Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Local Information Density and the Space-Time Limit: A Physical Framework Grounded in Attosecond Scanning Tunnelling Microscopy

Thomas Wayne Lish

Published Oct 26, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.23668433

Related papers

Tracking electrons at the space-time limit

Simon Maier, Raffael Spachtholz, Katharina Glöckl +12 more

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.

Nature Photonics•Jul 3, 2026•1 citation

Strong-Field Theory of Attosecond Tunneling Microscopy

Boyang Ma, Michael B. Kruger

Attosecond observations of coherent electron dynamics in molecules and nanostructures can be achieved by combining conventional scanning tunneling microscopy (STM) with ultrashort femtosecond laser pulses. While experimental studies in the subcycle regime are under way, a robust strong-field theory description has remained elusive. Here we devise a model based on the strong-field approximation. Valid in all regimes, it provides a surprising analogy to the standard model of STM. We show that the intuitive three-step model of attosecond science directly emerges from our model and we also describe the optimal conditions for attosecond STM experiments.

arXiv:2311.16626•Physical Review Letters•Dec 2, 2024•6 citations

Attosecond real-time observation of electron tunnelling and multi-electron dynamics in atoms

Martin Schultze, Matthias Uiberacker, Thorsten Uphues +15 more

This report presents the first real-time observation of electron tunnelling and multi-electron dynamics in atoms exposed to intense light. The observed sub-femtosecond ionization steps provide a powerful means of probing the transient population of short-lived valence electronic states in excited atoms offering direct, time-domain access to a wide range of multi-electron dynamics unfolding on an attosecond to femtosecond time scale. The results of pump-probe measurements are in good agreement with the predictions of the theory Keldysh put forward four decades ago.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2007•2 citations

Attosecond Qubits in Strong-Field Physics

Oren Cohen

This perspective introduces attosecond qubits: coherent two-level subsystems that arise naturally in strong-field physics from the interference of experimentally distinguishable quantum pathways. These attosecond qubits are dynamical superposition states formed during strong-field evolution and appear in diverse settings: short-long trajectories in HHG, early-late ionization bursts, polarization-selective recombination channels, and momentum- or energy-bin structures in ATI. Attosecond qubits can be prepared, rotated, and measured using existing attosecond techniques, providing a Hilbert-space description of sub-cycle electronic dynamics. Coulomb interaction, tunneling fluctuations, soft-photon dressing, and macroscopic propagation define ultrafast decoherence channels. This framework links attosecond physics with quantum information science and identifies new opportunities for coherence metrology, temporal quantum tests, ultrafast decoherence studies, and the exploration of quantum speed limits in strongly driven, time-dependent Hamiltonians.

•Dec 25, 2025•0 citations

Attosecond momentum-resolved resonant inelastic x-ray scattering for imaging coupled electron-hole dynamics

Maksim Radionov, Daria Popova-Gorelova

Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an $α$-sexithiophene molecule, in which coupled electron-hole dynamics are excited.

physics.comp-phCross-listedarXiv:2511.20161•Nov 26, 2025

Attosecond-resolved quantum fluctuations of light and matter

Matan Even Tzur, Chen Mor, Noa Yaffe +10 more

Until recently, attosecond optical spectroscopy and quantum optics evolved along non-overlapping directions. In attosecond science, attosecond pulses have been regarded as classical waves, applied to probe electron dynamics on their natural time scale. Here, we transfer fundamental concepts of quantum optics into attosecond physics, enabling control of both the properties of the XUV attosecond pulses and the quantum fluctuations of matter on attosecond time scales. By combining bright squeezed vacuum (BSV) with a strong laser field to drive high-harmonic generation, we transfer the quantum properties of the BSV onto the resulting XUV attosecond pulses. Applying advanced attosecond interferometry, we reconstruct the quantum state of the XUV high harmonics and their associated attosecond pulses with attosecond precision. Finally, we resolve the squeezing of the electron's wavepacket during one of the most fundamental strong-field phenomena - field induced tunneling. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond quantum electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.

physics.opticsCross-listedarXiv:2511.18362•Nov 25, 2025•2 citations
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.
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.
Attosecond observations of coherent electron dynamics in molecules and nanostructures can be achieved by combining conventional scanning tunneling microscopy (STM) with ultrashort femtosecond laser pulses. While experimental studies in the subcycle regime are under way, a robust strong-field theory description has remained elusive. Here we devise a model based on the strong-field approximation. Valid in all regimes, it provides a surprising analogy to the standard model of STM. We show that the intuitive three-step model of attosecond science directly emerges from our model and we also describe the optimal conditions for attosecond STM experiments.
This report presents the first real-time observation of electron tunnelling and multi-electron dynamics in atoms exposed to intense light. The observed sub-femtosecond ionization steps provide a powerful means of probing the transient population of short-lived valence electronic states in excited atoms offering direct, time-domain access to a wide range of multi-electron dynamics unfolding on an attosecond to femtosecond time scale. The results of pump-probe measurements are in good agreement with the predictions of the theory Keldysh put forward four decades ago.
This perspective introduces attosecond qubits: coherent two-level subsystems that arise naturally in strong-field physics from the interference of experimentally distinguishable quantum pathways. These attosecond qubits are dynamical superposition states formed during strong-field evolution and appear in diverse settings: short-long trajectories in HHG, early-late ionization bursts, polarization-selective recombination channels, and momentum- or energy-bin structures in ATI. Attosecond qubits can be prepared, rotated, and measured using existing attosecond techniques, providing a Hilbert-space description of sub-cycle electronic dynamics. Coulomb interaction, tunneling fluctuations, soft-photon dressing, and macroscopic propagation define ultrafast decoherence channels. This framework links attosecond physics with quantum information science and identifies new opportunities for coherence metrology, temporal quantum tests, ultrafast decoherence studies, and the exploration of quantum speed limits in strongly driven, time-dependent Hamiltonians.
Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an ααα-sexithiophene molecule, in which coupled electron-hole dynamics are excited.
Until recently, attosecond optical spectroscopy and quantum optics evolved along non-overlapping directions. In attosecond science, attosecond pulses have been regarded as classical waves, applied to probe electron dynamics on their natural time scale. Here, we transfer fundamental concepts of quantum optics into attosecond physics, enabling control of both the properties of the XUV attosecond pulses and the quantum fluctuations of matter on attosecond time scales. By combining bright squeezed vacuum (BSV) with a strong laser field to drive high-harmonic generation, we transfer the quantum properties of the BSV onto the resulting XUV attosecond pulses. Applying advanced attosecond interferometry, we reconstruct the quantum state of the XUV high harmonics and their associated attosecond pulses with attosecond precision. Finally, we resolve the squeezing of the electron's wavepacket during one of the most fundamental strong-field phenomena - field induced tunneling. The ability to measure and control quantum correlations in both electrons and XUV attosecond pulses establishes a foundation for attosecond quantum electrodynamics, manipulating the quantum state of electrons and photons with sub-cycle precision.