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Nature Photonics

Tracking electrons at the space-time limit

Simon Maier, Raffael Spachtholz, Katharina Glöckl, Carlos M. Bustamante, Sonja Lingl, Moritz Maczejka, J. Schön, A. Riedel, Klaus Richter, Franz J. Gießibl, Franco P. Bonafé, Markus A. Huber, Ángel Rubio, Jascha Repp, R. Huber

Published Jul 3, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1038/s41566-026-01932-0

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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].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations
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.
Perspective. The concept of local information density (I_d) has remained largely formal because no experimental technique could resolve the relevant spatio-temporal scales in a well-defined quantum environment. The recent demonstration of attosecond-resolution scanning tunnelling microscopy by Maier et al. (Nature Photonics, 2026, doi:10.1038/s41566-026-01932-0) changes this. By sculpting and tracing single-electron wavefunctions with sub-femtosecond temporal and atomic-scale spatial resolution during barrier crossing, Maier et al. provide the first experimental calibration of a tunable space-time volume for a quantum state. We introduce the dimensional proxy I_d^proxy ~ 1/(dx dy dz dt), show that the intermediate light-matter regime (Keldysh parameter ~ 1) observed in tunnelling junctions is formally analogous to the stochastic-coherent coexistence hypothesized to govern chromatin information maintenance, and propose a tiered experimental ladder connecting attosecond surface science to accessible assays of information density in macromolecular assemblies. Explicit scaling cautions and falsification criteria are stated.
Within this work, electron dynamics in atoms are experimentally and numerically investigated on their natural attosecond time scales. To access these dynamics, ultrashort and moderately-intense few-cycle laser pulses are superposed with attosecond pulsed radiation in the extreme-ultraviolet spectral region. Both these sources are combined in a new experimental vacuum setup which was designed and built up from scratch, also in order to generate the attosecond pulses. Novel experimental schemes are developed which involve the temporal and spectral interferometric utilization of both ultrashort light sources and include the multidimensional spectroscopy employing different dynamical parameters. These are the intensity and the carrier-envelope phase of the laser pulses, as well as their temporal delay with respect to the attosecond pulses. Scientifically, the observation and control of the quantum-motion of bound electrons, as well as the laser-driven quasi-classical motion of free electrons was a key goal of this work. In particular, a bound two-electron wave packet in helium on attosecond time scales was experimentally observed for the first time. This was realized by combining unprecedented high temporal and spectral resolution. In addition, a new coupling mechanism of several doubly-excited states to an effective single-electron continuum is identified and analyzed. Both these two-electron states as well as single-electron states are interferometrically investigated with access to the phase of their quantum-mechanical wave function. This allows the observation and control of the quantum dynamics of two correlated electrons in atoms on the attosecond time scale which was demonstrated within the scope of this work.
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
Attosecond chronoscopy enables the exploration of correlated electron dynamics in real time. One key observable of attosecond physics is the determination of "time zero" of photoionization, the time delay with which the wave packet of the ionized electron departs from the ionic core. This observable has become accessible by experimental advances in attosecond streaking and reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) techniques. In this Letter, we explore photoionization time delays by strong extreme ultraviolet fields beyond the linear-response limit. We identify novel signatures in time delays signifying strong coupling between atoms and light fields and the light-field dressing of the ion. As a prototypical case, we study the interelectronic coherence and entanglement in helium driven by a strong extreme ultraviolet field. By the numerical solution of the time-dependent Schrödinger equation in its full dimensionality, we show that the time delay of the photoionized electron allows one to monitor the ultrafast variations of coherence dynamics and entanglement in real time.
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].