C. D. Lin

Imaging ultrafast molecular dynamics with laser-induced electron diffraction

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-ångström 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 molecules and condensed-phase systems 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 structure. Here we show that this phenomenon can indeed be exploited for laser-induced electron diffraction (LIED), to image molecular structures with sub-ångström 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 Å 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.

Empirical formula for static field ionization rates of atoms and molecules by lasers in the barrier-suppression regime

We propose an empirical formula for the static field ionization rates of atoms and molecules by extending the well-known analytical tunnelling ionization rates to the barrier-suppression regime. The validity of this formula is checked against ionization rates calculated from solving the Schrodinger equation for a number of atoms and ions. The empirical formula retains the simplicity of the original tunnelling ionization rate expression but can be used to calculate the ionization rates of atoms and molecules by lasers at high intensities.

Review of fundamental processes and applications of atoms and ions

This book reviews the major progress made in the fields of atomic, molecular and optical physics in the last decade. It contains eleven chapters in which contributors have highlighted the major accomplishments made in a given subfield. Each chapter is not a comprehensive review, but rather a succinct survey of the most interesting developments achieved in recent years. This book contains information on many AMO subfields and can be used as a textbook for graduate students interested in entering AMO physics. It may also serve researchers who wish to familiarize themselves with other AMO subfields.

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

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.

Doubly Excited States, Including New Classification Schemes

Publisher Summary This chapter discusses a method of calculating the position and width of each doubly excited state of atoms and the approximate selection rules for different excitation processes. There are many theoretical approaches which are capable of predicting an accurate position and width of each doubly excited state. These methods, such as the configuration interaction method, the Feshbach projection technique, the close-coupling method, and the complex coordinate rotation technique have provide significant data required for sorting out the systematics of doubly excited states. A classification scheme of doubly excited states using the correlation quantum numbers K, T , and A is presented in the chapter. The adoption of quantum numbers in the asymptotic region for the description of doubly excited states seems unsatisfactory because important correlations occur in the region where the two electrons are close to each other.

Imaging an aligned polyatomic molecule with laser-induced electron diffraction

Laser-induced electron diffraction is an evolving tabletop method that aims to image ultrafast structural changes in gas-phase polyatomic molecules with sub-Ångström spatial and femtosecond temporal resolutions. Here we demonstrate the retrieval of multiple bond lengths from a polyatomic molecule by simultaneously measuring the C–C and C–H bond lengths in aligned acetylene. Our approach takes the method beyond the hitherto achieved imaging of simple diatomic molecules and is based on the combination of a 160 kHz mid-infrared few-cycle laser source with full three-dimensional electron–ion coincidence detection. Our technique provides an accessible and robust route towards imaging ultrafast processes in complex gas-phase molecules with atto- to femto-second temporal resolution.

Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene

Acetylenes scission visualized by selfie Can molecules take pictures of themselves? That is more or less the principle underlying laser-induced electron diffraction (LIED): A laser field strips an electron from a molecule and then sends it back to report on the structure of the remaining ion. Wolter et al. applied this technique to acetylene to track the cleavage of its C–H bond after double ionization (see the Perspective by Ruan). They imaged the full structure of the molecule and also distinguished more rapid dissociative dynamics when it was oriented parallel rather than perpendicular to the LIED field. Science, this issue p. 308; see also p. 283 An electron transiently stripped from a molecule is used to image that molecules dissociation. Visualizing chemical reactions as they occur requires atomic spatial and femtosecond temporal resolution. Here, we report imaging of the molecular structure of acetylene (C2H2) 9 femtoseconds after ionization. Using mid-infrared laser–induced electron diffraction (LIED), we obtained snapshots as a proton departs the [C2H2]2+ ion. By introducing an additional laser field, we also demonstrate control over the ultrafast dissociation process and resolve different bond dynamics for molecules oriented parallel versus perpendicular to the LIED field. These measurements are in excellent agreement with a quantum chemical description of field-dressed molecular dynamics.

Quantitative rescattering theory for laser-induced high-energy plateau photoelectron spectra

A comprehensive quantitative rescattering QRS theory for describing the production of high-energy photoelectrons generated by intense laser pulses is presented. According to the QRS, the momentum distributions of these electrons can be expressed as the product of a returning electron wave packet with the elastic differential cross sections DCS between free electrons with the target ion. We show that the returning electron wave packets are determined mostly by the lasers only and can be obtained from the strong field approximation. The validity of the QRS model is carefully examined by checking against accurate results from the solution of the time-dependent Schrodinger equation for atomic targets within the single active electron approximation. We further show that experimental photoelectron spectra for a wide range of laser intensity and wavelength can be explained by the QRS theory, and that the DCS between electrons and target ions can be extracted from experimental photoelectron spectra. By generalizing the QRS theory to molecular targets, we discuss how few-cycle infrared lasers offer a promising tool for dynamic chemical imaging with temporal resolution of a few femtoseconds. DOI: 10.1103/PhysRevA.79.033409

Relativistic Random-Phase Approximation

The relativistic random phase approximation RRPA is developed from linearized time-dependent Hartree-Fock theory. Applications of the resulting relativistic many-body equations to determine excitation energies and oscillator strengths along the He, Be, Mg, Zn and Ne isoelectronic sequences are discussed and compared with other recent experimental and theoretical work. The multi-channel RRPA treatment of photoionization is described and applications are given to total cross sections, branching ratios, angular distributions and to autoionizing resonances.

Probing molecular frame photoionization via laser generated high-order harmonics from aligned molecules.

Present experiments cannot measure molecular frame photoelectron angular distributions (MFPAD) for ionization from the outermost valence orbitals of molecules. We show that the details of MFPAD can be retrieved with high-order harmonics generated by infrared lasers from aligned molecules. Using accurately calculated photoionization transition dipole moments for fixed-in-space molecules, we show that the dependence of the magnitude and phase of the high-order harmonics on the alignment angle of the molecules observed in recent experiments can be quantitatively reproduced. This result provides the needed theoretical basis for ultrafast dynamic chemical imaging using infrared laser pulses.