Cold Target Recoil Ion Momentum Spectroscopy: a &momentum microscope' to view atomic collision dynamics

The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

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Interactions between Light Waves in a Nonlinear Dielectric

Molecular structures are imaged with sub-angstrom precision and exposure times of a few femtoseconds. Molecular imaging, or the determination of the positions of atoms in molecules, is an important technique in the physical, chemical and biological sciences. But going beyond mere structure determination, recent technical developments offer the tantalizing prospect of access to ultrafast snapshots of biological molecules and condensed-phase systems undergoing structural changes. One approach uses laser-ionized bursts of coherent electron wave packets to self-interrogate the parent molecular structure. Here, Blaga et al. use this laser-induced electron diffraction (LIED) method to map the structural responses of oxygen and nitrogen molecules to ionization. By measuring a 0.1-angstrom displacement in the oxygen bond length occurring in a time interval of about 5 femtoseconds, the authors establish LIED as a promising approach for imaging of gas-phase molecules with unprecedented spatio-temporal resolution. Establishing the structure of molecules and solids has always had an essential role in physics, chemistry and biology. The methods of choice are X-ray and electron diffraction, which are routinely used to determine atomic positions with sub-angstrom spatial resolution. Although both methods are currently limited to probing dynamics on timescales longer than a picosecond, the recent development of femtosecond sources of X-ray pulses and electron beams suggests that they might soon be capable of taking ultrafast snapshots of biological molecules1,2 and condensed-phase systems3,4,5,6 undergoing structural changes. The past decade has also witnessed the emergence of an alternative imaging approach based on laser-ionized bursts of coherent electron wave packets that self-interrogate the parent molecular structure7,8,9,10,11. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction10 (LIED), to image molecular structures with sub-angstrom precision and exposure times of a few femtoseconds. We apply the method to oxygen and nitrogen molecules, which on strong-field ionization at three mid-infrared wavelengths (1.7, 2.0 and 2.3 μm) emit photoelectrons with a momentum distribution from which we extract diffraction patterns. The long wavelength is essential for achieving atomic-scale spatial resolution, and the wavelength variation is equivalent to taking snapshots at different times. We show that the method has the sensitivity to measure a 0.1 A displacement in the oxygen bond length occurring in a time interval of ∼5 fs, which establishes LIED as a promising approach for the imaging of gas-phase molecules with unprecedented spatio-temporal resolution.

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Imaging ultrafast molecular dynamics with laser-induced electron diffraction

Advances in attosecond science have led to a wealth of important discoveries in atomic, molecular, and solid-state physics and are progressively directing their footsteps toward problems of chemical interest. Relevant technical achievements in the generation and application of extreme-ultraviolet subfemtosecond pulses, the introduction of experimental techniques able to follow in time the electron dynamics in quantum systems, and the development of sophisticated theoretical methods for the interpretation of the outcomes of such experiments have raised a continuous growing interest in attosecond phenomena, as demonstrated by the vast literature on the subject. In this review, after introducing the physical mechanisms at the basis of attosecond pulse generation and attosecond technology and describing the theoretical tools that complement experimental research in this field, we will concentrate on the application of attosecond methods to the investigation of ultrafast processes in molecules, with emphasis i...

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Attosecond Electron Dynamics in Molecules.

The emerging application of attosecond techniques to molecular systems allows the role of electronic coherence in the control of chemical reactions to be investigated. Prompt ionization of molecules by an attosecond pulse may induce charge migration across a molecular structure on attosecond to few-femtosecond timescales, thereby possibly determining the subsequent relaxation pathways that a molecule may take. We discuss how proposals for this 'charge-directed reactivity' fit within the current understanding of quantum control and review the current state of the art of attosecond molecular science. Specifically, we review the role of electronic coherence and coupling of the electronic and nuclear degrees of freedom in high-harmonic spectroscopy and in the first attosecond pump–probe experiments on molecular systems. Attosecond science allows the role of electronic coherence in the control of chemical reactions in molecular systems to be investigated. This article reviews recent activities in attosecond molecular science and identifies some promising directions for further development.

Attosecond molecular dynamics: fact or fiction?

