Signature of Molecular Orbital Symmetry in High-Order Harmonic Generation by Bichromatic Circularly Polarized Laser Pulses.

Molecular orbital symmetry is shown to be an important factor in determining orders and helicities (polarizations) of high-order harmonic generation (HHG) by intense femtosecond counter-rotating bichromatic circularly polarized laser pulses. Numerical solutions of time-dependent Schrödinger equations (TDSE) for the one-electron molecular ions H2+ and H32+ for different initial electronic states show that harmonic orders and helicities are dependent on orbital symmetries and of the net incident pulse electric field. The numerical results and properties of the harmonics are described by dynamical symmetry theory and time profile analysis of the high-order harmonics, thus confirming that orbital and laser pulse symmetry dependence are generic in HHG of molecules.

Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses.

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrödinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.

Ultrafast X-ray photoelectron diffraction in triatomic molecules by circularly polarized attosecond light pulses.

We theoretically study ultrafast photoelectron diffraction in triatomic molecules with cyclic geometry by ultrafast circular soft X-ray attosecond pulses. Molecular frame photoelectron distributions show complex diffraction patterns, arising from molecular multiple center interference and circular charge migration. It is found that photoelectron diffraction patterns depend on the initial electronic state, encoding the information of molecular orbital symmetries. In a resonant coherent electron excitation process, time-resolved photoelectron diffraction patterns enables us to reconstruct the charge migration with highly spatiotemporal resolutions. We simulate and analyze the results from ab initio calculations of the single electron triangular hydrogen molecular ion H32+ which is used as a benchmark molecular system in combination with an ultrafast multi-center and multi-state photoionization model. This approach presents a general scheme which can be applied to explore circular charge migration from electron orbits and attosecond coherent electron dynamics in polyatomic systems by circular ultrafast laser pulses.

Ultrafast X-ray Photoelectron Imaging of Attosecond Electron Dynamics in Molecular Coherent Excitation.

Ultrafast photoelectron imaging allows to measure information about coherent electron dynamic processes in materials or chemical compounds on femtosecond to attosecond time scales. We show that molecular time-resolved photoelectron diffraction produced by a time-delayed soft X-ray attosecond pulse can be used to monitor the ultrafast coherent excitation induced by a resonant UV pump pulse with variable carrier-envelope phases. Asymmetric diffraction angular patterns illustrate coherent electron dynamics of charge migration with spatiotemporal resolution on the attosecond and ångström scale. This allows the temporal reconstruction of phases and amplitudes of electronic states and geometry of molecules as a function of time delay of the probe pulse and carrier-envelope phases of the pump pulse. Results are obtained from solutions of time-dependent Schrödinger equations of the hydrogen molecular ion, and analyzed by ultrafast photoelectron diffraction models for coherent superposition of electronic states. The present demonstration provides a guiding principle for monitoring ultrafast spatiotemporal coherent electron dynamics and imaging molecular electronic structure in complex systems by ultrafast pump-probe experiments and their dependence on carrier-envelope phases and time delays.

Time-Resolved Photoelectron Imaging of Molecular Coherent Excitation and Charge Migration by Ultrashort Laser Pulses.

Charge migration is a fundamental and important process in the photochemistry of molecules and has been explored by time-resolved photoelectron angular distributions. A scheme based on UV pump and polarized soft X-ray probe techniques shows that photoelectron diffraction effects enable us to reconstruct electronic coherences encoding the information of the charge migration with extreme time resolutions. We discuss how probe pulse helicity influences the probing photoelectron spectra in the presence of molecular nonspherical Coulomb potentials. This phenomenon is analyzed theoretically and simulated via ab initio calculations for the molecular hydrogen ion, offering a reliable approach for measurements of charge migration and for the exploration of molecular structure in attosecond science.

Exploring coherent electron excitation and migration dynamics by electron diffraction with ultrashort X-ray pulses.

Exploring ultrafast charge migration is of great importance in biological and chemical reactions. We present a scheme to monitor attosecond charge migration in molecules by electron diffraction with spatial and temporal resolutions from ab initio numerical simulations. An ultraviolet pulse creates a coherent superposition of electronic states, after which a time-delayed attosecond X-ray pulse is used to ionize the molecule. It is found that diffraction patterns in the X-ray photoelectron spectra show an asymmetric structure, which is dependent on the time delay between the pump-probe pulses, encoding the information of molecular orbital symmetry and chemical bonding. We describe these phenomena by developing an electronic time-dependent ultrafast molecular photoionization model of a coherent superposition state. The periodical distortion of electron diffraction patterns illustrates the evolution of the electronic coherence, providing a tool for attosecond imaging of ultrafast molecular reaction processes.

