been investigated in a large range of control and metrology scenarios [6,7] . In the context of phase-sensitive metrology, the goal is to obtain the full set of complex photoionization matrix elements, hence characterise the photoelectron wavefunction, by analysis of sets of PAD measurements -this is a "complete" photoionization experiment [8,9].In the molecular case, the number of final |l, m states is typically large, and obtaining a sufficient dataset for a complete experiment remains a challenge. In the energy domain, a number of different schemes have been demonstrated in both the laboratory (LF) and molecular frames (MF) [10][11][12][13][14][15][16]. The common theme to all these measurements is some form of control over the experimental contributions to the photoionization interferometer (e.g. rotational state, polarization geometry), to which the intrinsic molecular contributions remain invariant. The difficulties in such cases are the ability to obtain a sufficiently large dataset, and molecular specificity in the methodologies, i.e. prerequisites such as low density of states [14], resonances [15] or dissociative channels [11][12][13].In the time-domain, rotational wavepackets can be utilized to control the geometric part of the interferometer. In this case, a high degree of spatio-temporal control of the axis distribution (alignment) of the ionizing molecular ensemble in the LF can be obtained via preparation of a broad rotational wavepacket. Although this idea is conceptually obvious, the theory is complex; it has been elucidated by multiple authors (e.g. refs. [5,[17][18][19][20][21]), but -to date -there have been no experimental d...

Angle dependence of strong-field single and double ionization of carbonyl sulfide

“…To extract ⌥(✓) from measurements of Y (t), we take advantage of the fact that S(✓, t) can be calculated with high accuracy for a thermal ensemble of (nearly) rigid molecular rotors with rotational temperature T subjected to an alignment pulse with a known time-dependent intensity [11,21,57]. Assuming S(✓, t) is known, one can write ⌥(✓) in terms of a complete set of real functions…”

“…We employ transient alignment in a pump-probe scheme, and measure the variation in the single and double ionization yields as a function of delay between the non-ionizing "alignment" and more intense "ionization" pulses. The delay-dependent yields are then fit to moments of the calculated delay-dependent rotational distributions [21,57]. The fitted coefficients of those moments define the angledependent ionization probabilities.…”

Electronic wavefunctions probed by all-optical attosecond interferometry

“…In the first approach, the angular dependence of the photoelectron spectra can be used to retrieve the phase information of the ionized wavefunction, at a given electron energy. These so-called "complete" photo-ionization experiments require recording photoelectron angular distributions for linear and circular ionizing radiation, and for fixed-in-space molecules using coincidence photo-electron photo-ion spectroscopy [1][2][3]. A recent two-dimensional momentum-resolved photo-ionization study enabled the isolation of a continuum wavefunction through an atomic resonance and, in addition, resolves its phase by interference with a reference wavefunction [4].…”

Photoelectron angular distributions from resonant two-photon ionisation of adiabatically aligned naphthalene and aniline molecules

“…Photoelectron angular distributions measured from aligned molecules under the fieldfree conditions provided by rotational revivals have been used to explore strong-field ionization, 12 femtosecond time-resolved photodissociation, 13 molecular orbital dynamics, 14 and single photon ionization with VUV pulses. [15][16][17][18] However, revivals typically provide efficient alignment for only a few hundred femtoseconds, which prevents observations of the dynamics of longer-lived molecular processes. Furthermore, a high degree of alignment at a revival is normally only possible for linear and symmetric top molecules, and the best alignment requires pulse-shaping and quantum state selection.…”