Layer-dependent ultrafast carrier dynamics of PdSe2 investigated by photoemission electron microscopy.

For atomically thin two-dimensional materials, variations in layer thickness can result in significant changes in the electronic energy band structure and physicochemical properties, thereby influencing the carrier dynamics and device performance. In this work, we employ time- and energy-resolved photoemission electron microscopy to reveal the ultrafast carrier dynamics of PdSe2 with different layer thicknesses. We find that for few-layer PdSe2 with a semiconductor phase, an ultrafast hot carrier cooling on a timescale of approximately 0.3 ps and an ultrafast defect trapping on a timescale of approximately 1.3 ps are unveiled, followed by a slower decay of approximately tens of picoseconds. However, for bulk PdSe2 with a semimetal phase, only an ultrafast hot carrier cooling and a slower decay of approximately tens of picoseconds are observed, while the contribution of defect trapping is suppressed with the increase of layer number. Theoretical calculations of the electronic energy band structure further confirm the transition from a semiconductor to a semimetal. Our work demonstrates that TR- and ER-PEEM with ultrahigh spatiotemporal resolution and wide-field imaging capability has great advantages in revealing the intricate details of ultrafast carrier dynamics of nanomaterials.

Reveal Ultrafast Electron Relaxation across Sub-bands of Tellurium by Time- and Energy-Resolved Photoemission Microscopy.

Exploring ultrafast carrier dynamics is crucial for the materials' fundamental properties and device design. In this work, we employ time- and energy-resolved photoemission electron microscopy with tunable pump wavelengths from visible to near-infrared to reveal the ultrafast carrier dynamics of the elemental semiconductor tellurium. We find that two discrete sub-bands around the Γ point of the conduction band are involved in excited-state electron ultrafast relaxation and reveal that hot electrons first go through ultrafast intra sub-band cooling on a time scale of about 0.3 ps and then transfer from the higher sub-band to the lower one on a time scale of approximately 1 ps. Additionally, theoretical calculations reveal that the lower one has flat-band characteristics, possessing a large density of states and a long electron lifetime. Our work demonstrates that TR- and ER-PEEM with broad tunable pump wavelengths are powerful techniques in revealing the details of ultrafast carrier dynamics in time and energy domains.

Ultrafast Electronic Dynamics in Anisotropic Indirect Interlayer Excitonic States of Monolayer WSe2/ReS2 Heterojunctions.

Understanding ultrafast electronic dynamics of the interlayer excitonic states in atomically thin transition metal dichalcogenides is of importance in engineering valleytronics and developing excitonic integrated circuits. In this work, we experimentally explored the ultrafast dynamics of indirect interlayer excitonic states in monolayer type II WSe2/ReS2 heterojunctions using time-resolved photoemission electron microscopy, which reveals its anisotropic behavior. The ultrafast cooling and decay of excited-state electrons exhibit significant linear dichroism. The ab initio theoretical calculations provide unambiguous evidence that this linear dichroism result is primarily associated with the anisotropic nonradiative recombination of indirect interlayer excitonic states. Measuring time-resolved photoemission energy spectra, we have further revealed the ultrafast evolution of excited-state electrons in anisotropic indirect interlayer excitonic states. The findings have important implications for controlling the interlayer moiré excitonic effects and designing anisotropic optoelectronic devices.

Efficient numerical approach to high-fidelity phase-modulated gates in long chains of trapped ions.

Almost every quantum circuit is built with two-qubit gates in the current stage, which are crucial to the quantum computing in any platform. The entangling gates based on Mølmer-Sørensen schemes are widely exploited in the trapped-ion system, with the utilization of the collective motional modes of ions and two laser-controlled internal states, which are served as qubits. The key to realize high-fidelity and robust gates is the minimization of the entanglement between the qubits and the motional modes under various sources of errors after the gate operation. In this work, we propose an efficient numerical method to search high-quality solutions for phase-modulated pulses. Instead of directly optimizing a cost function, which contains the fidelity and the robustness of the gates, we convert the problem to the combination of linear algebra and the solution to quadratic equations. Once a solution with the gate fidelity of 1 is found, the laser power can be further reduced while searching on the manifold where the fidelity remains 1. Our method largely overcomes the problem of the convergence and is shown to be effective up to 60 ions, which suffices the need of the gate design in current trapped-ion experiments.

Upper bound for permanent orientation of symmetric-top molecule induced by linearly polarized electric fields.