Monitoring coherent electron wave packet excitation dynamics by two-color attosecond laser pulses.

We propose a method to monitor coherent electron wave packet (CEWP) excitation dynamics with two-color attosecond laser pulses. Simulations are performed on aligned H2+ by numerically solving the three-dimensional time-dependent Schrödinger equation with combinations of a resonant linearly polarized λl= 100/70 nm pump pulse and a circularly polarized λc=5 nm attosecond probe pulse. It is found that time dependent diffraction patterns in molecular frame photoelectron angular distributions (MFPADs) produced by the circular probe pulse exhibit sensitivity to the molecular alignments and time-dependent geometry of the CEWPs during and after the coherent excitation between the ground and excited states induced by the linear pump pulse. The time dependent MFPADs are described by an ultrafast diffraction model for the ionization of the bound CEWPs.

Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H2(+) by circularly polarized ultraviolet laser pulses.

We study effects of pulse durations on molecular photoelectron angular distributions (MPADs) in ultrafast circular polarization ultraviolet resonant ionization processes. Simulations performed on aligned H2 (+) by numerically solving time dependent Schrödinger equations show rotations of MPADs with respect to the molecular symmetry axes. It is found that in multi-photon resonant ionization processes, rotation angles are sensitive to pulse durations, which we attribute to the coherent resonant excitation between the ground state and the intermediate excited electronic state induced by Rabi oscillations. Multi-photon nonresonant and single photon ionization processes are simulated and compared which exhibit a constant rotation angle. An asymmetry parameter is introduced to describe the pulse duration sensitivity by perturbation theory models. Influence of pulse frequency detunings on MPADs is also investigated where oscillations of rotations are absent at long pulse durations due to nonresonance excitation.

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.

Photon momentum sharing between an electron and an ion in photoionization: from one-photon (photoelectric effect) to multiphoton absorption.

We investigate photon-momentum sharing between an electron and an ion following different photoionization regimes. We find very different partitioning of the photon momentum in one-photon ionization (the photoelectric effect) as compared to multiphoton processes. In the photoelectric effect, the electron acquires a momentum that is much greater than the single photon momentum ℏω/c [up to (8/5) ℏω/c] whereas in the strong-field ionization regime, the photoelectron only acquires the momentum corresponding to the photons absorbed above the field-free ionization threshold plus a momentum corresponding to a fraction (3/10) of the ionization potential Ip. In both cases, due to the smallness of the electron-ion mass ratio, the ion takes nearly the entire momentum of all absorbed N photons (via the electron-ion center of mass). Additionally, the ion takes, as a recoil, the photoelectron momentum resulting from mutual electron-ion interaction in the electromagnetic field. Consequently, the momentum partitioning of the photofragments is very different in both regimes. This suggests that there is a rich, unexplored physics to be studied between these two limits which can be generated with current ultrafast laser technology.

Single circularly polarized attosecond pulse generation by intense few cycle elliptically polarized laser pulses and terahertz fields from molecular media.

We present a method for producing a single circularly polarized attosecond pulse by an intense few cycle elliptically polarized laser pulse combined with a terahertz field from numerical solutions of the time-dependent Schrödinger equation for the molecular ion H2(+). It is found that in the presence of a 62.5 THz (λ=4800 nm) field at an intensity of ∼10(14) W/cm2, a single circularly polarized 114 as pulse can be generated by an elliptical polarized laser pulse at a wavelength of 400 nm with an ellipticity of ϵ=0.59. The efficiency of circular polarization attosecond pulse generation is interpreted based on a classical model of single electron recollision with the parent ion.

Resonantly enhanced pair production in a simple diatomic model.

