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Tunnelling lies at the heart of quantum mechanics and is a fundamental process in attosecond science, molecular biology, and quantum devices. Whether tunnelling takes time and how a microscopic particle transits through a barrier have been debated since the early days of quantum mechanics. The time required for an electron to tunnel through an atomic potential barrier has been measured with attosecond angular streaking (attoclock), and a recent work on the hydrogen atom claimed that electron tunnelling is instantaneous. However, the time required for Rb atoms to tunnel through an optical potential barrier has been measured to be on the order of milliseconds with a recent Larmor clock measurement. The essence of electron and atom tunnelling is identical, but the reason for the contradictory conclusions remains unknown. Here, we demonstrate that the sub-barrier potential interaction is the root of the nonzero tunnelling delay time. We reveal that the wave-particle duality of a tunnelling electron must be fully taken into account when decoding the tunnelling delay time from the attoclock measurements. Based on energy-resolved attoclock measurements, we show that the tunnelling delay time of an electron ranges from 24 to 58 attoseconds, and the counterintuitive result that an electron with a lower energy may spend less time in the barrier is consistent with the velocity-dependent tunnelling time of atoms in Larmor clock measurements. Our results unify the tunnelling time of microscopic particles by highlighting the classically forbidden sub-barrier potential interactions of matter waves.

Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well-known that numerical band structure calculations typically provide electronic wave functions with an undetermined k-dependent phase which results in matrix elements which contain arbitrary k-dependent phases. In addition, such approaches usually mix degenerate bands and bands with an energy difference smaller than the numerical precision in an arbitrary way for each point in k-space. These ambiguities are problematic if one considers the dynamics induced by electric fields since the matrix elements of the position operator involve a derivative of the wave functions with respect to k. When the light-matter interaction is described in the length gauge, the problem of arbitrary phases and degenerate subspace mixing of Bloch states is solved by adopting a smooth gauge transformation along the field direction. The results obtained within this method are validated by comparing with calculations in the velocity gauge. Although we obtain in both gauges the same overall result, the length gauge is advantageous since it converges with a smaller number of bands and thus requires significantly less numerical effort than the velocity gauge. Also an unique distinction between inter- and intraband contributions and thus an instructive physical interpretation is possible in the length gauge whereas in the velocity gauge this is unclear. The computed polarization-direction-dependent high-harmonic spectra agree well with experimental data reported for GaAs. Furthermore, it is demonstrated that, under proper conditions, the Berry curvature is largely responsible for the even-order harmonics which are polarized perpendicular to the driving field., Comment: 7 pages, 3 figures

An improved quantum trajectory Monte Carlo method involving the Stark shift of the initial state, Coulomb potential, and multielectron polarization-induced dipole potential is used to revisit the origin of the low-energy interference structure in the photoelectron momentum distribution of the xenon atom subjected to an intense laser field, and resolve the different contributions of these three effects. In addition to the well-studied radial finger-like interference structure, a ring-like interference structure induced by interference among electron wave packets emitted from multi-cycle time windows of the laser field is found in the low energy part of the photoelectron momentum spectrum. It is attributed to the combined effect of the Coulomb potential and Stark shift. Our finding provides new insight into the imaging of electron dynamics of atoms and molecules with intense laser fields.

Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view. However, the complete characterization of quantum wave function with infinite paths is a formidable challenge, which greatly limits the application potential, especially in the strong-field physics and attosecond science. Instead of brute-force tracking every path one by one, here we propose deep-learning-performed strong-field Feynman's formulation with pre-classification scheme which can predict directly the final results only with data of initial conditions, so as to attack unsurmountable tasks by existing strong-field methods and explore new physics. Our results build up a bridge between deep learning and strong-field physics through the Feynman's path integral, which would boost applications of deep learning to study the ultrafast time-dependent dynamics in strong-field physics and attosecond science, and shed a new light on the quantum-classical correspondence.