Many symmetric top molecules are among the most important polyatomic molecules. The orientation of a polyatomic molecule is a challenging task, which is at the heart of its quantum control and crucial for many subsequent applications in various fields. Most recent studies focus on the temporary orientation achieved via the quantum revivals. In this study, we reveal the underlying mechanism behind the observed permanent orientation and discuss strategies for a higher degree of permanent orientation. By a careful analysis of symmetry and unitary, it is possible to estimate an upper bound of ⟨⟨cosθ⟩⟩<(2-2)/4≈0.1464 for a molecule in its thermal equilibrium states using a linear field. We show that this bound can be reached for an oblate symmetric-top molecule in the high temperature limit. To demonstrate different possible schemes, we take CHCl3 as an example. Simply with designed microwave fields, one can permanently orient CHCl3 with a degree of ⟨cos θ⟩ ≈ 0.045. We show that this value can be significantly increased by adding one or more pump pulses.

Multiscale numerical tool for studying nonlinear dynamics in solids induced by strong laser pulses.

Strong-field phenomena in solids exhibit extreme high-order nonlinear optical effects, which have triggered many theoretical and experimental investigations. However, there is still a lack of highly efficient numerical tools to simulate the relevant phenomena. In this paper, a versatile multiscale numerical tool set is developed for studying high-order nonlinear optical effects in solids, generated by ultrafast strong laser pulses. This tool is based on the tight-binding model approximation of the crystal structure, the related parameters of which are obtained from the density functional theory calculations. And the nonlinear effects are explored by solving the Maxwell equations coupled with the semiconductor Bloch equations. Our numerical tool can provide not only basic electronic structures and optical responses of the crystal, but also the real-time evolution of the macroscopic electromagnetic fields and the current density. The high-performance parallel computing and the interpolation method in our tool make it possible to study the strong-field nonlinear responses and propagation effects on a large spatial and temporal scale. Finally, three theoretical or experimental results published recently are satisfactorily reproduced, showing a good performance of the current toolbox.

Manipulation of the high-order harmonic generation in monolayer hexagonal boron nitride by two-color laser field.

We theoretically investigate the high-order harmonic generation (HHG) of the monolayer hexagonal boron nitride by two-color laser pulses, based on the ab initio time-dependent density-functional theory. We find that the waveform of the two-color laser field can dramatically control the harmonic spectrum. The two-color laser field can enhance the harmonic radiation more efficiently than the monochromatic pulse laser with the same incident energy. We investigate the influence of incident laser pulse parameters on the harmonic radiation, such as the relative phase of the two-color field, the amplitude ratio between component electric fields, and the laser orientation. We show that the HHG spectrum is controlled by both the electric field and the vector potential. The electronic band structure and the laser-matter energy transfer play an important role in determining the laser polarization for optimal HHG in the hBN crystal. Our work supplies a scheme to manipulate HHGs in two-dimensional materials and provides a potential methodology for the generation of intense extreme-ultraviolet pulses.

Two-Electron Interference in Strong-Field Ionization of He by a Short Intense Extreme Ultraviolet Laser Pulse.

Double ionization of helium by a single intense (above 10^{18} W/cm^{2}) linearly polarized extreme ultraviolet laser pulse is studied by numerically solving the full-dimensional time-dependent Schrödinger equation. For the laser intensities well beyond the perturbative limit, novel gridlike interference fringes are found in the correlated energy spectrum of the two photoelectrons. The interference can be traced to the multitude of two-electron wave packets emitted at different ionization times. A semianalytical model for the dressed two-photon double ionization is shown to qualitatively account for the interference patterns in the joint energy spectrum. Similar signatures of interferences between transient induced time-delayed ionization bursts are expected for other atomic and molecular multielectron systems.

Photon Momentum Transfer in Single-Photon Double Ionization of Helium.

We theoretically and experimentally investigate the photon momentum transfer in single-photon double ionization of helium at various large photon energies. We find that the forward shifts of the momenta along the light propagation of the two photoelectrons are roughly proportional to their fraction of the excess energy. The mean value of the forward momentum is about 8/5 of the electron energy divided by the speed of light. This holds for fast and slow electrons despite the fact that the energy sharing is highly asymmetric and the slow electron is known to be ejected by secondary processes of shake off and knockout rather than directly taking its energy from the photon. The biggest deviations from this rule are found for the region of equal energy sharing where the quasifree mechanism dominates double ionization.

Accurate in situ Measurement of Ellipticity Based on Subcycle Ionization Dynamics.

