Structure factors for tunneling ionization rates of molecules: General grid-based methodology and convergence studies.

We present a general methodology for evaluating structure factors defining the orientation dependence of tunneling ionization rates of molecules, which is a key process in strong-field physics. The method is implemented at the Hartree-Fock level of electronic structure theory and is based on an integral-equation approach to the weak-field asymptotic theory of tunneling ionization, which expresses the structure factor in terms of an integral involving the ionizing orbital and a known analytical function. The evaluation of the required integrals is done by three-dimensional quadrature which allows calculations using conventional quantum chemistry software packages. This extends the applications of the weak-field asymptotic theory to polyatomic molecules of almost arbitrary size. The method is tested by comparison with previous results and illustrated by calculating structure factors for the two degenerate highest occupied molecular orbitals (HOMOs) of benzene and for the HOMO and HOMO-1 of naphthalene.

Near-Forward Rescattering Photoelectron Holography in Strong-Field Ionization: Extraction of the Phase of the Scattering Amplitude.

We revisit the concept of near-forward rescattering strong-field photoelectron holography introduced by Y. Huismans et al. [Science 331, 61 (2011)]. The recently developed adiabatic theory is used to show how the phase of the scattering amplitude for near-forward rescattering of an ionized electron by the parent ion is encoded in and can be read out from the corresponding interference pattern in photoelectron momentum distributions (PEMDs) produced in the ionization of atoms and molecules by intense laser pulses. A procedure to extract the phase is proposed. Its application to PEMDs obtained by solving the time-dependent Schrödinger equation for a model atom yields results in good agreement with scattering calculations. This establishes a novel general approach to extracting structural information from strong-field observables capable of providing time-resolved imaging of ultrafast processes.

Imaging Electronic Excitation of NO by Ultrafast Laser Tunneling Ionization.

Tunneling-ionization imaging of photoexcitation of NO has been demonstrated by using few-cycle near-infrared intense laser pulses (8 fs, 800 nm, 1.1×10^{14} W/cm^{2}). The ion image of N^{+} fragment ions produced by dissociative ionization of NO in the ground state, NO (X^{2}Π,2π)→NO^{+}+e^{-}→N^{+}+O+e^{-}, exhibits a characteristic momentum distribution peaked at 45° with respect to the laser polarization direction. On the other hand, a broad distribution centered at ∼0° appears when the A^{2}Σ^{+} (3sσ) excited state is prepared as the initial state by deep-UV photoexcitation. The observed angular distributions are in good agreement with the corresponding theoretical tunneling ionization yields, showing that the fragment anisotropy reflects changes of the highest-occupied molecular orbital by photoexcitation.

Role of Multi-Electron Effects in the Asymmetry of Strong-Field Ionization and Fragmentation of Polar Molecules: The Methyl Halide Series.

We report angle- and momentum-resolved measurements of the dissociative ionization and Coulomb explosion of methyl halides (CH3F, CH3Cl, CH3Br, and CH3I) in intense phase-controlled two-color laser fields. At moderate laser intensities, we find that the emission asymmetry of low-energy CH3(+) fragments from the CH3(+) + X(+) (X = F, Cl, Br, or I) channel reflects the asymmetry of the highest occupied molecular orbital of the neutral molecule with important contributions from the Stark effect. This asymmetry is correctly predicted by the weak-field asymptotic theory, provided that the Stark effect on the ionization potentials is calculated using a nonperturbative multielectron approach. In the case of high laser intensities, we observe a reversal of the emission asymmetries for high-energy CH3(+) fragments, originating from the dissociation of CH3X(q+) with q ≥ 2. We propose ionization to electronically excited states to be at the origin of the reversed asymmetries. We also report the measurements of the emission asymmetry of H3(+), which is found to be identical to that of the low-energy CH3(+) fragments measured at moderate laser intensities. All observed fragmentation channels are assigned with the help of CCSD(T) calculations. Our results provide a benchmark for theories of strong-field processes and demonstrate the importance of multielectron effects in new aspects of the molecular response to intense laser fields.

