Electron Wave Packet Research Articles

Signature of Attochemical Quantum Interference upon Ionization and Excitation of an Electronic Wave Packet in Fluorobenzene

Ultrashort pulses can excite or ionize molecules and populate coherent electronic wave packets, inducing complex dynamics. In this Letter, we simulate the coupled electron-nuclear dynamics upon ionization to different electronic wave packets of (deuterated) benzene and fluoro-benzene molecules, quantum mechanically and in full dimensionality. In fluoro-benzene, the calculations unravel both interstate and intrastate quantum interferences that leave clear signatures of attochemistry and charge-directed dynamics in the shape of the autocorrelation function. The latter are in agreement with experimental high-harmonic spectroscopy measurements of benzenes and fluoro-benzene. Published by the American Physical Society 2024

Spontaneous photon emission by shaped quantum electron wavepackets and the QED origin of bunched electron beam superradiance.

It has been shown that the spontaneous emission rate of photons by free electrons, unlike stimulated emission, is independent of the shape or modulation of the quantum electron wavefunction (QEW). Nevertheless, here we show that the quantum state of the emitted photons is non-classical and does depend on the QEW shape. This non-classicality originates from the shape dependent off-diagonal terms of the photon density matrix. This is manifested in the Wigner distribution function and would be observable experimentally through homodyne detection techniques as a squeezing effect. Considering a scheme of electrons interaction with a single microcavity mode, we present a QED formulation of spontaneous emission by multiple modulated QEWs through a build-up process. Our findings indicate that in the case of a density modulated QEWs beam, the phase of the off-diagonal terms of the photon state emitted by the modulated QEWs is the harbinger of bunched beam superradiance, where the spontaneous emission is proportional to N_e^2 . This observation offers a potential for enhancement of other quantum electron interactions with quantum systems by a modulated QEWs beam carrying coherence and quantum properties of the modulation.

Observation of Attosecond Time Delays in Above-Threshold Ionization.

Attosecond-scale temporal characterization of photoionization is essential in understanding how light and matter interact on the most fundamental level. However, characterizing the temporal property of strong-field above-threshold ionization has remained unreached. Here, we propose a novel photoelectron interferometric method to disentangle the contribution of Coulomb effect from an attoclock, allowing us to clock energy-resolved time delays of strong-field above-threshold ionization. We disentangle two types of Coulomb effects for the attoclock, i.e., one arising from the Coulomb disturbance of a single electron trajectory and the second effect arising from the photoelectron phase space distortion due to the Coulomb field. We find that the second Coulomb effect manifests itself as an energy-resolved attosecond time delay in the electron emission, which is relevant to the effect of nonadiabatic initial longitudinal momentum at the tunnel exit. Our study further indicates a sensitivity of the time delay to the temporal profile of the released electron wave packet within one half laser cycle. The temporal width of the released electron wave packet is found to increase with energy, which contradicts the common assumption in the adiabatic picture.

Enhancing X-ray generation from twisted multilayer van der Waals materials by shaping electron wavepackets

We study twisted bilayer van der Waals (vdW) materials as a platform to generate versatile bremsstrahlung X-rays, and show that the twist angle in bilayer vdW materials provides an unprecedented degree of controllability over various properties of bremsstrahlung radiation from these materials. Specifically, we combine the waveshaping of the free electron’s quantum wavepacket with the unique crystalline atomic positioning of twisted bilayers to realize shaped bremsstrahlung X-rays, which feature enhancements in directionality and intensity. In the process, we present a theoretical model for bremsstrahlung radiation that is applicable to twisted multilayer vdW materials in general. We also investigate the dependence of our X-ray emission mechanism on physical parameters, including the interlayer spacing and number of layers. Our findings pave the way for the use of twisted multilayer van der Waals materials in the generation of tailored X-ray spectra for applications like X-ray imaging, X-ray fluorescence, and X-ray treatment.

Zitterbewegung damping in structures based on Dirac crystals

The possibilities of controlling the time of damping of Zitterbewegung oscillations in graphene and graphene superlattice have been investigated. The decay time of Zitterbewegung oscillations in graphene in the presence of high-frequency radiation has been calculated. An increase in the duration of the Zitterbewegung with the inclusion of an alternating field has been explicitly demonstrated. The decay time of the Zitterbewegung for a graphene superlattice has been shown to be controlled by changing the ratio between the period of the superlattice and the width of the electron wave packet.