Elliptically polarized laser pulses (EPLPs) are widely applied in many fields of ultrafast sciences, but the ellipticity (ϵ) has never been in situ measured in the interaction zone of the laser focus. In this Letter, we propose and realize a robust scheme to retrieve the ϵ by temporally overlapping two identical counterrotating EPLPs. The combined linearly electric field is coherently controlled to ionize Xe atoms by varying the phase delay between the two EPLPs. The electron spectra of the above-threshold ionization and the ion yield are sensitively modulated by the phase delay. We demonstrate that these modulations can be used to accurately determine ϵ of the EPLP. We show that the present method is highly reliable and is applicable in a wide range of laser parameters. The accurate retrieval of ϵ offers a better characterization of a laser pulse, promising a more delicate and quantitative control of the subcycle dynamics in many strong field processes.

Proposal for Measuring Electron Displacement Induced by a Short Laser Pulse.

In laser-matter interaction, most previous studies have focused on the change of the electron momentum induced by the external fields. Here, we theoretically investigate the electron displacement induced by an ultrashort pulse, whose precise waveform is hard to determine experimentally. We propose and numerically demonstrate a scheme to accurately measure the electron displacement using a ruler formed by the interfering spirals in the photoelectron momentum distribution generated by two oppositely circularly polarized pulses. The scheme is robust against the focusing volume effects and the jitter of the carrier envelope phase of the two circular pulses. The ability to measure the electron displacement by an arbitrary pulse may pave the way to quantitative control of the charge migration in matter on the scale of Ångström.

Efficient time-sampling method in Coulomb-corrected strong-field approximation.

One of the main goals of strong-field physics is to understand the complex structures formed in the momentum plane of the photoelectron. For this purpose, different semiclassical methods have been developed to seek an intuitive picture of the underlying mechanism. The most popular ones are the quantum trajectory Monte Carlo (QTMC) method and the Coulomb-corrected strong-field approximation (CCSFA), both of which take the classical action into consideration and can describe the interference effect. The CCSFA is more widely applicable in a large range of laser parameters due to its nonadiabatic nature in treating the initial tunneling dynamics. However, the CCSFA is much more time consuming than the QTMC method because of the numerical solution to the saddle-point equations. In the present work, we present a time-sampling method to overcome this disadvantage. Our method is as efficient as the fast QTMC method and as accurate as the original treatment in CCSFA. The performance of our method is verified by comparing the results of these methods with that of the exact solution to the time-dependent Schrödinger equation.

Virtual Sequential Picture for Nonsequential Two-Photon Double Ionization of Helium.

By using a model based on the second-order time-dependent perturbation theory, we show that the nonsequential two-photon double ionization of He can be understood in a virtual sequential picture: to excite the final double continuum state |k_{1},k_{2}⟩ by absorbing two photons from the ground state |1s^{2},^{1}S_{0}⟩, the single continuum states |1s,k_{1}⟩ and |1s,k_{2}⟩ serve as the dominant intermediate states. This virtual sequential picture is verified by the perfect agreement of the total ionization cross section, respectively, calculated by this model and by the sophisticated numerical solution to the full-dimensional time-dependent Schrödinger equation. This model, without the consideration of the electron correlation in the final double continuum state, works well for a wide range of laser parameters extending from the nonsequential to the sequential regime. The present Letter demonstrates that the electron correlation in the final double continuum state is not important in evaluating the total cross section, while it is indispensable for an accurate computation of a triply differential cross section. In addition, the virtual sequential picture bridges the sequential and nonsequential two-photon double ionization and reveals connections and distinctions between them.

Nonadiabatic Electron Dynamics in Orthogonal Two-Color Laser Fields with Comparable Intensities.

We theoretically investigate the nonadiabatic subcycle electron dynamics in orthogonally polarized two-color laser fields with comparable intensities. The photoelectron dynamics is simulated by exact solution to the 3D time-dependent Schrödinger equation, and also by two other semiclassical methods, i.e., the quantum trajectory Monte Carlo simulation and the Coulomb-corrected strong field approximation. Through these methods, we identify the underlying mechanisms of the subcycle electron dynamics and find that both the nonadiabatic effects and the Coulomb potential play very important roles. The contribution of the nonadiabatic effects manifest in two aspects, i.e., the nonadiabatic ionization rate and the nonzero initial velocities at the tunneling exit. The Coulomb potential has a different impact on the electrons' trajectories for different relative phases between the two pulses.