A new mechanism for the production of electron-positron pairs from the interaction of a laser field and a fully ionized diatomic molecule in the tunneling regime is presented. When the laser field is turned off, the Dirac operator has resonances in both the positive and the negative energy continua while bound states are in the mass gap. When this system is immersed in a strong laser field, the resonances move in the complex energy plane: the negative energy resonances are pushed to higher energies while the bound states are Stark shifted [F. Fillion-Gourdeau et al., J. Phys. A 45, 215304 (2012)]. It is argued here that there is a pair production enhancement at the crossing of resonances by looking at a simple one-dimensional model: the nuclei are modeled simply by Dirac delta potential wells while the laser field is assumed to be static and of finite spatial extent. The average rate for the number of electron-positron pairs produced is evaluated and the results are compared to the one and zero nucleus cases. It is shown that positrons are produced by the resonantly enhanced pair production mechanism, which is analogous to the resonantly enhanced ionization of molecular physics. This phenomenon could be used to increase the number of pairs produced at low field strength, allowing the study of the Dirac vacuum.

Electron interference in molecular photoionization by attosecond laser pulses.

Molecular photoionization by intense attosecond linearly and circularly polarized X-ray laser pulses is investigated from numerical solutions of time-dependent Schrödinger equations for the one-electron systems H2(+) and H3(++). Both momentum stripes and rings in photoelectron angular distributions are observed. The first with momentum intervals Δp(s)=2 π/R, where R is the molecular internuclear distance, results from interference of the coherent continuum scattering electron wave packets, which is shown to be insensitive to the laser polarization and wavelength. Diffraction of the directly ionized electrons leads to the momentum rings defined by the angle theta(p(r)R=cos(-1)(2nπ)/p(r)R between the electron momentum p(r) and the molecular internuclear R axis. These patterns are well described by multi-center interference models. Such complex patterns allow us to probe intermolecular structures.

Dipole moment surfaces of the CH4 + •X → CH3• + HX (X = F, Cl) reactions from atomic dipole moment surfaces, and the origins of the sharp extrema of the dipole moments near the transition states.

The partitioning of the dipole moment of an isolated molecule or that of a reacting system is reviewed and applied to a dynamic reacting system whereby the system's dipole moment surface is constructed in parallel to its potential energy surface. The dipole moment surface is then decomposed into two origin-independent surfaces: (1) an atomic polarization (AP) surface and a charge transfer (CT) surface. The dipole moment surface as well as its two composing AP and CT surfaces are all further broken down into atomic and/or group contributions with the aid of the quantum theory of atoms in molecules (QTAIM). This approach is applied to the title's laser-induced chemical reactions [CH4 + (•)X → CH3(•) + HX (X = F, Cl)] previously studied by Bandrauk et al. [ J. Chem. Phys. 2004 , 121 , 7764 - 7775 ], and which were found to exhibit marked peaks in the dipole moment and in the polarizability tensor component at (or near) the transition state. These peaks afford a means to control the kinetics of these reactions with the proper adjustment of an external laser field intensity and phase. The entrance channel potentials of these reactions have recently been probed by photodetachment spectroscopy by Bowman and collaborators [ J. Chem. Phys. 2011 , 134 , 191102_1 - 4 ]. The understanding of the origin of the peaks in the dipole moment can provide, eventually, an additional layer of control in the design of reactions tunable by external fields through the proper selection of the reactants to maximize the field-molecule interaction.

Rotations of molecular photoelectron angular distributions with intense ultrashort circularly polarized attosecond laser pulses.

Molecular photoelectron angular distributions (MPADs) by intense (I0 ≥ 10(14) W/cm(2)) circularly polarized ultrashort, few cycle (attosecond) ultraviolet laser pulses are presented from numerical solutions of time dependent Schrödinger equations. For the aligned molecular ion H2(+), the MPADs exhibit rotations with respect to the polarization and molecular symmetry axes which are determined by the symmetry of the initial electronics states. It is also found that the rotation angle of MPADs is insensitive to the pulse intensity. We attribute these effects to the asymmetry between the parallel and perpendicular (to the molecular axis) polarization photoionization. Influence of the molecular alignment and ionizing pulse ellipticity on the rotation of MPADs is also shown to allow control of the nonsymmetric ionization.

Attosecond time-resolved imaging of molecular structure by photoelectron holography.

Dynamic imaging of the molecular structure of H(2)(+) is investigated by attosecond photoelectron holography. The interference between direct (reference) and backward rescattered (signal) photoelectrons in attosecond photoelectron holography reveals the birth time of both channels and the spatial information of molecular structure. This is confirmed by simulations with a semiclassical model and numerical solutions of the corresponding time-dependent Schrödinger equation, suggesting an attosecond time-resolved way of imaging molecular structure obtained from laser induced rescattering of ionized electrons. It is shown that both short and long rescattered electron trajectories can be imaged from the momentum distribution.

