Attosecond probing of vibrational dynamics with high-harmonic generation

Effect of Initial Vibrational-State Excitation on Subfemtosecond Photodynamics of Water

We discuss the effect of initial vibrational-state excitation on the subfemtosecond photodynamics of water. Photoelectron spectra of Franck-Condon ionization to the (2)B1 state of the H2O(+) (D2O(+)) from the ground and several vibrationally excited states of the neutral are reported. Also calculated are ratios of the high-order harmonic generation (HHG) signals as a function of time for each initial vibrational state of the neutral molecule as predicted from the ratios of the square of the autocorrelation functions for D2O(+) and H2O(+). They reveal maxima as a function of time for each vibrational state of the neutral molecule. In turn, the HHG signals are found to be enhanced with vibrational excitation, with the calculated expectation values of the bond lengths and bond angle revealing quasiperiodic oscillations in time for all initial vibrational states of the neutral species. Although the bond lengths show only a marginal increase, the bond angle is found to be enhanced markedly by vibrational excitation, this being therefore responsible for the observed rise in the HHG signal.

Structural evolution of the methane cation in subfemtosecond photodynamics

An ab initio quantum dynamics study has been performed to explore the structural rearrangement of ground state CH4 (+) in subfemtosecond resolved photodynamics. The method utilizes time-dependent wave-packet propagation on the X˜(2)T2 electronic manifold of the title cation in full dimensionality, including nonadiabatic coupling of the three electronic sheets. Good agreement is obtained with recent experiments [Baker et al., Science 312, 424 (2006)] which use high-order harmonic generation to probe the attosecond proton dynamics. The novel results provide direct theoretical support of the observations while unravelling the underlying details. With the geometrical changes obtained by calculating the expectation values of the nuclear coordinates as a function of time, the structural evolution is predicted to begin through activation of the totally symmetric a1 and doubly degenerate e modes. While the former retains the original Td symmetry of the cation, the Jahn-Teller active e mode conducts it to a D2d structure. At ∼1.85 fs, the intermediate D2d structure is further predicted to rearrange to local C2v minimum geometry via Jahn-Teller active bending vibrations of t2 symmetry.

Sub-femtosecond quantum dynamics of the strong-field ionization of water to the X ̃(2)B1 and Ã(2)A1 states of the cation

Motivated by recent efforts to achieve sub-femtosecond structural resolution in various molecular systems, we have performed a femtosecond quantum dynamics study of the water cation in the X ̃(2)B1 and Ã(2)A1 electronic states. Autocorrelation functions for H2O(+) and D2O(+) are calculated for such electronic states by solving numerically the time-dependent Schrödinger equation. From the ratio of the squared autocorrelation functions of D2O(+) and H2O(+), the high-order harmonic generation signals are calculated. Substantial vibrational dynamics is found in the Ã(2)A1 state as compared to the one in X ̃(2)B1, which supports recent experimental findings of Farrell et al., Phys. Rev. Lett., 2011, 107, 083001. Maxima in the above ratio are also predicted at ∼1.1 fs and ∼1.6 fs for the X ̃(2)B1 and Ã(2)A1 states, respectively. The expectation values of the positions of the atoms in H2O(+) as a function of time reveal a strong excitation of the bending mode in the Ã(2)A1 state, which explains the observed vibrational dynamics. The peaks in the ratios of the squared autocorrelation functions are also explained in terms of the evolving geometries of the water cation.

Theoretical investigation of the asymmetric molecular harmonic emission and the attosecond pulse generation

The harmonic emission of the asymmetric charged molecule HeH(2+) ion is theoretically investigated by solving the one-dimensional-time-dependent Schrödinger equation. Results show that the laser-induced electron transfer process between the vibrational state and the ground electronic state is responsible for the resonant peak on the harmonic spectrum, and that the two ionization pathways are behind the two identified cutoff energies. In addition, by optimizing the asymmetric harmonic emission, the generations of the ultrashort attosecond pulses are also discussed.