When an atom or molecule is exposed to a short intense laser pulse, electrons that were removed at an earlier time may be driven back by the oscillating electric field of the laser to recollide with the parent ion, to incur processes like high-order harmonic generation (HHG), high-energy above-threshold ionization (HATI) and nonsequential double ionization (NSDI). Over the years, a rescattering model (the three-step model) has been used to understand these strong field phenomena qualitatively, but not quantitatively. Recently we have established such a quantitative rescattering (QRS) theory. According to QRS, the yields for HHG, HATI and NSDI can be expressed as the product of a returning electron wave packet with various field-free electron–ion scattering cross sections, namely photo-recombination, elastic electron scattering and electron-impact ionization, respectively. The validity of QRS is first demonstrated by comparing with accurate numerical results from solving the time-dependent Schrodinger equation (TDSE) for atoms. It is then applied to atoms and molecules to explain recent experimental data. According to QRS, accurate field-free electron scattering and photoionization cross sections can be obtained from the HATI and HHG spectra, respectively. These cross sections are the conventional tools for studying the structure of a molecule; thus, QRS serves to provide the required theoretical foundation for the self-imaging of a molecule in strong fields by its own electrons. Since infrared lasers of duration of a few femtoseconds are readily available today, these results imply that they are suitable for probing the dynamics of molecules with temporal resolutions of a few femtoseconds.

https://iopscience.iop.org/article/10.1088/0953-4075/43/12/122001/pdf

Strong-field rescattering physics: self—imaging of a molecule by its own electrons

High-order harmonic spectra from solid materials driven by single-color multicycle laser fields sometimes contain even harmonics. In this work we attribute the appearance of even harmonics to the nonzero transition dipole phase (TDP) when the solid system has broken symmetry. By calculating the harmonic efficiency from graphene and gapped graphene by using the semiconductor Bloch equations under the tight-binding approximation, we demonstrate the role of the TDP, which has been ignored for a long time. When the crystal has inversion symmetry, or reflection symmetry with the symmetry plane perpendicular to the laser polarization direction, the TDP can be neglected. Without such symmetry, however, the TDP will lead to the appearance of even harmonics. We further show that the TDP is sensitive to the crystal geometry. To extract the structure information from the harmonic spectra of a solid the TDP cannot be ignored.

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Effect of transition dipole phase on high-order-harmonic generation in solid materials

In the strong field molecular tunneling ionization theory of Tong et al. [Phys. Rev. A 66, 033402 (2002)], the ionization rate depends on the asymptotic wave function of the molecular orbital from which the electron is removed. The orbital wave functions obtained from standard quantum chemistry packages in general are not good enough in the asymptotic region. Here we construct a one-electron model potential for several linear molecules using density functional theory. We show that the asymptotic wave function can be improved with an iteration method and after one iteration accurate asymptotic wave functions and structure parameters are determined. With the new parameters we examine the alignment-dependent tunneling ionization probabilities for several molecules and compare with other calculations and with recent measurements, including ionization from inner molecular orbitals.

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New determination of structure parameters in strong field tunneling ionization theory of molecules

Doubly excited states of atoms were first detected and discussed in the 30’s,1 but their systematic study dates from the UV photoabsorption spectroscopy of helium in the early 60’s by Madden and Codling.2–3 In the spectra, two series of resonances, one intense and the other fainter and sharper, were observed. These resonances were attributed to the temporary formation of discrete states of the doubly excited intermediate, He , which eventually autoionize into He+ (N=1)+e- . It took the great insight of Fano to recognize the important implication of the observed strong contrast in the strength of the two series. Cooper, Fano and Prats argued that these doubly excited states cannot be adequately described by the independent electron model. The designation of states such as 2snp and 2pns P° would imply that the two series have nearly identical strength. They pointed out that the experimental data indicated that the two series are better approximated as 2snp+2pns and 2snp-2pns, and labelled as the ‘+’ and the ‘-’ series, respectively.

Classification of Doubly Excited States of Two-Electron Atoms

Electron excitation and transfer to 2s and 2p states in H/sup +/-H 1s collisions is studied in the energy range from 1 to 20 keV with the use of a modified two-center atomic-expansion method. It is shown that the inclusion of united-atom orbitals, in addition to the atomic orbitals of the separated atoms, in a two-center expansion allows for the extension of this method to the low-collision-energy regime. The results of our calculations at low energies from 1 to 5 keV agree with experiments and with the recent multistate molecular-orbital calculations by Kimura and Thorson but differ from the molecular-orbital calculations by Crothers and Hughes. At higher energies our results agree qualitatively with experiments and confirm the dip in 2s and 2p excitation cross sections at Eapprox.11 keV. The impact-parameter dependence of excitation and capture probabilities is also examined to illustrate the evolution of the excitation mechanism from the rotational coupling at lower collision energies to the direct excitation process at higher energies.

C. D. Lin

Papers

Strong-field rescattering physics: self—imaging of a molecule by its own electrons

Effect of transition dipole phase on high-order-harmonic generation in solid materials

New determination of structure parameters in strong field tunneling ionization theory of molecules

Classification of Doubly Excited States of Two-Electron Atoms

Excitation and charge transfer to 2s and 2p states in 1--20-keV H/sup +/-H collisions