High-harmonic spectroscopy of impulsively aligned 1,3-cyclohexadiene: Signatures of attosecond charge migration.

High-harmonic spectroscopy is an all-optical technique with inherent attosecond temporal resolution that has been successfully employed to reconstruct charge migration, electron-tunneling dynamics, and conical-intersection dynamics. Here, we demonstrate the extension of two key components of high-harmonic spectroscopy, i.e., impulsive alignment and measurements with multiple driving wavelengths to 1,3-cyclohexadiene and benzene. In the case of 1,3-cyclohexadiene, we find that the temporal sequence of maximal and minimal emitted high-harmonic intensities as a function of the delay between the alignment and probe pulses inverts between 25 and 30 eV and again between 35 and 40 eV when an 800-nm driver is used, but no inversions are observed with a 1420-nm driver. This observation is explained by the wavelength-dependent interference of emission from multiple molecular orbitals (HOMO to HOMO-3), as demonstrated by calculations based on the weak-field asymptotic theory and accurate photorecombination matrix elements. These results indicate that attosecond charge migration takes place in the 1,3-cyclohexadiene cation and can potentially be reconstructed with the help of additional measurements. Our experiments also demonstrate a pathway toward studying photochemical reactions in the molecular frame of 1,3-cyclohexadiene.

Retardation effects and the Born-Oppenheimer approximation: theory of tunneling ionization of molecules revisited.

We show that retardation in adjusting an electronic state to an instantaneous internuclear configuration caused by the finiteness of the electron's velocity breaks the validity of the Born-Oppenheimer (BO) approximation at large electron-nuclei distances. This applies even to the ground state. As a result, the BO approximation in the theory of tunneling ionization of molecules breaks down at sufficiently weak fields. We also show that to account for nuclear motion the weak-field asymptotic expansion for the tunneling ionization rate must be restructured. The predictions for the rate using the BO approximation and the asymptotic expansion are compared with numerical results for a one-dimensional three-body system modeling a diatomic molecule, with both electronic and nuclear motions treated exactly.

Asymmetric Dissociative Tunneling Ionization of Tetrafluoromethane in ω - 2ω Intense Laser Fields.

Dissociative ionization of tetrafluoromethane (CF4) in linearly polarized ω-2ω ultrashort intense laser fields (1.4 × 1014 W/cm2, 800 and 400 nm) has been investigated by three-dimensional momentum ion imaging. The spatial distribution of C F 3 + produced by CF4 → C F 3 + + F + e- exhibited a clear asymmetry with respect to the laser polarization direction. The degree of the asymmetry varies by the relative phase of the ω and 2ω laser fields, showing that 1) the breaking of the four equivalent C-F bonds can be manipulated by the laser pulse shape and 2) the C-F bond directed along the larger amplitude side of the ω-2ω electric fields tends to be broken. Weak-field asymptotic theory (WFAT) shows that the tunneling ionization from the 4t 2 second highest-occupied molecular orbital (HOMO-1) surpasses that from the 1t 1 HOMO. This predicts the enhancement of the tunneling ionization with electric fields pointing from F to C, in the direction opposite to that observed for the asymmetric fragment ejection. Possible mechanisms involved in the asymmetric dissociative ionization, such as post-ionization interactions, are discussed.

Slow electrons generated by intense high-frequency laser pulses.

A very slow electron is shown to emerge when an intense high-frequency laser pulse is applied to a hydrogen negative ion. This counterintuitive effect cannot be accounted for by multiphoton or tunneling ionization mechanisms. We explore the effect and show that in the high-frequency regime the atomic electron is promoted to the continuum via a nonadiabatic transition caused by slow deformation of the dressed potential that follows a variation of the envelope of the laser pulse. This is a general mechanism, and a slow electron peak should always appear in the photoelectron spectrum when an atom is irradiated by a high-frequency pulse of finite length.