Probing nuclear motion by frequency modulation of molecular high-order harmonic generation

Molecular high-order harmonic generation (MHOHG) in a non-Born-Oppenheimer treatment of H(2)(+), D(2)(+), is investigated by numerical simulations of the corresponding time-dependent Schrödinger equations in full dimensions. As opposed to previous studies on amplitude modulation of intracycle dynamics in MHOHG, we demonstrate redshifts as frequency modulation (FM) of intercycle dynamics in MHOHG. The FM is induced by nuclear motion using intense laser pulses. Compared to fixed-nuclei approximations, the intensity of MHOHG is much higher due to the dependence of enhanced ionization on the internuclear distance. The width and symmetry of the spectrum of each harmonic in MHOHG encode rich information on the dissociation process of molecules at the rising and falling parts of the laser pulses, which can be used to retrieve the nuclear dynamics. Isotope effects are studied to confirm the FM mechanism.

Theoretical investigation of the competitive mechanism between dissociation and ionization of H₂⁺ in intense field

The competitive mechanism between dissociation and ionization of hydrogen molecular ion in intense field has been theoretically investigated by using an accurate non-Born-Oppenheimer method. The relative yield of fragments indicates that the dissociation and ionization channels are competitive with the increasing laser intensity from 5.0 × 10(13) to 2.0 × 10(14) W/cm(2). In the case of intensity lower than 1.0 × 10(14) W/cm(2), the dissociation channel is dominant, with a minor contribution from ionization. The mechanism of dissociation includes the contributions from the bond softening, bond hardening, below-threshold dissociation, and above-threshold dissociation, which are strongly dependent on the laser intensity and initial vibrational state. Furthermore, the ionization dominates over the dissociation channel at the highest intensity of 2.0 × 10(14) W/cm(2). The reasonable origin of ionization is ascribed as the above-threshold Coulomb explosion, which has been demonstrated by the space-time dependent ionization rate. Moreover, the competition mechanism between dissociation and ionization channels are displayed on the total kinetic energy resolved (KER) spectra, which could be tested at current experimental conditions.

High-order harmonic generation spectroscopy of correlation-driven electron hole dynamics

We show how high-order harmonic generation spectroscopy can be used to follow correlation-driven electron hole dynamics with attosecond time resolution. The technique is applicable both to normal Auger transitions and to electron hole migration processes that do not lead to secondary electron emission. We theoretically simulate the proposed spectroscopy for M(4,5)NN Auger decay in Kr and for correlation-driven inner-valence hole dynamics in trans-butadiene and propanal.

Theoretical study of the inversion motion of the ammonia cation with subfemtosecond resolution for high-harmonic spectroscopy

In a recent PACER (Probing Attosecond dynamics with Chirp-Encoded Recollisions) experiment on ammonia that comprises a comparison of the high-harmonic spectra of the isotopes NH3 and ND3, the nuclear dynamics of the created ammonia cation is traced with a time resolution of about 100 attoseconds. For modelling the experiment the autocorrelation functions between the neutral initial state and the ionic wave packet are extracted from experimental photoelectron spectra incorporating a correction for the geometry-dependent strong-field ionisation probability. Good agreement is found between model and experiment, but in addition an unexpected maximum in the autocorrelation ratio is predicted by the model, however occurring at 5 fs and thus outside the experimentally covered time interval. In this work the autocorrelation functions are calculated explicitly using a one-dimensional model for describing the inversion motion of ammonia and its cation, adopting a position-dependent mass for considering the coupling with the stretching mode of the hydrogen atoms in neutral ammonia. This results in a clear physical picture explaining the occurrence of the previously predicted maximum in the ratio of the autocorrelation functions. Furthermore, different initial states and two different ways of incorporating strong-field corrections to the Franck-Condon approximation are briefly discussed.