Attosecond impulsive stimulated X-ray Raman scattering in liquid water.

We report the measurement of impulsive stimulated x-ray Raman scattering in neutral liquid water. An attosecond pulse drives the excitations of an electronic wavepacket in water molecules. The process comprises two steps: a transition to core-excited states near the oxygen atoms accompanied by transition to valence-excited states. Thus, the wavepacket is impulsively created at a specific atomic site within a few hundred attoseconds through a nonlinear interaction between the water and the x-ray pulse. We observe this nonlinear signature in an intensity-dependent Stokes Raman sideband at 526 eV. Our measurements are supported by our state-of-the-art calculations based on the polarization response of water dimers in bulk solvation and propagation of attosecond x-ray pulses at liquid density.

Ultra-Nonlinear Subcycle Photoemission of Few-Electron States from Sharp Gold Nanotapers.

The generation of ultrashort electron wavepackets is crucial for the development of ultrafast electron microscopes. Recent studies on Coulomb-correlated few-electron number states, photoemitted from sharp metallic tapers, have shown emission nonlinearities in the multiphoton photoemission regime which scale with the electron number. Here, we study few-electron photoemission from gold nanotapers triggered by few-cycle near-infrared pulses, demonstrating extreme 20th-order nonlinearities for electron triplets. We report interferometric autocorrelation traces of the electron yield that are quenched to a single emission peak with subfemtosecond duration due to these high nonlinearities. The modulation of the emission yield by the carrier-envelope phase suggests that electron emission predominantly occurs during a single half cycle of the driving laser field. When applying a bias voltage to the tip, recollisions in the electron trajectories are suppressed and coherent subcycle electron beams are generated with promising prospects for ultrafast electron microscopy with subcycle time resolution.

Mechanism of quantum chaos in molecular nonadiabatic electron dynamics.

The quantum nuclear kinematic interactions with electrons (or nonadiabatic interactions) are the inherent driving force that possibly causes a mixture of the adiabatic electronic states in molecules. Particularly in systems whose electron wavepackets lie in a densely quasi-degenerate electronic-state manifold where many-dimensional and many-state nonadiabatic interactions last continually, we have found before that those extensive mixings can lead to a quantum electronic-state chaos [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 159, 074110 (2023)]. This chaos of electron dynamics is a new kind yet generic. This Communication identifies the mathematical/physical mechanism of this class of chaos by means of the collective coordinate analysis of the nonadiabatic interactions, along with the numerical applications to excited states of boron clusters. Some physical consequences of the present chaos are also discussed.

Manifestation of the quantum metric in chiral lattice systems

Recent years have seen a surge in research on the role of quantum geometry in condensed matter physics. For instance, the Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields due to an obstruction in space associated with a magnetic flux. A similar effect can be observed in solid-state systems, where the topology of the Berry connection can influence electron dynamics. These are paradigmatic examples of how the dynamics can be affected by the system’s geometry. Here, we show that in chiral-symmetric processes the quantum metric has a measurable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk and demonstrates an effect that can be attributed directly to the geometry of the state space.

Effects of edge disorder on the stability of quantum oscillations in two-dimensional coupled systems

This paper utilizes the theory of quantum diffusion to analyze the electron probability and spreading width of a wavepacket on each layer in a two-dimensional (2D) coupled system with edge disorder, aiming to clarify the effects of edge disorder on the stability of the electron periodic oscillations in 2D coupled systems. Using coupled 2D square lattices with edge disorder as an example, we show that, the electron probability and wavepacket spreading width exhibit periodic oscillations and damped oscillations, respectively, before and after the wavepacket reaches the boundary. Furthermore, these electron oscillations exhibit strong resistance against disorder perturbation with a longer decay time in the regime of large disorder, due to the combined influences of ordered and disordered site energies in the central and edge regions. Finally, we numerically verified the universality of the results through bilayer graphene, demonstrating that this anomalous quantum oscillatory behavior is independent of lattice geometry. Our findings are helpful in designing relevant quantum devices and understanding the influence of edge disorder on the stability of electron periodic oscillations in 2D coupled systems.

Rise and Fall of Anderson Localization by Lattice Vibrations: A Time-Dependent Machine Learning Approach.

