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.

We demonstrate a method to simultaneously measure the rotational temperature and pump intensity in laser-induced molecular alignment by the time-resolved high harmonic spectroscopy (HHS). It relies on the sensitive dependence of the arising times of the local minima and maxima of the harmonic yields at the rotational revivals on the pump intensity and rotational temperature. By measuring the arising times of these local extrema from the time-resolved harmonic signals, the rotational temperature and pump intensity can be accurately measured. We have demonstrated our method using N2 molecules. The validity and robustness of our method are tested with different harmonic orders and by changing the gas pressures as well as the distance between the gas exit and the optical axis. Moreover, we have also demonstrated the versatility of our method by applying it to CO2 molecules.

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We measure the molecular alignment induced in gas using molecular rotational echo spectroscopy. Our results show that the echo intensity and the time interval between the local extremas of the echo responses depend sensitively on the pump intensities and the initial molecular rotational temperature, respectively. This allows us to accurately extract these experimental parameters from the echo signals and then further determine the molecular alignment in experiments. The accuracy of our method has been verified by comparing the simulation with the extracted parameters from the molecular alignment experiment performed with a femtosecond pump pulse.

We theoretically investigate the formation of the high-order fractional alignment echo in OCS molecule and systematically study the dependence of echo intensity on the intensities and time delay of the two excitation pulses. Our simulations reveal an intricate dependence of the intensity of high-order fractional alignment echo on the laser conditions. Based on the analysis with rotational density matrix, this intricate dependence is further demonstrated to arise from the interference of multiple quantum pathways that involve multilevel rotational transitions. Our result provides a comprehensive multilevel picture of the quantum dynamics of high-order fractional alignment echo in molecular ensembles, which will facilitate the development of “rotational echo spectroscopy.”

Characterizing an isolated attosecond pulse (IAP) is essential for its potential applications. A complete characterization of an IAP ultimately requires the determination of its electric field in both time and space domains. However, previous methods, like the widely-used RABBITT and attosecond streaking, only measure the temporal profile of the attosecond pulse. Here we demonstrate an all-optical method for the measurement of the space-time properties of an IAP. By introducing a non-collinear perturbing pulse to the driving field, the process of IAP generation is modified both spatially and temporally, manifesting as a spatial and a frequency modulation in the harmonic spectrum. By using a FROG-like retrieval method, the spatio-spectral phases of the harmonic spectrum are faithfully extracted from the induced spatio-spectral modulations, which allows a thoroughgoing characterization of the IAP in both time and space. With this method, the spatio-temporal structures of the IAP generated in a two-color driving field in both the near- and far-field are fully reconstructed, from which a weak spatio-temporal coupling in the IAP generation is revealed. Our approach overcomes the limitation in the temporal measurement in conventional in situ scheme, providing a reliable and holistic metrology for IAP characterization.

Ultrafast electron migration in molecules is the progenitor of all chemical reactions and biological functions after light-matter interaction [1–4]. Following this ultrafast dynamics, however, has been an enduring endeavor [5, 6]. Recently, it has been shown that high-harmonic spectroscopy (HHS) is able to probe dynamics with attosecond temporal and sub-angstrom spatial resolution [7–10]. Still, real-time visualization of single-molecule dynamics continues to be a great challenge because experimental harmonic spectra are due to the coherent averages of light emission from individual molecules of different alignments. Here, we show that from high harmonics generated with single-color and two-color probe lasers in a pump-probe experiment, the complex amplitude and phase of harmonics from a single fixed-in-space molecule can be reconstructed using modern machine learning (ML) algorithm. From the complex single-molecule dipoles for different harmonics, we construct a series of film clips of hole density distributions of the cation at time steps of 50 attoseconds (1 as=10^{−18} s) to make a classical “movie” of electron migration after tunnel ionization of the molecule. Moreover, the angular dependence of molecular charge migration is fully resolved. By examining these clips, we observed that holes do not just “migrate” along the laser direction, but they may “swirl” around the atom centers. The ML-based HHS proposed here establishes a general reconstruction scheme for studying ultrafast charge migration in molecules, paving a way for further advance in tracing and controlling photochemical reactions by femtosecond lasers.

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. Recently, it has been suggested that high-harmonic spectroscopy (HHS) is able to probe dynamics with attosecond temporal and sub-˚angstr¨om spatial resolution. Still, real-time visualization of single-molecule dynamics continues to be a great challenge because experimental harmonic spectra are due to the coherent averages of light emission from individual molecules of different alignments. Here we demonstrate that the uniting of machine learning (ML) algorithm and HHS in two-color laser pulses enables us to retrieve the complex amplitude and phase of harmonics from single fixed-in-space molecule. From the complex single-molecule dipoles for different harmonics, we construct a movie of electron migration after tunnel ionization of the molecules at time steps of 50 attoseconds. Moreover, the angular dependence of molecular charge migration is fully resolved. By examining the movie, we observe that electron holes do not just “migrate” along the laser direction, but may “swirl” around the atom centers. Our ML-based HHS establishes a general reconstruction scheme for studying ultrafast charge migration in molecules, paving a way for further advance in tracing and controlling photochemical reactions by femtosecond lasers.