Attosecond nuclear dynamics in the ammonia cation: relation between high-harmonic and photoelectron spectroscopies

We report measurements of the umbrella motion in the ammonia cation on the attosecond time scale. The motion is prepared by strong-field ionization and probed by photorecombination through the process of high-harmonic generation. Performing such measurements at multiple wavelengths (0.8, 1.44, 1.8 μm) enables us to follow the nuclear dynamics over a broad temporal range (0.8-3.8 fs). The intensity of the driving field is found to have a significant impact on the observed dynamics through the vibrational-state dependence of the strong-field ionization rates. We derive a general model that includes these effects and establishes a new link between high-harmonic spectroscopy and classical photoelectron spectroscopy. Our model reproduces the observed dynamics and their dependence on the intensity of the driving field. Moreover, the model predicts much richer nuclear dynamics on the few-fs timescale than most previous theories. The newly predicted features are shown to reflect the quantized vibronic level structure of the molecular cation.

Anomalous isotopic effect on electron-directed reactivity by a 3-μm midinfrared pulse

We have theoretically studied the effect of nuclear mass on electron localization in dissociating H₂⁺ and its isotopes subjected to a few-cycle 3-μm pulse. Our results reveal an anomalous isotopic effect in which the degree of electron-directed reactivity can be even higher for heavier isotopes in the intense midinfrared field. We show, for the first time, the pronounced electron localization can be established through the interferences among the multi-photon coupling channels. Due to the relative enhancement of higher-order coupling channels with growing mass, the interference maxima at different kinetic energy of the spectra gradually become in phase, ultimately resulting in the larger dissociation asymmetries of heavier isotopes.

Theory of high harmonic generation for probing time-resolved large-amplitude molecular vibrations with ultrashort intense lasers

We present a theory that incorporates the vibrational degrees of freedom in a high-order harmonic generation (HHG) process with ultrashort intense laser pulses. In this model, laser-induced time-dependent transition dipoles for each fixed molecular geometry are added coherently, weighted by the laser-driven time-dependent nuclear wave packet distribution. We show that the nuclear distribution can be strongly modified by the HHG driving laser. The validity of this model is first checked against results from the numerical solution of the time-dependent Schrödinger equation for a simple model system. We show that in combination with the established quantitative rescattering theory this model is able to reproduce the time-resolved pump-probe HHG spectra of N(2)O(4) reported by Li et al. [Science 322, 1207 (2008)].

Application of discrete variable representation to planar H2+ in strong xuv laser fields

We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.

Imaging orbitals with attosecond and Ångström resolutions: toward attochemistry?

The recently developed attosecond light sources make the investigation of ultrafast processes in matter possible with unprecedented time resolution. It has been proposed that the very mechanism underlying the attosecond emission allows the imaging of valence orbitals with Ångström space resolution. This controversial idea together with the possibility of combining attosecond and Ångström resolutions in the same measurements has become a hot topic in strong-field science. Indeed, this could provide a new way to image the evolution of the molecular electron cloud during, e.g. a chemical reaction in 'real time'. Here we review both experimental and theoretical challenges raised by the implementation of these prospects. In particular, we show how the valence orbital structure is encoded in the spectral phase of the recombination dipole moment calculated for Coulomb scattering states, which allows a tomographic reconstruction of the orbital using first-order corrections to the plane-wave approach. The possibility of disentangling multi-channel contributions to the attosecond emission is discussed as well as the necessary compromise between the temporal and spatial resolutions.

Monitoring atomic cluster expansion by high-harmonic generation

High-harmonic generation is shown to be capable of providing time-resolved information about the particle density of a complex system. As an example, we study numerically high-harmonic generation from expanding xenon clusters in a pump-probe laser scheme, where the pump laser pulse induces the cluster explosion and the probe pulse generates harmonics in the expanding cluster. We show that the high-harmonic spectra characterize the properties of the expanding cluster. Hence, measuring the dependence of the harmonic signal on the pump-probe delay suggests itself as an experimental tool to monitor many-particle dynamics with unique temporal resolution; based on optical measurements, this technique is naturally free from any spatial charge effects.

Strong field ionization to multiple electronic states in water

High harmonic spectra show that laser-induced strong field ionization of water has a significant contribution from an inner-valence orbital. Our experiment uses the ratio of H(2)O and D(2)O high harmonic yields to isolate the characteristic nuclear motion of the molecular ionic states. The nuclear motion initiated via ionization of the highest occupied molecular orbital (HOMO) is small and is expected to lead to similar harmonic yields for the two isotopes. In contrast, ionization of the second least bound orbital (HOMO-1) exhibits itself via a strong bending motion which creates a significant isotope effect. We elaborate on this interpretation by solving the time-dependent Schrödinger equation to simulate strong field ionization and high harmonic generation from the water isotopes. We expect that this isotope marking scheme for probing excited ionic states in strong field processes can be generalized to other molecules.