The intricate relationship between electrons and the crystal lattice is a linchpin in condensed matter, traditionally described by the Fröhlich model encompassing the lowest-order lattice-electron coupling. Recently developed quantum acoustics, emphasizing the wave nature of lattice vibrations, has enabled the exploration of previously uncharted territories of electron-lattice interaction not accessible with conventional tools such as perturbation theory. In this context, our agenda here is two-fold. First, we showcase the application of machine learning methods to categorize various interaction regimes within the subtle interplay of electrons and the dynamical lattice landscape. Second, we shed light on a nebulous region of electron dynamics identified by the machine learning approach and then attribute it to transient localization, where strong lattice vibrations result in a momentary Anderson prison for electronic wavepackets, which are later released by the evolution of the lattice. Overall, our research illuminates the spectrum of dynamics within the Fröhlich model, such as transient localization, which has been suggested as a pivotal factor contributing to the mysteries surrounding strange metals. Furthermore, this paves the way for utilizing time-dependent perspectives in machine learning techniques for designing materials with tailored electron-lattice properties.

Attosecond two-color x-ray free-electron lasers with dual chirp-taper configuration and bunching inheritance

Attosecond x-ray pulses play a crucial role in the study of ultrafast phenomena occurring within inner and valence electrons. To achieve attosecond time-resolution studies and gain control over electronic wave functions, it is crucial to develop techniques capable of generating and synchronizing two-color x-ray pulses at the attosecond scale. In this paper, we present a novel approach for generating attosecond pulse pairs using a dual chirp-taper free-electron laser with bunching inheritance. An electron beam with a sinusoidal energy chirp, introduced by the external laser, passes through the main undulator and afterburner, both with tapers. Two-color x-ray pulses are generated from the main undulator and the afterburner, respectively, with temporal separations of several femtoseconds and energy separations of tens of electron volts. Notably, the afterburner is much shorter than the main undulator due to the bunching inheritance, which reduces the distance between two source points and alleviates the beamline focusing requirements of the two-color pulses. A comprehensive stability analysis is conducted in this paper, considering the individual effects of shot noise from self-amplified spontaneous emission and carrier-envelope phase jitter of the few-cycle laser. The results show that the radiation from the afterburner exhibits excellent stability in the proposed scheme, which is beneficial for x-ray pump-probe experiments. The proposed scheme opens up new possibilities for attosecond science enabled by x-ray attosecond pump-probe techniques and coherent control of ultrafast electronic wave packets in quantum systems. Published by the American Physical Society 2024

Water Solvent Reorganization upon Ultrafast Resonant Stimulated X-ray Raman Excitation of a Metalloporphyrin Dimer.

We propose an X-ray Raman pump-X-ray diffraction probe scheme to follow solvation dynamics upon charge migration in a solute molecule. The X-ray Raman pump selectively prepares a valence electronic wavepacket in the solute, while the probe provides information about the entire molecular ensemble. A combination of molecular dynamics and ab initio quantum chemistry simulations is applied to a Zn-Ni porphyrin dimer in water. Using time-resolved X-ray diffraction and pair distribution functions, we extracted solvation shell dynamics.

Strong-field photoelectron holography in the subcycle limit

Strong-field photoelectron holography is promising for the study of electron dynamics and structure in atoms and molecules, with superior spatiotemporal resolution compared to conventional electron and X-ray diffractometry. However, the application of strong-field photoelectron holography has been hindered by inter-cycle interference from multicycle fields. Here, we address this challenge by employing a near-single-cycle field to suppress the inter-cycle interference. We observed and separated two distinct holographic patterns for the first time. Our measurements allow us not only to identify the Gouy phase effect on electron wavepackets and holographic patterns but also to correctly extract the internuclear separation of the target molecule from the holographic pattern. Our work leads to a leap jump from theory to application in the field of strong-field photoelectron holography-based ultrafast imaging of molecular structures.

Scattering of ultrashort electron wave packets: optical theorem, differential phase contrast and angular asymmetries

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1 fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams.

