Role of Spin-Orbit Coupling in High-Order Harmonic Generation Revealed by Supercycle Rydberg Trajectories.

High-harmonic generation is typically thought of as a sub-laser-cycle process, with the electron's excursion in the continuum lasting a fraction of the optical cycle. However, it was recently suggested that long-lived Rydberg states can play a particularly important role in high harmonic generation by atoms driven by the combination of the counterrotating circularly polarized fundamental light field and its second harmonic. Here we report direct experimental evidence of very long and stable Rydberg trajectories contributing to high-harmonic generation in such fields. We track their dynamics inside the laser pulse using the spin-orbit evolution in the ionic core, utilizing the spin-orbit Larmor clock. We confirm their effect on harmonic emission both via microscopic simulations and by showing how this radiation can lead to a well-collimated macroscopic far-field signal. Our observations contrast sharply with the general view that long-lived Rydberg orbits should generate negligible contribution to the macroscopic far-field high harmonic response of the medium.

Dissecting Strong-Field Excitation Dynamics with Atomic-Momentum Spectroscopy.

Observation of internal quantum dynamics relies on correlations between the system being observed and the measurement apparatus. We propose using the c.m. degrees of freedom of atoms and molecules as a "built-in" monitoring device for observing their internal dynamics in nonperturbative laser fields. We illustrate the idea on the simplest model system-the hydrogen atom in an intense, tightly focused infrared laser beam. To this end, we develop a numerically tractable, quantum-mechanical treatment of correlations between internal and c.m. dynamics. We show that the transverse momentum records the time excited states experience the field, allowing femtosecond reconstruction of the strong-field excitation process. The ground state becomes weak-field seeking, an unambiguous and long sought-for signature of the Kramers-Henneberger regime.

State-Resolved Probing of Attosecond Timescale Molecular Dipoles.

We report an experimental study of iodomethane attosecond transient absorption spectroscopy (ATAS) in the region of iodine 4d core-to-valence/Rydberg excitation. Similar to previous atomic experiments, extreme ultraviolet near-infrared (XUV-NIR) delay-dependent absorbance changes reflect a light-induced phase due to an NIR-field driven AC Stark shift of the excited states, as well as pathway interferences arising from couplings between neighboring states. As a novel aspect of molecular ATAS, we observe pronounced differences between the ATAS signatures of valence and Rydberg states. While the core-to-valence transitions carry the majority of the XUV oscillator strength, the core-to-Rydberg transitions are dominantly affected by a moderately strong, nonionizing NIR field. Our experimental findings are corroborated by ab initio calculations and ATAS simulations.

Orientation-dependent stereo Wigner time delay and electron localization in a small molecule.

Attosecond metrology of atoms has accessed the time scale of the most fundamental processes in quantum mechanics. Transferring the time-resolved photoelectric effect from atoms to molecules considerably increases experimental and theoretical challenges. Here we show that orientation- and energy-resolved measurements characterize the molecular stereo Wigner time delay. This observable provides direct information on the localization of the excited electron wave packet within the molecular potential. Furthermore, we demonstrate that photoelectrons resulting from the dissociative ionization process of the CO molecule are preferentially emitted from the carbon end for dissociative 2Σ states and from the center and oxygen end for the 2Π states of the molecular ion. Supported by comprehensive theoretical calculations, this work constitutes a complete spatially and temporally resolved reconstruction of the molecular photoelectric effect.

Unified Time and Frequency Picture of Ultrafast Atomic Excitation in Strong Laser Fields.

Excitation and ionization in strong laser fields lies at the heart of such diverse research directions as high-harmonic generation and spectroscopy, laser-induced diffraction imaging, emission of femtosecond electron bunches from nanotips, self-guiding, filamentation and mirrorless lasing during propagation of light in atmospheres. While extensive quantum mechanical and semiclassical calculations on strong-field ionization are well backed by sophisticated experiments, the existing scattered theoretical work aiming at a full quantitative understanding of strong-field excitation lacks experimental confirmation. Here we present experiments on strong-field excitation in both the tunneling and multiphoton regimes and their rigorous interpretation by time dependent Schrödinger equation calculations, which finally consolidates the seemingly opposing strong-field regimes with their complementary pictures. Most strikingly, we observe an unprecedented enhancement of excitation yields, which opens new possibilities in ultrafast strong-field control of Rydberg wave packet excitation and laser intensity characterization.

Communication: XUV transient absorption spectroscopy of iodomethane and iodobenzene photodissociation.

Time-resolved extreme ultraviolet (XUV) transient absorption spectroscopy of iodomethane and iodobenzene photodissociation at the iodine pre-N4,5 edge is presented, using femtosecond UV pump pulses and XUV probe pulses from high harmonic generation. For both molecules the molecular core-to-valence absorption lines fade immediately, within the pump-probe time-resolution. Absorption lines converging to the atomic iodine product emerge promptly in CH3I but are time-delayed in C6H5I. We attribute this delay to the initial π → σ(*) excitation in iodobenzene, which is distant from the iodine reporter atom. We measure a continuous shift in energy of the emerging atomic absorption lines in CH3I, attributed to relaxation of the excited valence shell. An independent particle model is used to rationalize the observed experimental findings.

