Retrieving angular distributions of high-order harmonic generation from a single molecule

Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Filming movies of attosecond charge migration in single molecules with high harmonic spectroscopy

Electron migration in molecules is the progenitor of chemical reactions and biological functions after light-matter interaction. Following this ultrafast dynamics, however, has been an enduring endeavor. Here we demonstrate that, by using machine learning algorithm to analyze high-order harmonics generated by two-color laser pulses, we are able to retrieve the complex amplitudes and phases of harmonics of single fixed-in-space molecules. These complex dipoles enable us to construct movies of laser-driven electron migration after tunnel ionization of N₂ and CO₂ molecules at time steps of 50 attoseconds. Moreover, the angular dependence of the migration dynamics is fully resolved. By examining the movies, we observe that electron holes do not just migrate along the laser polarization direction, but may swirl around the atom centers. Our result establishes a general scheme for studying ultrafast electron dynamics in molecules, paving a way for further advance in tracing and controlling photochemical reactions by femtosecond lasers.

All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation

An all-optical measurement of high-order fractional molecular echoes is demonstrated by using high-order harmonic generation (HHG). Excited by a pair of time-delayed short laser pulses, the signatures of full and high order fractional (1/2 and 1/3) alignment echoes are observed in the HHG signals measured from CO ₂ molecules at various time delays of the probe pulse. By increasing the time delay of the pump pulses, much higher order fractional (1/4) alignment echo is also observed in N ₂O molecules. With an analytic model based on the impulsive approximation, the spatiotemporal dynamics of the echo process are retrieved from the experiment. Compared to the typical molecular alignment revivals, high-order fractional molecular echoes are demonstrated to dephase more rapidly, which will open a new route towards the ultrashort-time measurement. The proposed HHG method paves an efficient way for accessing the high-order fractional echoes in molecules.

High-Harmonic and Terahertz Spectroscopy (HATS): Methods and Applications

Electrons driven from atom or molecule by intense dual-color laser fields can coherently radiate high harmonics from extreme ultraviolet to soft X-ray, as well as an intense terahertz (THz) wave from millimeter to sub-millimeter wavelength. The joint measurement of high-harmonic and terahertz spectroscopy (HATS) was established and further developed as a unique tool for monitoring electron dynamics of argon from picoseconds to attoseconds and for studying the molecular structures of nitrogen. More insights on the rescattering process could be gained by correlating the fast and slow electron motions via observing and manipulating the HATS from atoms and molecules. We also propose the potential investigations of HATS of polar molecules, and solid and liquid sources.

Real-Time Observation of Molecular Spinning with Angular High-Harmonic Spectroscopy

We demonstrate an angular high-harmonic spectroscopy method to probe the spinning dynamics of a molecular rotation wave packet in real time. With the excitation of two time-delayed, polarization-skewed pump pulses, the molecular ensemble is impulsively kicked to rotate unidirectionally, which is subsequently irradiated by another delayed probe pulse for high-order harmonic generation (HHG). The spatiotemporal evolution of the molecular rotation wave packet is visualized from the time-dependent angular distributions of the HHG yields and frequency shift measured at various polarization directions and time delays of the probe pulse. The observed frequency shift in HHG is demonstrated to arise from the nonadiabatic effect induced by molecular spinning. Different from the previous spectroscopic and Coulomb explosion imaging techniques, the angular high-harmonic spectroscopy method can reveal additionally the electronic structure and multiple orbitals of the sampled molecule. All the experimental findings are well reproduced by numerical simulations. Further extension of this method would provide a powerful tool for probing complex polyatomic molecules with HHG spectroscopy.

Single-shot molecular orbital tomography with orthogonal two-color fields

Molecular orbital tomography (MOT) based on high-order-harmonic generation opens a way to track the molecular electron dynamics or even follow a chemical reaction. However, the real-time imaging of the evolution of electron orbitals is hampered by the multi-shot measurement of high-order harmonics. Here, we report a single-shot MOT scheme with orthogonal two-color (OTC) fields. This scheme enables the tomographic imaging of molecular orbital with single-shot measurement in experiment, owing to the two-dimensional manipulation of the electron motion in OTC fields. Our work paves the way towards tracking the molecular electron dynamics with combined attosecond temporal and sub-Ångström spatial resolutions.

Coulomb-corrected molecular orbital tomography of nitrogen

High-order harmonic generation (HHG) from aligned molecules has provided a promising way to probe the molecular orbital with an Ångström resolution. This method, usually called molecular orbital tomography (MOT) replies on a simple assumption of the plane-wave approximation (PW), which has long been questioned due to that PW approximation is known to be valid in the keV energy region. However, the photon energy is usually no more than 100 eV in HHG. In this work, we experimentally reconstruct the highest occupied molecular orbital (HOMO) of nitrogen (N₂) by using a Coulomb-corrected MOT (CCMOT) method. In our scheme, the molecular continuum states are described by a Coulomb wave function instead of the PW approximation. With CCMOT, the reconstructed orbital is demonstrated to agree well with the theoretical prediction and retain the main features of the HOMO of N₂. Compared to the PW approximation method, the CCMOT shows a significant improvement in eliminating the artificial structures caused by PW approximation.

Joint Measurements of Terahertz Wave Generation and High-Harmonic Generation from Aligned Nitrogen Molecules Reveal Angle-Resolved Molecular Structures

We report the synchronized measurements of terahertz wave generation and high-harmonic generation from aligned nitrogen molecules in dual-color laser fields. Both yields are found to be alignment dependent, showing the importance of molecular structures in the generation processes. By calibrating the angular ionization rates with the terahertz yields, we present a new way of retrieving the angular differential photoionization cross section (PICS) from the harmonic signals which avoids specific model calculations or separate measurements of the alignment-dependent ionization rates. The measured PICS is found to be consistent with theoretical predications, although some discrepancies exist. This all-optical method provides a new alternative for investigating molecular structures.

Revealing the Cooper minimum of N2 by molecular frame high-harmonic spectroscopy

Molecular frame high-harmonic spectra of aligned N2 molecules reveal a Cooper-like minimum. By deconvolving the laboratory frame alignment distribution, what was previously thought to be a maximum of emission along the molecular axis is found to be maxima at 35 degrees off axis, with a spectral minimum on axis. Both of these features are supported by photoionization calculations that underline the relationship between high-harmonic spectroscopy and photoionization measurements. The calculations reveal that the on axis spectral minimum is a Cooper-like minimum that arises from the destructive interference of the p and f partial wave contributions to high-harmonic photorecombination. Features such as Cooper minima and shape resonances are ubiquitous in molecular photoionization or recombination.

Scaling law for energy-momentum spectra of atomic photoelectrons

A scaling law which was used to classify photoelectron angular distributions (PADs) is now extended to photoelectron kinetic energy spectra. Both a theoretical proof and an independent verification are presented. Considering PADs are of photoelectron momentum spectra, this extension really extends the scaling law to the entire energy-momentum spectra. The scaling law for photoelectron energy-momentum spectra applies to both directly ionized and rescattered photoelectrons. Re-scaling experimental input parameters without loosing the physical essence with this scaling law may ease the experimental conditions and reduce the material and the energy consumptions in the experiments.