Attosecond resolved electron release in two-color near-threshold photoionization of N2

We have simulated two-color photoionization of N(2) by solving the time-dependent Schrödinger equation with a simple model accounting for the correlated vibronic dynamics of the molecule and of the ion N(2)(+). Our results, in very good agreement with recent experiments [Haessler et al., Phys. Rev. A 80, 011404 (2009)], show how a resonance embedded in the molecular continuum dramatically affects the phases of the two-photon transition amplitudes. In addition, we introduce a formal relation between these measurable phases and the photoelectron release time, opening the way to attosecond time-resolved measurements, equivalent to double-slit experiments in the time domain.

Molecular high harmonic generation in a two-color field

We experimentally investigate the high harmonic generation (HHG) from CH4 molecules and Xe atoms in a two-color field (using the 800 nm laser and the tunable laser with the longer wavelength from 1500 nm to 1900 nm), and observe that the longer wavelength component can destructively suppress the HHG from CH4 molecules. By controlling the time delay between the two color laser pulses or tuning the laser intensity of the longer wavelength component, the suppressions of the HHG from CH4 molecules and the enhancements of the HHG from Xe atoms at the same laser condition are observed. The results indicate that the longer wavelength component around the molecular infrared absorption can suppress the molecular HHG process.

Yoctosecond photon pulses from quark-gluon plasmas

Present ultrafast laser optics is at the frontier between atto- and zeptosecond photon pulses, giving rise to unprecedented applications. We show that high-energetic photon pulses down to the yoctosecond time scale can be produced in heavy-ion collisions. We focus on photons produced during the initial phase of the expanding quark-gluon plasma. We study how the time evolution and properties of the plasma may influence the duration and shape of the photon pulse. Prospects for achieving double-peak structures suitable for pump-probe experiments at the yoctosecond time scale are discussed.

Strong-field control and spectroscopy of attosecond electron-hole dynamics in molecules

Molecular structures, dynamics and chemical properties are determined by shared electrons in valence shells. We show how one can selectively remove a valence electron from either Pi vs. Sigma or bonding vs. nonbonding orbital by applying an intense infrared laser field to an ensemble of aligned molecules. In molecules, such ionization often induces multielectron dynamics on the attosecond time scale. Ionizing laser field also allows one to record and reconstruct these dynamics with attosecond temporal and sub-Angstrom spatial resolution. Reconstruction relies on monitoring and controlling high-frequency emission produced when the liberated electron recombines with the valence shell hole created by ionization.

Wavelength effect on atomic and molecular high harmonic generation driven by a tunable infrared parametric source

We experimentally investigate the wavelength effect on high-order harmonic generation (HHG) in CH(4) molecules and Xe atoms driven by a tunable infrared parametric source, and observe that the molecular HHG around the vibrational resonance is more sensitive to the driver wavelength than HHG from an atomic gas with comparable ionization potential. The results can be attributed to the light nuclear motion induced by the driving laser field, and it becomes possible to control the proton vibration in the molecular HHG by tuning the infrared wavelength of the driving laser.

High harmonic interferometry of multi-electron dynamics in molecules

High harmonic emission occurs when an electron, liberated from a molecule by an incident intense laser field, gains energy from the field and recombines with the parent molecular ion. The emission provides a snapshot of the structure and dynamics of the recombining system, encoded in the amplitudes, phases and polarization of the harmonic light. Here we show with CO(2) molecules that high harmonic interferometry can retrieve this structural and dynamic information: by measuring the phases and amplitudes of the harmonic emission, we reveal 'fingerprints' of multiple molecular orbitals participating in the process and decode the underlying attosecond multi-electron dynamics, including the dynamics of electron rearrangement upon ionization. These findings establish high harmonic interferometry as an effective approach to resolving multi-electron dynamics with sub-Angström spatial resolution arising from the de Broglie wavelength of the recombining electron, and attosecond temporal resolution arising from the timescale of the recombination event.

