Research

Atoms are ideal systems to study electronic correlation without the considerable geometric and dynamical complications brought about by the presence of multiple nuclei. Due to atoms’ rotational invariance, all the angular components of the many-body wave function can be treated analytically, which accelerates numerical calculations and allow us to achieve more precision than it is possible in molecules. Rare gases (He, Ne, Ar, Kr, Xe) are a darling of experimentalists because they are harmless, easy to handle, and they do not gunk up or corrode the equipment, so many experiments in attosecond science have rare gases as a target.

Our group has developed several programs to describe atomic ionization:

Attosecond pulses typically trigger the emission of a photoelectron. The probability with which a photoelectron is emitted in a certain range of energies and angles (photoelectron distribution) carries information on the state of the target when the ionizing pulse invested it. It is no surprise, therefore, that the detection of photoelectrons is one of the main tools used by physicists in attosecond experiments. In contrast to traditional linear photoelectron spectroscopy, attosecond spectroscopies rely on the exchange of multiple photons from pulses with variable temporal delays to activate alternative quantum paths that can interfere. For example, if an atom absorbs a 60eV photon and 1.5eV photon, the result is the same as if it absorbs a 63eV photon and emits a 1.5eV photon. In attosecond spectroscopies, all these photons are present at the same time, with stable relative phases. As a result, both quantum paths are active and they can interfere destructively or constructively. From this interference, it is possible to determine the relative phase between the quantum paths and reconstruct the delay with which an electron is emitted to the continuum. This is the principle at the basis of RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions), one of the most widely used techniques in attosecond science.

One-photon double ionization strongly depends on electron correlation, which is a quantity of primary importance in determining the properties of atoms and molecules. In a pump-probe setting, the emission of a second electron by means of the absorption of multiple photons allows us to directly image, as a function of time, the reaction of the residual electrons in the target after the first photoelectron has been emitted. In single-ionization spectroscopy, this reaction can only indirectly be reconstructed. If two photons are absorbed in sequence, and each absorption is associated with the emission of a photoelectron, we say the process occurs in the sequential regime, i.e., two single ionizations taking place one after the other: simple enough. If the two photons are absorbed very close to each other, however, or if the photon energy is sufficient to eject an electron from the neutral target but not from the resulting charged ion, a more complex non-sequential regime sets in.

Molecules differ from atoms in that they have several nuclei instead of just one. This circumstance is accompanied by several theoretical challenges. Once one gives up a single center where the positive charge is located, the symmetry of the system is drastically reduced, the separation between angular and radial degrees of freedom is lost, and so is the great simplification that spherical symmetry affords us in atoms. A reliable structure code for the electronic continuum within the fixed-nuclei approximation is a necessary prerequisite to any molecular calculation.

Nuclei, of course, are not static. While they normally move slowly compared to electrons, electrons occasionally move as slowly as the nuclei. When that happens, the nuclear and the electronic degrees of freedom become entangled. These so-called non-adiabatic couplings occur when the electronic potential energy surfaces in Born-Oppenheimer approximation are close to each other. In attosecond science, which concerns itself with the electronic continuum, these complications are compounded by the challenges inherent to the description of molecular scattering wave functions.

The ionization of molecules from core orbitals has several unique features that distinguish it from valence ionization. Core orbitals are typically highly localized on individual atoms. As a result, their excitation is highly sensitive to the chemical environment local to that atom. Since the photoelectron emerges from a well-defined center, diffraction from nearby atoms appears in the photoelectron angular distribution of pre-oriented molecules, allowing one to reconstruct their geometry. Core ionization is generally followed by Auger decay: one electron from the valence or inner valence fills the vacancy in the core orbital and the excess energy thus liberated is absorbed by another electron which leaves the molecule. Auger decay is an extremely interesting process because it informs us on the correlation between the pair of electrons that participate in it. The scattering of the photoelectron from nearby atoms manifests itself also in the integral cross section as EXAFS like oscillations, which also incorporate information on the molecular structure (see figure on the side).

As attosecond science matures, its focus is shifting from proof-of-principle experiments in elementary systems to the study of ultrafast transformations in molecules of chemical and even biological interest. Elucidating the role of electronic correlation and entanglement in these processes requires many-body tools such as molecular close-coupling methods or multi-reference time-dependent self-consistent-field methods. As mentioned above, our group works at the development of close-coupling methods, such as ASTRA and XCHEM, which offer advantages in the asymptotic representation of the photoelectron wave packets.

A particularly interesting phenomenon is charge migration: an attosecond pulse, or a short intense infrared pulse ionizes a target molecule giving rise to a non-stationary localized vacancy, which wanders across the molecule. The interest in this phenomenon is due to the possibility of using it to transmit charge at high speed, as well as to localize, by means of a second pulse, the charge on a specific moiety, thus altering the molecular reactivity altogether.

Over time, the picture of charge migration provided by calculations in fixed-nuclei approximation becomes less and less reliable. Since electronic and nuclear motions are entangled, the separate motion of either becomes blurred within a handful of femtoseconds, a process known as decoherence. While the molecule as a whole may remain in a well-defined quantum-mechanical state, it is difficult to monitor and control multiple degrees of freedom at the same time. For practical purposes, therefore, the original quantum coherence is effectively lost. In fact, if the ultrafast process starts with an ionization event, the emerging ion and the photoelectron are entangled at the outset. Unless the quantum states of the ion and of the photoelectron are detected in coincidence, therefore, the molecular ion is only partly coherent from the get-go.

Things become even more interesting when one considers non-adiabatic effects, which affect the motion of nuclear wave packets in proximity of tightly avoided crossings, conical intersection seams, and exceptional points. Until recently, tackling theoretically these processes in the electronic continuum from first principles would not only be a hard proposition, but also one destined to be frustrated, since these processes could not be observed experimentally with the required temporal resolution anyway. With the advent and maturation of attosecond technology, however, the proposition remains hard, but at least it becomes worth the effort.