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Physical Review Letters

Attosecond Imaging of Electronic Wave Packets

Gabriel A. Stewart, Paul Hoerner, Duke A. Debrah, Suk Kyoung Lee, H. Bernhard Schlegel, Wen Li

Published Feb 21, 2023• 16 citations
Publisher

Abstract

An electronic wave packet has significant spatial evolution besides its temporal evolution, due to the delocalized nature of composing electronic states. The spatial evolution was not previously accessible to experimental investigations at the attosecond timescale. A phase-resolved two-electron-angular-streaking method is developed to image the shape of the hole density of an ultrafast spin-orbit wave packet in the krypton cation. Furthermore, the motion of an even faster wave packet in the xenon cation is captured for the first time: An electronic hole is refilled 1.2 fs after it is produced, and the hole filling is observed on the opposite side where the hole is born.

DOI
10.1103/physrevlett.130.083202

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An electronic wave packet has significant spatial evolution besides its temporal evolution, due to the delocalized nature of composing electronic states. The spatial evolution was not previously accessible to experimental investigations at the attosecond timescale. A phase-resolved two-electron-angular-streaking method is developed to image the shape of the hole density of an ultrafast spin-orbit wave packet in the krypton cation. Furthermore, the motion of an even faster wave packet in the xenon cation is captured for the first time: An electronic hole is refilled 1.2 fs after it is produced, and the hole filling is observed on the opposite side where the hole is born.
It is observed in a double-slit experiment by Tonomura and coworkers that single electrons recorded as dots on a detector screen build up to show an interference pattern, which is delocalized over the screen [1]. This observation indicates that a delocalized wave function of an isolated electron interacts with the screen, which is a bulk solid composed of many nuclei and electrons interacting with each other, and becomes localized in space. This change, referred to as “collapse” in quantum mechanics, is often accepted as a discontinuous event, but a basic question arises: when and how the delocalized wave function becomes localized? It could be hypothesized that the wave function is delocalized over many particles in the screen just after the arrival of an electron, and the interaction among those many particles promotes localization of this delocalized wave function continuously, but very fast as if it changed discontinuously. My dream is testing this hypothesis by observing the spatiotemporal evolution of a wave function delocalized over many particles interacting with each other. Having this dream in mind, we have developed an experimental toolbox in which ultrafast wave-packet interference in a molecule is visualized and controlled by tailored laser fields with precisions on the picometer spatial and attosecond temporal scales [2-5].
The quantum interference of two molecular wave packets has been precisely controlled in the B electronic state of the I2 molecule by using a pair of fs laser pulses whose relative phase is locked within the attosecond time scale and its real-time evolution has been observed by another fs laser pulse. It is clearly observed that the temporal evolution changes drastically as a function of the relative phase between the locked pulses, allowing us to read both amplitude and phase information stored in the wave functions of the molecular ensemble.
We combine bichromatic polarization pulse shaping with photoelectron imaging tomography for time-resolved spatial imaging of ultrafast spin–orbit wave packet (SOWP) dynamics in atoms. Polarization-shaped two-color pump-probe sequences are generated by spectral amplitude and phase modulation of a femtosecond input pulse and used to excite SOWPs in the potassium fine-structure doublet. By selecting different spectral bands for pump and probe pulse, we achieve interference-free detection of the spatiotemporal SOWP dynamics. Using tomographic techniques, we reconstruct the three-dimensional photoelectron momentum distribution (3D-ED) created by the probe pulse. Time-resolved measurement of the 3D-ED reveals the orbital realignment dynamics induced by spin–orbit interaction in the neutral atom.
Summary form only given. Angstrom and attosecond control of free electron wave packets is one of the pinnacles of attosecond science. Orthogonally polarized two-color (OTC) laser fields allow to control the motion of field-ionizing electronic wave packets both in time and space[1]. In OTC pulses time and space are connected and thus an attosecond time scale is established in the polarization plane for both the emitted and the re-colliding wave packets[2,3].In this submission, we report on experiments that use OTC pulses for studying atomic single and double ionization. The three-dimensional momentum vector of electrons and ions created by single and double ionization of neon atoms was measured with the COLTRIMS technique as a function of the sub-cycle shape of the OTC pulses. We introduce a concept similar to attosecond streaking that allows reading sub-cycle timing information from the momentum vector of emitted electrons. The concept is then applied to gaining information about the influence of the long-range Coulomb potential on the trajectories of tunneling electrons.Fig.1 (a) shows the measured momentum distributions of electrons correlated with singly ionized neon in the polarization plane of the OTC field with relative phase Δφ between the two color components. The spectra show that the electron emission direction is sensitive to Δφ. Furthermore, the spectra feature a prominent x-shaped central structure and weaker fine-scale modulations due to wave packet interferences. To compare with simulated spectra with strong field approximation (SFA) and solving two-dimensional time-dependent Schrödinger equation (TDSE) with single active electron approximation, we conclude that Coulomb effect plays important role on the spatial distribution of released electron wave packets. In the conference, we will furthermore demonstrate control over the correlation between the two electrons emitted during double ionization upon electron recollision by tuning the shape of the electric field of the OTC pulses on the sub-cycle scale. The results of these experiments are in agreement with theoretical predictions [4].
The dynamics of an electronic wavefunction often have non-trivial consequences on its spatial distribution, for example, during tunnelling or chemical bond formation. Yet, revealing spatio-temporal coupling requires ultrafast videography at the intrinsic size of electronic wavefunctions, at the so-called space-time limit. Here we experimentally access the intrinsic quantum motion of individual electrons at the space-time limit while they are tunnelling through an energy barrier, using atomic-scale lightwave-driven scanning tunnelling microscopy with attosecond time resolution. While modulating the tunnelling barrier with two time-delayed near-infrared pulses forming phase-controlled single-cycle waveforms, isolated electron tunnelling transients shorter than 1 fs are identified. The measured spatial extension depends on the interplay of multi-photon and field-driven dynamics, as confirmed by full quantum simulations. We experimentally localize the attosecond-confined tunnelling wave packet on the angstrom scale and use it to map a single copper adatom on a silver surface. This fusion of attosecond science with atomic-scale scanning tunnelling microscopy makes it possible to study wavefunction dynamics inside atoms, molecules and solids.
Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.