Mechanisms of below-threshold harmonic generation in atoms.

Most previous studies have focused on high-order harmonic generation beyond the ionization threshold; mechanisms of below-threshold harmonics are less understood. We schematically study the harmonic emission process in this region by numerically solving the time-dependent Schrödinger equation of an atom in laser fields. We show that, besides the quantum path interference mechanism recently identified, the effects induced by the Coulomb potential also have a critical impact on these harmonics. These mechanisms can be distinguished in the structure of harmonic spectra by changing the laser wavelength and peak intensity. We find that the long quantum orbits can influence lower-order harmonics at a higher laser intensity. In addition, we show that the intensity-dependent steps of harmonic yield can disappear for certain harmonic orders, due to the trapping in the Rydberg states before recombination, which can explain recent experimental observations.

Classical-quantum correspondence for above-threshold ionization.

We measure high resolution photoelectron angular distributions (PADs) for above-threshold ionization of xenon atoms in infrared laser fields. Based on the Ammosov-Delone-Krainov theory, we develop an intuitive quantum-trajectory Monte Carlo model encoded with Feynman's path-integral approach, in which the Coulomb effect on electron trajectories and interference patterns are fully considered. We achieve a good agreement with the measured PADs of atoms for above-threshold ionization. The quantum-trajectory Monte Carlo theory sheds light on the role of ionic potential on PADs along the longitudinal and transverse direction with respect to the laser polarization, allowing us to unravel the classical coordinates (i.e., tunneling phase and initial momentum) at the tunnel exit for all of the photoelectrons of the PADs. We study the classical-quantum correspondence and build a bridge between the above-threshold ionization and the tunneling theory.

Subcycle dynamics of Coulomb asymmetry in strong elliptical laser fields.

We measure photoelectron angular distributions of noble gases in intense elliptically polarized laser fields, which indicate strong structure-dependent Coulomb asymmetry. Using a dedicated semiclassical model, we have disentangled the contribution of direct ionization and multiple forward scattering on Coulomb asymmetry in elliptical laser fields. Our theory quantifies the roles of the ionic potential and initial transverse momentum on Coulomb asymmetry, proving that the small lobes of asymmetry are induced by direct ionization and the strong asymmetry is induced by multiple forward scattering in the ionic potential. Both processes are distorted by the Coulomb force acting on the electrons after tunneling. Lowering the ionization potential, the relative contribution of direct ionization on Coulomb asymmetry substantially decreases and Coulomb focusing on multiple rescattering is more important. We do not observe evident initial longitudinal momentum spread at the tunnel exit according to our simulation.

Nonsequential and sequential fragmentation of CO2(3+) in intense laser fields.

We experimentally studied the three-body fragmentation dynamics of CO(2) initiated by intense femtosecond laser pulses. Sequential and nonsequential fragmentations were precisely separated and identified for CO(2)(3+) to break up into O(+) + C(+) + O(+) ions. With accurate measurements of three-dimensional momentum vectors of the correlated atomic ions and calculations of the high-level ab initio potential of CO(2)(3+), we reconstructed the geometric structure of CO(2)(3+) before fragmentation, which turns out to be very close to that of the neutral CO(2) molecule before laser irradiation. Our study indicated that Coulomb explosion is a promising approach for imaging geometric structures of polyatomic molecules if the fragmentation dynamics can be clearly clarified and the appropriate dissociation potential is provided for multiply charged molecular ions.

Application of discrete variable representation to planar H2+ in strong xuv laser fields.

We present an efficient and accurate grid method to study the strong field dynamics of planar H(2)(+) under Born-Oppenheimer approximation. After introducing the elliptical coordinates to the planar H(2)(+), we show that the Coulomb singularities at the nuclei can be successfully overcome so that both bound and continuum states can be accurately calculated by the method of separation of variables. The time-dependent Schrödinger equation (TDSE) can be accurately solved by a two-dimensional discrete variable representation (DVR) method, where the radial coordinate is discretized with the finite-element discrete variable representation for easy parallel computation and the angular coordinate with the trigonometric DVR which can describe the periodicity in this direction. The bound states energies can be accurately calculated by the imaginary time propagation of TDSE, which agree very well with those computed by the separation of variables. We apply the TDSE to study the ionization dynamics of the planar H(2)(+) by short extreme ultra-violet (xuv) pulses, in which case the differential momentum distributions from both the length and the velocity gauge agree very well with those calculated by the lowest order perturbation theory.