Electron tunneling reveals a space-time limit at attosecond scale

By Rebecca Stone

An international team at the University of Regensburg observed electron tunneling on attosecond timescales; quantum simulations found that the electrons lagged behind the laser field by approximately 500 attoseconds.

The University of Regensburg released the result on Nov. 7, 2026. The paper, “Tracking electrons at the space-time limit,” appears in Nature Photonics, volume 20, issue 8, page 961, with DOI 10.1038/s41566-026-01932-0.

What did the experiment establish?

The work provides experimental evidence for a “space-time limit”: defining an electron’s motion more precisely in time requires more energy and broadens the particle’s wave packet in space.

That limitation differs from Werner Heisenberg’s familiar position–momentum uncertainty, which prevents position and momentum from being measured with unlimited precision. The limit comes from quantum law, not microscope quality. The new result concerns position and time, two quantities that the standard uncertainty principle does not restrict in the same way.

The experiment brought together groups at the Regensburg Center for Ultrafast Nanoscopy, or RUN, led by Jascha Repp, Rupert Huber, Franz Giessibl and Klaus Richter, and a Max Planck Institute in Hamburg team led by Angel Rubio. Simon Maier is the paper’s lead author.

At RUN, researchers are developing ultrafast microscopes capable of recording the movements of electrons, atoms and molecules with exceptional precision in space and time. A static microscopic image captures location, but not how a process changes; ultrafast methods effectively create slow-motion films of atomic-scale events.

About 10 years ago, Regensburg scientists used ultrafast scanning tunneling microscopy to resolve a single molecule’s movement across space and time for the first time. Tracking individual electrons was harder because they can move roughly 1,000 times faster than atoms and molecules, with consequential changes unfolding over attoseconds.

One attosecond is one-billionth of a billionth of a second. An atom is approximately 10 million times smaller than a millimeter, while the gap between an attosecond and one second is comparable to the gap between one second and the universe’s age.

How did the team time the motion?

The researchers built a new laser system with finer time resolution than earlier work. Precisely timed pulses drove electrons from an extremely sharp metal tip toward a silver surface across a gap of only a few atomic diameters.

They detected the motion through the resulting electrical current. A second light pulse followed the first after a controlled interval, allowing the team to establish when the electron had crossed. Maier said that varying that interval let the researchers directly observe how the electrons responded.

The pulses transferred electrons even across an energy barrier that classical physics says they lacked the energy to cross. Their behavior was that of quantum waves rather than ordinary particles, demonstrating quantum tunneling.

Co-author and doctoral student Katharina Glöckl characterized the setup as a high-speed camera for electron wave packets because it showed the point in time at which tunneling occurred.

What did the simulations reveal?

Quantum simulations by the group working with Rubio closely reproduced the measurements and identified an approximately 500-attosecond delay between the light field and the electrons’ motion.

The team also found that the laser pulses could not be described fully as either waves or as particles of light called photons; their effects showed characteristics of both descriptions. That mixed behavior was essential when the team probed motion near the space-time limit.

Timing the electrons also changed their spatial distribution. Quantum mechanics represents each electron through a wave packet describing how its wave properties extend across locations. The closer the team pinned down the motion in time, the more broadly that packet spread through space.

Raffael Spachtholz, another co-author, stated the tradeoff directly: “The more precisely we want to pin down the electron's position in time, the more energy we need to provide. And as a result, the electron wave packet spreads out more spatially.”

The team tested the relationship by placing one atom on the surface, confining the electron wave packets immediately before the laser pulses arrived. Even with substantial pulse energy, the packets stayed localized well enough for microscopy with atomic spatial resolution and attosecond time resolution.

What could the result enable?

The immediate target is chemistry. Repp said the next step is to use controlled wave packets to trigger specific chemical reactions and observe, at the length and time scales that matter, how chemical bonds break or change.

Transferring one electron to a molecule is the smallest possible transfer of electric charge. When that electron occupies an exceptionally small region of space and time, the local peak current density can reach 1 trillion amperes per square meter, a condition that could give researchers a new handle on chemical bonds.

The wider research context spans clean energy, quantum computing and electronics for artificial intelligence, all of which depend on understanding chemical reactions, light–material interactions and electron transport through devices. Better control of electron motion may eventually inform faster electronic devices and quantum-information systems.

Can electronics run 100,000 times faster?

No commercial device emerged from the work. The experiment demonstrated a fundamental constraint and a measurement method, not a faster processor, memory device or commercial electronics architecture.

Rupert Huber said: “In the long term, the insights gained could also contribute to operating electronics and quantum information processing at the intrinsic speed limit of electron motion itself—hundreds of thousands of times faster than the currently dominant CMOS technology.”

That remains a long-term technological goal, not a demonstrated commercial roadmap. Repp and Huber argue that the eventual range of applications may depend more on human creativity than on relaxing nature’s constraint. The next test is whether controlled wave packets can trigger and track chemical-bond changes on the relevant length and time scales; the paper does not demonstrate the 100,000-fold speedup, only a limitation that future electronics would have to overcome.