Accessing precisely to the phase variation of electronic wave-packet (EWP) provides unprecedented spatiotemporal information of microworld. A radial interference pattern at near-zero energy has been widely observed in experiments of strong-field photoionization. However, the underlying physical picture of this interference pattern is still under debate. Here we report an experimental and theoretical investigation of this low-energy interference structure (LEIS) in mid-infrared laser fields. We clarify that the LEIS arises due to the soft-recollision mechanism, which was previously found to play a pivotal role in producing the pronounced low-energy structure. Specifically, the LEIS is induced by the interference between direct and soft-recollision EWPs launched within a 1/18 laser-cycle time scale in our experiments. Moreover, the observation of LEIS is independent of laser wavelength and specific atomic targets. Our result opens a promising new avenue for retrieving the structure and dynamics of EWPs in atoms and molecules with attosecond time resolution.

We investigate high-order harmonic generation in ZnO driven by linearly polarized multi-color pulses. It is shown that the intensities of the harmonics in the plateau region can be enhanced by two to three orders of magnitude when driven by two- or three-color fields as compared with the single-color pulse excitation. By analyzing the time-dependent population in the conduction band as function of both the initial and the moving crystal momenta, we demonstrate that this remarkable enhancement originates from the intraband preacceleration of electrons from their initial momenta to the top of the valence band where interband excitation takes place. We show that this preacceleration strongly increases the population in the conduction band and correspondingly the intensities of high harmonics in the plateau region. Our results confirm the very recently proposed four-step model for high harmonic generation in semiconductors [Phys. Rev. Lett. 122, 193901 (2019)] and provide an effective way to enhance the intensities of harmonics in the plateau region which has significant implications for the generation of bright attosecond light sources from semiconductors., Comment: 6 pages, 3 figures

We analyze the two-dimensional photoelectrons momentum distribution of Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below 2Up. By using a generalized quantum trajectory Monte Carlo (GQTMC) simulation and comparing with the numerical solution of time-dependent Schrodinger equation (TDSE), we show that in the deep tunneling regime, the rescattered electron trajectories plays unimportant role and the interplay between the intracycle and inter-cycle results in a ring-like interference pattern. The ring-like interference pattern will mask the holographic interference structure in the low longitudinal momentum region. When the nonadiabatic tunneling contributes significantly to ionization, i.e., the Keldysh parameter 1, the contribution of the rescattered electron trajectories become large, thus holographic interference pattern can be clearly observed. Our results help paving the way for gaining physical insight into ultrafast electron dynamic process with attosecond temporal resolution., Comment: 8 pages, 8 figures

Strong field photoelectron holography has been proposed as a means for interrogating the spatial and temporal information of electrons and ions in a dynamic system. After ionization, part of the electron wave packet may directly go to the detector (the reference wave), while another part may be driven back to the ion where it scatters off (the signal wave). The interference hologram of the two waves may be used to retrieve the target information. However, unlike conventional optical holography, the propagations of electron wave packets are affected by the Coulomb potential as well as by the laser field. In addition, electrons are emitted over the whole laser pulse duration, thus multiple interferences may occur. In this work, we used a generalized quantum-trajectory Monte Carlo method to investigate the effect of Coulomb potential and the nonadiabatic subcycle ionization on the photoelectron hologram. We showed that photoelectron hologram can be well described only when the nonadiabatic effect in ionization is accounted for, and Coulomb potential can be neglected only in the tunnel ionization regime. Our results help establishing photoelectron holography for probing spatial and dynamic properties of atoms and molecules., Comment: 8 pages, 6 figures

A novel and universal interference structure is found in the photoelectron momentum distribution of atoms in intense infrared laser field. Theoretical analysis shows that this structure can be attributed to a new form of Coulomb-field-driven backward-scattering of photoelectrons in the direction perpendicular to the laser field, in contrast to the conventional rescattering along the laser polarization direction. This transverse backward-scattering process is closely related to a family of photoelectrons initially ionized within a time interval of less than 200 attosecond around the crest of the laser electric field. Those electrons, acquiring near-zero return energy in the laser field, will be pulled back solely by the ionic Coulomb field and backscattered in the transverse direction. Moreover, this rescattering process mainly occurs at the first or the second return times, giving rise to different phases of the photoelectrons. The interference between these photoelectrons leads to unique curved interference fringes which are observable for most current intense field experiments, opening a new way to record the electron dynamics in atoms and molecules on a time scale much shorter than an optical cycle., Comment: 6 pages,3 figures