Multi-channel electronic and vibrational dynamics in polyatomic resonant high-order harmonic generation.

High-order harmonic generation in polyatomic molecules generally involves multiple channels of ionization. Their relative contribution can be strongly influenced by the presence of resonances, whose assignment remains a major challenge for high-harmonic spectroscopy. Here we present a multi-modal approach for the investigation of unaligned polyatomic molecules, using SF6 as an example. We combine methods from extreme-ultraviolet spectroscopy, above-threshold ionization and attosecond metrology. Fragment-resolved above-threshold ionization measurements reveal that strong-field ionization opens at least three channels. A shape resonance in one of them is found to dominate the signal in the 20-26 eV range. This resonance induces a phase jump in the harmonic emission, a switch in the polarization state and different dynamical responses to molecular vibrations. This study demonstrates a method for extending high-harmonic spectroscopy to polyatomic molecules, where complex attosecond dynamics are expected.

Probing polar molecules with high harmonic spectroscopy.

We bring the methodology of orienting polar molecules together with the phase sensitivity of high harmonic spectroscopy to experimentally compare the phase difference of attosecond bursts of radiation emitted upon electron recollision from different ends of a polar molecule. This phase difference has an impact on harmonics from aligned polar molecules, suppressing emission from the molecules parallel to the driving laser field while favoring the perpendicular ones. For oriented molecules, we measure the amplitude ratio of even to odd harmonics produced when intense light irradiates CO molecules and determine the degree of orientation and the phase difference of attosecond bursts using molecular frame ionization and recombination amplitudes. The sensitivity of the high harmonic spectrum to subtle phase differences in the emitted radiation makes it a detailed probe of polar molecules and will drive major advances in the theory of high harmonic generation.

Influence of quantum effects on the physisorption of molecular hydrogen in model carbon foams.

The physisorption of molecular hydrogen in model carbon foams has been investigated from 50 K to room temperature. The study is carried out within the framework of the density functional theory for quantum liquids at finite temperatures. Calculations are performed in the grand canonical ensemble, i.e., the adsorbed fluid is assumed to be in equilibrium with an external gas of hydrogen molecules with concentrations ranging from 8×10(-4) kg m(-3) to n=71 kg m(-3). It is shown that, while strong zero-point energy effects are present even at room temperature, the adsorption isotherms exhibit only a weak dependence on the explicit incorporation of the bosonic exchange symmetry of hydrogen molecules. The increase of the average particle density prevents the deviations from the Maxwell-Boltzmann statistics to become noticeable if the system is cooled down. The volumetric storage capacity of these materials at low temperatures is about one half of the U. S. Department of Energy goal, while the gravimetric capacity is still far from the standards required by mobile applications. The relation between the microscopic structure of the hydrogen fluid and the calculated adsorption properties is also addressed.

Conical intersection dynamics in NO2 probed by homodyne high-harmonic spectroscopy.

Conical intersections play a crucial role in the chemistry of most polyatomic molecules, ranging from the simplest bimolecular reactions to the photostability of DNA. The real-time study of the associated electronic dynamics poses a major challenge to the latest techniques of ultrafast measurement. We show that high-harmonic spectroscopy reveals oscillations in the electronic character that occur in nitrogen dioxide when a photoexcited wave packet crosses a conical intersection. At longer delays, we observe the onset of statistical dissociation dynamics. The present results demonstrate that high-harmonic spectroscopy could become a powerful tool to highlight electronic dynamics occurring along nonadiabatic chemical reaction pathways.

High harmonic spectroscopy of multichannel dynamics in strong-field ionization.

We perform high harmonic generation spectroscopy of aligned nitrogen molecules to characterize the attosecond dynamics of multielectron rearrangement during strong-field ionization. We use the spectrum and ellipticity of the harmonic light to reconstruct the relative phase between different ionization continua participating in the ionization, and thus determine the shape and location of the hole left in the molecule by strong-field ionization. Our interferometric technique uses transitions between the ionic states, induced by the laser field on the subcycle time scale.

Angular tunneling ionization probability of fixed-in-space H2 molecules in intense laser pulses.

We propose a new approach to obtain molecular frame photoelectron angular distributions from molecules ionized by intense laser pulses. With our method we study the angular tunnel ionization probability of H2 at a wavelength of 800 nm over an intensity range of 2-4.5 x 10(14) W/cm2. We find an anisotropy that is stronger than predicted by any existing model. To explain the observed anisotropy and its strong intensity dependence we develop an analytical model in the framework of the strong-field approximation. It expresses molecular ionization as a product of atomic ionization rate and a Fourier transform of the highest occupied molecular orbital filtered by the strong-field ionization process.

Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance.

The spin-other-orbit (SOO) contribution to the g-tensor (DeltagSOO) of electron paramagnetic resonance arises due to the interaction of electron-spin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magnetic-shielding tensors sigma. We demonstrate that analogous to sigma, paramagnetic DeltagSOO contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to DeltagSOO are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant DeltagSOO values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant DeltagSOO values typically amount to less than 500 parts per million (ppm), and are small compared to other g-tensor contributions. For the first-row transition-metal compounds, DeltagSOO may contribute several thousand ppm to the g-tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magnetic-field gauge, the individual gauge-variant contributions may be an order of magnitude higher, and do not provide a reliable estimation of DeltagSOO.

Ordering of hydrogen bonds in high-pressure low-temperature H2O.

The near K-edge structure of oxygen in liquid water and ices III, II, and IX at 0.25 GPa and several low temperatures down to 4 K has been studied using inelastic x-ray scattering at 9884.7 eV with a total energy resolution of 305 and 175 meV. A marked decrease of the preedge intensity from the liquid phase and ice III to ices II and IX is attributed to ordering of the hydrogen bonds in the proton-ordered lattice of the latter phases. Density functional theory calculations including the influence of the Madelung potential of the ice IX crystal correctly account for the remaining preedge feature. Furthermore, we obtain spectroscopic evidence suggesting a possible new phase of ice at temperatures between 4 and 50 K.

Laser-induced interference, focusing, and diffraction of rescattering molecular photoelectrons.

We solve the time-dependent Schrödinger equation in three dimensions for H+2 in a one-cycle laser pulse of moderate intensity. We consider fixed nuclear positions and Coulomb electron-nuclear interaction potentials. We analyze the field-induced electron interference and diffraction patterns. To extract the ionization dynamics we subtract the excitations to low-lying bound states explicitly. We follow the time evolution of a well-defined wave packet that is formed near the first peak of the laser field. We observe the fragmentation of the wave packet due to molecular focusing. We show how to retrieve a diffraction molecular image by taking the ratio of the momentum distributions in the two lateral directions. The positions of the diffraction peaks are well described by the classical double slit diffraction rule.

Structural origin of two paramagnetic species in six-coordinated nitrosoiron(II) porphyrins revealed by density functional theory analysis of the g tensors.

Potential energy and electron paramagnetic resonance (EPR) g tensor surfaces of model five- and six-coordinated porphyrins were examined. For both types of complexes, the NO ligand is preferably coordinated end-on, with a Fe-N-O bond angle of approximately 140 degrees. In the free five-coordinated structure, NO undergoes free rotation around the axial Fe-N(NO) bond. This motion is strongly coupled to the saddle-type distortion of the porphyrin ligand. Coordination by the second axial ligand (imidazole) raises the calculated barrier for NO rotation to about 1 kcal/mol, which is further increased by displacements of imidazole from the ideal axial position. The potential energy surface for the dissociation of the weakly coordinated imidazole ligand is exceptionally flat, with variation of the Fe-N(Im) bond length between 2.1 and 2.5 A changing the energy by less than 1 kcal/mol. Experimental orientations of both axial ligands, as well as the Fe-N(Im) bond length, are therefore likely to be determined by the environment of the complex. In contrast to the total energy, calculated EPR g-tensors are sensitive to the orientation of the NO ligand and to the Fe-N(Im) bond length. Contrary to a common assumption, the g tensor component closest to the free-electron value does not coincide with the direction of the Fe-N(NO) bond. From comparison of the calculated and experimental g-tensor components for a range of structures, the rhombic ("type I") EPR signal is assigned to a static structure with NO oriented toward the meso-C atom of the prophyrin ring, and RFe-N(Im) approximately 2.1 A (calcd g1 = 1.95, g2 = 2.00, g3 = 2.04; exptl g1 = 1.96-1.98, g2 = 2.00, g3 = 2.06-2.08). The axial ("type II") EPR signal cannot correspond to any of the static structures studied presently. It is tentatively assigned to a partially dissociated six-coordinated complex (RFe-N(Im) > 2.5 A), with a freely rotating NO ligand (calcd g parallel = 2.00, g perpendicular = 2.03; exptl g parallel = 1.99-2.00, g perpendicular = 2.02-2.03).

Analytical second derivatives of the energy in MNDO methods.

Analytical second derivatives of the energy are derived and efficiently implemented for semiempirical MNDO-type methods including AM1, PM3, and MNDO/d. A new algorithm for the simultaneous solution of several CPHF equations is proposed in which the amount of memory required is independent of the number of iterations. The analytical approach is faster than the numerical approach typically by a factor of 5 and exhibits a reliable convergence over a wide range of molecules. The asymptotic memory and secondary storage requirements of the reported procedure can be as low as O(N(2) ) without significant degradation of the performance. © 1996 by John Wiley & Sons, Inc.