Effect of nuclear motion on molecular high order harmonic pump probe spectroscopy.

We study pump-probe schemes for the real time observation of electronic motion on attosecond time scale in the molecular ion H(2)(+) and its heavier isotope T(2)(+) while these molecules dissociate on femtosecond time scale by solving numerically the non-Born-Oppenheimer time-dependent Schrödinger equation. The UV pump laser pulse prepares a coherent superposition of the three lowest lying quantum states and the time-delayed mid-infrared, intense few-femtosecond probe pulse subsequently generates molecular high-order harmonics (MHOHG) from this coherent electron-nuclear wavepacket (CENWP). Varying the pump-probe time delay by a few hundreds of attoseconds, the MHOHG signal intensity is shown to vary by orders of magnitude. Due to nuclear movement, the coherence of these two upper states and the ground state is lost after a few femtoseconds and the MHOHG intensity variations as function of pump-probe delay time are shown to be equal to the period of electron oscillation in the coherent superposition of the two upper dissociative quantum states. Although this electron oscillation period and hence the periodicity of the harmonic spectra are quite constant over a wide range of internuclear distances, a strong signature of nuclear motion is seen in the actual shapes and ways in which these spectra change as a function of pump-probe delay time, which is illustrated by comparison of the MHOHG spectra generated by the two isotopes H(2)(+) and T(2)(+). Two different regimes corresponding roughly to internuclear distances R < 4a(0) and R > 4a(0) are identified: For R < 4a(0), the intensity of a whole range of frequencies in the plateau region is decreased by orders of magnitude when the delay time is changed by a few hundred attoseconds whereas in the cutoff region the peaks in the MHOHG spectra are red-shifted with increasing pump-probe time delay. For R > 4a(0), on the other hand, the peaks both in the cutoff and plateau region are red-shifted with increasing delay times with only slight variations in the peak intensities. A time-frequency analysis shows that in the case of a two-cycle probe pulse the sole contribution of one long and associated short trajectory correlates with the attenuation of a whole range of frequencies in the plateau region for R < 4a(0) whereas the observed red shift for R > 4a(0), even in the plateau region, correlates with a single electron return within one-half laser cycle.

Charge resonance enhanced ionization of CO2 probed by laser Coulomb explosion imaging.

The process by which a molecule in an intense laser field ionizes more efficiently as its bond length increases towards a critical distance R(c) is known as charge resonance enhanced ionization (CREI). We make a series of measurements of this process for CO(2), by varying pulse duration from 7 to 200 fs, in order to identify the charge states and time scales involved. We find that for the 4+ and higher charge states, 100 fs is the time scale required to reach the critical geometry ≈ 2.1 Å and <θ(OCO)> ≈ 163° (equilibrium CO(2) geometry is ≈ 1.16 Å and <θ(OCO)> ≈ 172°). The CO(2)(3+) molecule, however, appears always to begin dissociation from closer than 1.7 Å indicating that dynamics on charge states lower than 3+ is not sufficient to initiate CREI. Finally, we make quantum ab initio calculations of ionization rates for CO(2) and identify the electronic states responsible for CREI.

Long-range energy transfer and ionization in extended quantum systems driven by ultrashort spatially shaped laser pulses.

The processes of ionization and energy transfer in a quantum system composed of two distant H atoms with an initial internuclear separation of 100 atomic units (5.29 nm) have been studied by the numerical solution of the time-dependent Schrödinger equation beyond the Born-Oppenheimer approximation. Thereby it has been assumed that only one of the two H atoms was excited by temporally and spatially shaped laser pulses at various laser carrier frequencies. The quantum dynamics of the extended H-H system, which was taken to be initially either in an unentangled or an entangled ground state, has been explored within a linear three-dimensional model, including the two z coordinates of the electrons and the internuclear distance R. An efficient energy transfer from the laser-excited H atom (atom A) to the other H atom (atom B) and the ionization of the latter have been found. It has been shown that the physical mechanisms of the energy transfer as well as of the ionization of atom B are the Coulomb attraction of the laser driven electron of atom A by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions strongly overlap in the domain of atom B.