Towards the analysis of attosecond dynamics in complex systems.

We study from a theoretical perspective the ionization of molecules and clusters induced by irradiation of a combined two-color laser field consisting of a train of attosecond XUV pulses in the presence of an IR field. We use time-dependent density-functional theory (TDDFT) in real time and real space as a theoretical tool. The calculated results are compared to experimental data when available. We also compare TDDFT with results obtained using a time-dependent Schrödinger equation (TDSE), which is well suited to simple systems while TDDFT allows dealing with more complex molecules and clusters. As a key observable, we study ionization versus delay time of the XUV pulses with respect to the IR background pulse. Experiments in simple atoms (He and Ar) show a regular modulation of this signal with half the IR period. This feature is recovered by TDDFT as well as by the TDSE (although total ionization differs by an order of magnitude). As more complex systems, we consider a C3 chain molecule and Na clusters. Here we encounter a different picture as the ionization signal develops a more involved pattern with several peaks per half IR period and as the TDSE produces a different pattern to TDDFT. Both effects could be related to the appearance of strong resonance modes in these more complex systems.

Towards time-dependent current-density-functional theory in the non-linear regime.

Time-Dependent Density-Functional Theory (TDDFT) is a well-established theoretical approach to describe and understand irradiation processes in clusters and molecules. However, within the so-called adiabatic local density approximation (ALDA) to the exchange-correlation (xc) potential, TDDFT can show insufficiencies, particularly in violently dynamical processes. This is because within ALDA the xc potential is instantaneous and is a local functional of the density, which means that this approximation neglects memory effects and long-range effects. A way to go beyond ALDA is to use Time-Dependent Current-Density-Functional Theory (TDCDFT), in which the basic quantity is the current density rather than the density as in TDDFT. This has been shown to offer an adequate account of dissipation in the linear domain when the Vignale-Kohn (VK) functional is used. Here, we go beyond the linear regime and we explore this formulation in the time domain. In this case, the equations become very involved making the computation out of reach; we hence propose an approximation to the VK functional which allows us to calculate the dynamics in real time and at the same time to keep most of the physics described by the VK functional. We apply this formulation to the calculation of the time-dependent dipole moment of Ca, Mg and Na2. Our results show trends similar to what was previously observed in model systems or within linear response. In the non-linear domain, our results show that relaxation times do not decrease with increasing deposited excitation energy, which sets some limitations to the practical use of TDCDFT in such a domain of excitations.

Probing time-dependent molecular dipoles on the attosecond time scale.

Photoinduced molecular processes start with the interaction of the instantaneous electric field of the incident light with the electronic degrees of freedom. This early attosecond electronic motion impacts the fate of the photoinduced reactions. We report the first observation of attosecond time scale electron dynamics in a series of small- and medium-sized neutral molecules (N(2), CO(2), and C(2)H(4)), monitoring time-dependent variations of the parent molecular ion yield in the ionization by an attosecond pulse, and thereby probing the time-dependent dipole induced by a moderately strong near-infrared laser field. This approach can be generalized to other molecular species and may be regarded as a first example of molecular attosecond Stark spectroscopy.

On transition rates in surface hopping.

Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work, we aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely (i) non-zero electronic transition rate ("hopping probability") at avoided crossings; (ii) rescaling of the nuclear velocities to conserve total energy; (iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration.

Time-dependent density-functional theory with a self-interaction correction.

We discuss an implementation of the self-interaction correction for the local-density approximation to time-dependent density-functional theory. A variational formulation is given, taking care of the necessary constraints. A manageable and transparent propagation scheme using two sets of wave functions is proposed and applied to laser excitation with subsequent ionization of a dimer molecule.

Simple DFT model of clusters embedded in rare gas matrix: trapping sites and spectroscopic properties of Na embedded in Ar.

We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na(2), Na(4), and Na(8). For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na(2), the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na(4) the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na(8) differences are less pronounced.

Crossed beam pump and probe dynamics in metal clusters.

We investigate theoretically pump and probe dynamics in metal clusters with crossed-polarization laser beams. We explore the relation between the pronounced Mie plasmon resonance and the laser frequency. The resonance moves with the cluster radius and splits according to the actual deformation. We demonstrate that probe pulses with different (linear) polarization axes allow one to resolve the global shape oscillations of the cluster in monopole and quadrupole degrees of freedom.

Towards single-particle spectroscopy of small metal clusters

We investigate the kinetic-energy spectra of electrons emitted from a metal cluster following laser excitation. This is done in the framework of a coupled ionic and electronic dynamics. Properly chosen laser parameters, leading to gentle excitations, yield kinetic-energy spectra which nicely resolve the multiphoton processes for each occupied state separately. This gives access to the single-particle energies in clusters, provided one works at sufficiently low temperatures and low electron flow.

Impact of ionic motion on ionization of metal clusters under intense laser pulses

We discuss the impact of ionic motion on ionization of metal clusters subject to intense laser pulses in a microscopic approach. We show that for long enough pulses, ionic expansion can drive the system into resonance with the electronic plasmon resonance, which leads to a strongly enhanced ionization.