Nuclear dynamics in polyatomic molecules and high-order harmonic generation

High-order harmonic generation in molecular gases is accompanied by short-time evolution of the nuclear vibrational wave function. Using normal coordinate representation, I derive a simple analytical theory of short-time autocorrelation functions and apply it to a test set of 15 small molecules. The results explain large isotope effects observed in CH4. At the harmonic cutoff in 800 nm driving field, nuclear dynamics reduces the emission intensity from NO and NO2 molecules by more than 50%. Autocorrelation functions are sensitive to the initial vibrational state, with the nodal structure of the initial vibrational wave packet reflected in the frequency spectrum of the harmonics.

Attosecond circular dichroism spectroscopy of polyatomic molecules

We describe the roles of multiple electronic continua in high-harmonic generation from aligned molecules. First, we show how the circularity of emitted harmonics tracks the interplay of different electronic continua participating in the nonlinear response. Second, we show that the interplay of different continua can lead to large variations of harmonic phases. Finally, we show how multiple electronic continua allow one to shape the polarization of high harmonics and attosecond pulses.

Effect of nuclear motion on molecular high-order harmonics and on generation of attosecond pulses in intense laser pulses

We calculate harmonic spectra and shapes of attosecond-pulse trains using numerical solutions of Non-Born-Oppenheimer time-dependent Shrödinger equation for 1D H2 molecules in an intense laser pulse. A very strong signature of nuclear motion is seen in the time profiles of high-order harmonics. In general the nuclear motion shortens the part of the attosecond-pulse train originating from the first electron contribution, but it may enhance the second electron contribution for longer pulses. The shape of time profiles of harmonics can thus be used for monitoring the nuclear motion.

Dynamic two-center interference in high-order harmonic generation from molecules with attosecond nuclear motion

We report a new dynamic two-center interference effect in high-harmonic generation from H2, in which the attosecond nuclear motion of H2+ initiated at ionization causes interference to be observed at lower harmonic orders than would be the case for static nuclei. To enable this measurement we utilize a recently developed technique for probing the attosecond nuclear dynamics of small molecules. The experimental results are reproduced by a theoretical analysis based upon the strong-field approximation which incorporates the temporally dependent two-center interference term.

Attosecond-resolution quantum dynamics calculations for atoms and molecules in strong laser fields

A parallel quantum electron and nuclei wave packet computer code, LZH-DICP, has been developed to study laser-atom-molecule interaction in the nonperturbative regime with attosecond resolution. The nonlinear phenomena occurring in that regime can be studied with the code in a rigorous way by numerically solving the time-dependent Schrödinger equation of electrons and nuclei. Time propagation of the wave functions is performed using a split-operator approach, and based on a sine discrete variable representation. Photoelectron spectra for hydrogen and kinetic-energy spectra for molecular hydrogen ion in linearly polarized laser fields are calculated using a flux operator scheme, which testifies to the validity and the high efficiency of LZH-DICP.

High-order harmonic transient grating spectroscopy in a molecular jet

We study high-order harmonic generation in excited media using a four-wave-mixing-like configuration. We analyze the spatial profile of high harmonics emitted by a grating of rotationally excited molecules as a function of the pump-probe delay. We demonstrate a dramatic improvement in the contrast of the diffracted signal relative to the total high harmonic signal. This allows us to observe subtle effects in the rotational wave packet excitation such as the pump-intensity dependence of the wave packet dynamics. High harmonic transient grating spectroscopy can be extended to all forms of molecular excitation and to weak resonant excitation.

Effective fields in laser-driven electron recollision and charge localization

We propose a model to describe correlated two-electron dynamics in strong laser fields during laser-induced recollision between an electron and its parent ion. We derive an effective interaction potential which describes the effect of the laser-driven electron collision with an ion while retaining the correlation between the colliding and the bound electron. Using dissociative ionization of molecular hydrogen as an example, we analyze the dynamics of correlation-driven electron localization in a dissociating hydrogen molecular ion.

