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arXiv:2311.16626 · Physical Review Letters

Strong-Field Theory of Attosecond Tunneling Microscopy

Boyang Ma, Michael B. Kruger

Published Dec 2, 2024• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.133.236901

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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.
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 physics enables the study of ultrafast coherent electron dynamics in matter upon photoexcitation and photoionization, revealing spectacular effects such as hole migration and coherent Auger dynamics in molecules. In the photoionization scenario, there has been a strong focus on probing the physical manifestations of internal quantum coherence within the individual parent ion and photoelectron systems. However, quantum correlations between these two subsystems emerging from attosecond photoionization events have thus far remained much more elusive. In this work, we design theoretically and model numerically a direct probe of quantum entanglement in attosecond photoionization in the form of a Bell test. We simulate from first principles a Bell test protocol for the case of noble gas atoms photoionized by ultrashort, circularly polarized infrared laser pulses in the strong-field regime predicting robust violation of the Bell inequality. This theoretical result paves the way for the direct observation of entanglement in the context of ultrafast photoionization of many-electron systems. Our work provides a novel perspective on attosecond physics directed toward the detection of quantum correlations between systems born during attosecond photoionization and unraveling the signatures of entanglement in ultrafast coherent molecular dynamics, including in the chemical decomposition pathways of molecular ions. Published by the American Physical Society 2024
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.
Multielectron tunneling ionization creates ionic coherence crucial for lasing and driving electron motion in molecules. While tunneling is well understood as a single active electron process, less emphasis has been placed on theoretical descriptions of bound electrons during tunneling. This work systematically investigates multielectron tunneling ionization based on the strong field approximation, establishing a theoretical foundation and demonstrating the equivalence of wave function and density matrix approaches for subcycle ionic dynamics. An accurate subcycle nonadiabatic ionization rate is also derived and incorporated into the theory to improve its quantitative accuracy. Applying the theory to N2_{2}2​ and CO2_{2}2​, this work showcases how an intense laser field can induce ionic coherence in molecules as observed in previous experiments. These findings encourage future investigations into multielectron tunneling ionization and its applications in lasing and in controlling chemical reactions.
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.