For the past several decades, we have been able to directly probe the motion of atoms that is associated with chemical transformations and which occurs on the femtosecond (10(-15)-s) timescale. However, studying the inner workings of atoms and molecules on the electronic timescale has become possible only with the recent development of isolated attosecond (10(-18)-s) laser pulses. Such pulses have been used to investigate atomic photoexcitation and photoionization and electron dynamics in solids, and in molecules could help explore the prompt charge redistribution and localization that accompany photoexcitation processes. In recent work, the dissociative ionization of H(2) and D(2) was monitored on femtosecond timescales and controlled using few-cycle near-infrared laser pulses. Here we report a molecular attosecond pump-probe experiment based on that work: H(2) and D(2) are dissociatively ionized by a sequence comprising an isolated attosecond ultraviolet pulse and an intense few-cycle infrared pulse, and a localization of the electronic charge distribution within the molecule is measured that depends-with attosecond time resolution-on the delay between the pump and probe pulses. The localization occurs by means of two mechanisms, where the infrared laser influences the photoionization or the dissociation of the molecular ion. In the first case, charge localization arises from quantum mechanical interference involving autoionizing states and the laser-altered wavefunction of the departing electron. In the second case, charge localization arises owing to laser-driven population transfer between different electronic states of the molecular ion. These results establish attosecond pump-probe strategies as a powerful tool for investigating the complex molecular dynamics that result from the coupling between electronic and nuclear motions beyond the usual Born-Oppenheimer approximation.

We report experiments where hydrogen molecules were dissociatively ionized by an attosecond pulse train in the presence of a near-infrared field. Fragment ion yields from distinguishable ionization channels oscillate with a period that is half the optical cycle of the IR field. For molecules aligned parallel to the laser polarization axis, the oscillations are reproduced in two-electron quantum simulations, and can be explained in terms of an interference between ionization pathways that involve different harmonic orders and a laser-induced coupling between the 1s g and 2p u states of the molecular ion. This leads to a situation where the ionization probability is sensitive to the instantaneous polarization of the molecule by the IR electric field and demonstrates that we have probed the IR-induced electron dynamics with attosecond pulses. The prospect of observing and controlling ultrafast electron dynamics in molecular systems is the basis of the current interest to apply attosecond (1 as ¼ 10 À18 s) laser pulses to physical chemistry. Since the first demonstration of attosecond pulses [1,2], pioneering experiments have demonstrated their potential in atoms [3,4], solid state systems [5], and, most recently, molecules [6], where interest has been stimulated by numerical studies which suggest that an electronic (i.e., attosecond or fewfemtosecond) time scale may be important in fundamental chemical processes [7,8]. The inherent multielectron nature of the electron dynamics in many molecular systems is a formidable challenge to theoreticians and experimentalists alike, and requires the development of novel theoretical and experimental techniques.Attosecond pump-probe spectroscopy is based on the generation of attosecond light pulses by high harmonic generation. Presently, attosecond pulses exist as attosecond pulse trains (APTs) [1] and as isolated attosecond pulses [2]. The first application of attosecond pulses to follow rapid electron dynamics in a molecule revealed that the dissociative ionization of hydrogen by a two-color extreme-ultraviolet ðXUVÞ þ IR field results in a localization of the bound electron in the molecular ion that depends with attosecond time resolution on the time delay between the attosecond XUV pulse and the IR laser pulse [6]. This could be observed via an asymmetry of the ejected fragments in the laboratory frame, i.e., after the dissociation was complete [9]. A similar experimental result was also obtained using an APT [10]. In these experiments the attosecond pulses initiated electron dynamics that was subsequently addressed by an IR pulse. A next challenge is to use attosecond pulses as a probe of ultrafast molecular electron dynamics. In this Letter we do so by investigating how a moderately intense IR field influences the electronic states that are accessed in photoionization of hydrogen using an APT.In the experiment, an XUV APT (with two pulses per IR cycle) and a 30 fs FWHM 780 nm (IR) pulse (3 Â 10 13 W=cm 2 ) with identical linear polarization were collinearly propagated and...