Two-dimensional nonlinear spectroscopy in the extreme ultraviolet to study dynamics of atomic and molecular gases

We present a two-dimensional (2D) nonlinear four-wave mixing scheme in the extreme ultraviolet (XUV) to investigate ultrafast electronic wave-packets dynamics of multi-electron states in the above-threshold ionization region, using atomic argon and molecular nitrogen as examples. Coherent light sources in the range between 24 and 45 eV is generated by phase-matched cascaded four-wave mixing processes with a collinear configuration of laser fields 800 nm and 1400 nm. Motion of the electrons involving the excited states 3s3p6np (1P10) of argon gas, theF2Σg+ state and the predissociation state C2Σu+ of molecular nitrogen ion N2+ are unravelled through the ‘on-axis’ and ‘off-axis’ features of the two-dimensional spectra. Interpretation of the experimental data is supported by a theoretical dipole control model. Hence, results of this study may be promising for studies of dynamics of electrons in more complex systems.

Nonspreading relativistic electron wavepacket in a strong laser field

A solution of the Dirac equation in a strong laser field presenting a nonspreading wave packet of the electron is derived. It consists of a generalization of the self-accelerating free electron wavepacket [I. Kaminer , ] to the case with the background of a strong laser field. Built upon the notion of nonspreading for an extended relativistic wavepacket, the concept of Born rigidity for accelerated motion in relativity is the key ingredient of the solution. At its core, the solution comes from the connection between the self-accelerated free electron wavepacket and the eigenstate of a Dirac electron in a constant and homogeneous gravitational field via the equivalence principle. The solution is an essential step towards the realization of the laser-driven relativistic collider [S. Meuren , ], where the large spreading of a common Gaussian wavepacket during the excursion in a strong laser field strongly limits the expectable yields. Published by the American Physical Society 2024

Control of quantum paths in harmonic generation through orthogonal fields specific frequency ratios

By solving a two-dimensional, time-dependent Schrödinger equation, we investigate high-order harmonic generation for the H2+ molecular ion in orthogonally polarized two-color laser pulses. We find that harmonic generation depends on the frequency ratio n=ωyωx . When the wavelength is 800 nm and n = 1.2, the harmonic plateau becomes smoother, and the quantum orbital interference decreases. We change the fundamental wavelength and find that the harmonic spectrum exhibits a supercontinuum structure, and the quantum orbital is controllable. When the wavelength is 1600 nm and 2000 nm, and n = 1.2, we gain a deeper understanding of the physical process of harmonics. We have provided the time-frequency distribution and the probability density of an electron wave packet picture. Next, we analyzed the impact of the carrier-envelope phase on harmonics, and we combined Lissajous figures to continue our analysis. The research results find that when the carrier-envelope phase is 0, 0.5π, π, and 1.5π, the harmonic intensity becomes higher, and all exhibit a supercontinuum structure. We chose certain orders of harmonics, and isolated attosecond pulses can be synthesized.

Ultrafast Kapitza-Dirac effect.

Similar to the optical diffraction of light passing through a material grating, the Kapitza-Dirac effect occurs when an electron is diffracted by a standing light wave. In its original description, the effect is time independent. Here, we extended the Kapitza-Dirac effect to the time domain. By tracking the spatiotemporal evolution of a pulsed electron wave packet diffracted by a 60-femtosecond (where one femtosecond = 10-15 seconds) standing wave pulse in a pump-probe scheme, we observed time-dependent diffraction patterns. The fringe spacing in the observed pattern differs from that generated by the conventional Kapitza-Dirac effect. By exploiting this time-resolved diffraction scheme, we can access the time evolution of the phase properties of a free electron and potentially image ionic potentials and electronic decoherences.

Simulating Attochemistry: Which Dynamics Method to Use?

Attochemistry aims to exploit the properties of coherent electronic wavepackets excited via attosecond pulses to control the formation of photoproducts. Such molecular processes can, in principle, be simulated with various nonadiabatic dynamics methods, yet the impact of the approximations underlying the methods is rarely assessed. The performances of widely used mixed quantum-classical approaches, Tully surface hopping, and classical Ehrenfest methods are evaluated against the high-accuracy DD-vMCG quantum dynamics. This comparison is conducted for the valence ionization of fluorobenzene. Analyzing the nuclear motion induced in the branching space of the nearby conical intersection, the results show that the mixed quantum-classical methods reproduce quantitatively the average motion of a quantum wavepacket when initiated on a single electronic state. However, they fail to properly capture the nuclear motion induced by an electronic wavepacket along the derivative coupling, the latter originating from the quantum electronic coherence property, key to attochemistry.