Ultrafast electronuclear dynamics of H(2) double ionization

The ultrafast electronic and nuclear dynamics of H(2) laser-induced double ionization is studied using a time-dependent wave packet approach that goes beyond the fixed nuclei approximation. The double ionization pathways are analyzed by following the evolution of the total wave function during and after the pulse. The rescattering of the first ionized electron produces a coherent superposition of excited molecular states which presents a pronounced transient H(+)H(-) character. This attosecond excitation is followed by field-induced double ionization and by the formation of short-lived autoionizing states which decay via double ionization. These two double ionization mechanisms may be identified by their signatures imprinted in the kinetic-energy distribution of the ejected protons.

High harmonic generation and molecular orbital tomography in multielectron systems

High harmonic radiation is produced when atoms or molecules are ionized by an intense femtosecond laser pulse. The radiated spectrum has been shown experimentally to contain information on the electronic structure of the molecule, which can be interpreted as an image of a single molecular orbital. Previous theory for high harmonic generation has been limited to the single-active-electron approximation. Utilizing semisudden approximation, the authors develop a theory of the recombination step in high harmonic generation and tomographic reconstruction in multielectron systems, taking into account electron spin statistics and electron-electron correlations within the parent molecule and the ion. They show that the resulting corrections significantly modify the theoretical predictions, and bring them in a better agreement with experiment. They further show that exchange contributions to harmonic radiation can be used to extract additional information on the electronic wave function.

Enhanced recollisions for antisymmetric molecular orbitals in intense laser fields

The peculiarities of antisymmetric molecular orbitals are investigated in very intense linearly polarized laser pulses. For this purpose, the ionization-recollision quantum dynamics is evaluated theoretically beyond the dipole approximation. As opposed to the usual situation, the laser magnetic field component is found to strongly enhance recollision probabilities for particularly oriented antisymmetric molecular orbitals. Harmonic generation and related processes are thus allowed at high laser intensities without the common limitations by the laser magnetic field.

Monitoring molecular dynamics using coherent electrons from high harmonic generation

We report a previously undescribed spectroscopic probe that makes use of electrons rescattered during the process of high-order harmonic generation. We excite coherent vibrations in SF(6) using impulsive stimulated Raman scattering with a short laser pulse. A second, more intense laser pulse generates high-order harmonics of the fundamental laser, at wavelengths of approximately 20-50 nm. The high-order harmonic yield is observed to oscillate, at frequencies corresponding to all of the Raman-active modes of SF(6), with an asymmetric mode most visible. The data also show evidence of relaxation dynamics after impulsive excitation of the molecule. Theoretical modeling indicates that the high harmonic yield should be modulated by both Raman and infrared-active vibrational modes. Our results indicate that high harmonic generation is a very sensitive probe of vibrational dynamics and may yield more information simultaneously than conventional ultrafast spectroscopic techniques. Because the de Broglie wavelength of the recolliding electron is on the order of interatomic distances, i.e., approximately 1.5 A, small changes in the shape of the molecule lead to large changes in the high harmonic yield. This work therefore demonstrates a previously undescribed spectroscopic technique for probing ultrafast internal dynamics in molecules and, in particular, on the chemically important ground-state potential surface.

Probing Proton Dynamics in Molecules on an Attosecond Time Scale

We demonstrate a technique that uses high-order harmonic generation in molecules to probe nuclear dynamics and structural rearrangement on a subfemtosecond time scale. The chirped nature of the electron wavepacket produced by laser ionization in a strong field gives rise to a similar chirp in the photons emitted upon electron-ion recombination. Use of this chirp in the emitted light allows information about nuclear dynamics to be gained with 100-attosecond temporal resolution, from excitation by an 8-femtosecond pulse, in a single laser shot. Measurements on molecular hydrogen and deuterium agreed well with calculations of ultrafast nuclear dynamics in the H2+ molecule, confirming the validity of the method. We then measured harmonic spectra from CH4 and CD4 to demonstrate a few-femtosecond time scale for the onset of proton rearrangement in methane upon ionization.