We present a nonperturbative time-dependent theoretical method to study H 2 ionization with femtosecond laser pulses when the photon energy is large enough to populate the Q 1 ͑25-28 eV͒ and Q 2 ͑30-37 eV͒ doubly excited autoionizing states. We have investigated the role of these states in dissociative ionization of H 2 and analyzed, in the time domain, the onset of the resonant peaks appearing in the proton kinetic energy distribution. Their dependence on photon frequency and pulse duration is also analyzed. The results are compared with available experimental data and with previous theoretical results obtained within a stationary perturbative approach. The method allows us as well to obtain dissociation yields corresponding to the decay of doubly excited states into two H atoms. The calculated H͑n =2͒ yields are in good agreement with the experimental ones.

The quantum photodynamics of a simple diatomic molecule with a permanent dipole immersed within an optical cavity containing a quantized radiation field is studied in detail. The chosen molecule under study, lithium fluoride (LiF), is characterized by the presence of an avoided crossing between the two lowest 1 Σ potential energy curves (covalent-ionic diabatic crossing). Without field, after prompt excitation from the ground state 1 1 Σ, the excited nuclear wave packet moves back and forth in the upper 2 1 Σ state, but in the proximity of the avoided crossing, the nonadiabatic coupling transfers part of the nuclear wave packet to the lower 1 1 Σ state, which eventually leads to dissociation. The quantized field of a cavity also induces an additional light crossing in the modified dressed potential energy curves with similar transfer properties. To understand the entangled photonic-nuclear dynamics we solve the time dependent Schrödinger equation by using the multiconfigurational time dependent Hartree method (MCTDH). The single mode quantized field of the cavity is represented in the coordinate space instead of in the Fock space, which allows us to deal with the field as an additional vibrational mode within the MCTDH procedure on equal footing. We prepare the cavity with different quantum states of light, namely, Fock states, coherent states and squeezed coherent states. Our results reveal pure quantum light effects on the molecular photodynamics and the dissociation yields of LiF, which are quite different from the light-undressed case and that cannot be described in general by a semiclassical approach using classical electromagnetic fields.

Attosecond science, born at the beginning of this century with the generation of the first bursts of light with durations shorter than a femtosecond, has opened the way to look at electron dynamics in atoms and molecules at its natural timescale. Thus controlling chemical reactions at the electronic level or obtaining time-resolved images of the electronic motion has become a goal for many physics and chemistry laboratories all over the world. The new experimental capabilities have spurred the development of sophisticated theoretical methods that can accurately predict phenomena occurring in the sub-fs timescale. This review provides an overview of the capabilities of existing theoretical tools to describe electron and nuclear dynamics resulting from the interaction of femto- and attosecond UV/XUV radiation with simple molecular targets. We describe one of these methods in more detail, the time-dependent Feshbach close-coupling (TDFCC) formalism, which has been used successfully over the years to investigate various attosecond phenomena in the hydrogen molecule and can easily be extended to other diatomics. In addition to describing the details of the method and discussing its advantages and limitations, we also provide examples of the new physics that one can learn by applying it to different problems: from the study of the autoionization decay that follows attosecond UV excitation to the imaging of the coupled electron and nuclear dynamics in H2 using different UV-pump/IR-probe and UV-pump/UV-probe schemes.

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Shannon entropy and Fisher information calculated from one-particle density distributions and von Neumann and linear entropies (the latter two as measures of entanglement) computed from the reduced one-particle density matrix are analyzed for the 1

Circular dichroism is a consequence of chirality. However, nonchiral molecules can also exhibit it when the measurement itself introduces chirality, e.g., when measuring molecular-frame photoelectron angular distributions. The few such experiments performed on homonuclear diatomic molecules show that, as expected, circular dichroism vanishes when the molecular-frame photoelectron angular distributions are integrated over the polar electron emission angle. Here we show that this is not the case in resonant dissociative ionization of H2 for photons of 30-35 eV, which is the consequence of the delayed ionization from molecular doubly excited states into ionic states of different inversion symmetry.