A research team led by Profs. Jascha Repp, Rupert Huber, Franz Giessibl, and Klaus Richter at RUN, as well as a team led by Angel Rubio at the Max Planck Institute in Hamburg, discovered for the first time that the location and time evolution of an electron cannot be measured with arbitrary precision at the same time. The results were reported in Nature Photonics.
Artist’s rendering of an extremely short electron wave packet (blue) at the boundary between space and time. The electron flash, which lasts only attoseconds, is generated between the tip of a special microscope and a material sample. It is triggered by precisely controlled infrared light pulses (not shown). A cloud of electrons surrounds the system, made visible by computer simulations. Image Credit: Brad Baxley (parttowhole.com)
Heisenberg's renowned uncertainty principle describes one of the most intriguing aspects of quantum physics: certain pairs of physical quantities that characterize a particle, such as position and momentum, cannot both be determined with arbitrary precision at the same time. This limitation is not the result of imperfect measuring instruments, but a fundamental property of nature itself. By contrast, there is no Heisenberg uncertainty principle relating location and time.
The so-called space-time resolution limit has significant implications for future technologies.
Many emerging technologies, including green energy, quantum technologies, and high-performance electronics for artificial intelligence, depend on a precise understanding of matter at the microscopic level. This includes understanding how chemical reactions occur, how light interacts with matter, and how electrons move through electronic components.
High-resolution still images of the fundamental building blocks of matter are insufficient. Instead, time-resolved, slow-motion movies of the nanocosmos are needed to capture these processes in real time.
The Regensburg Center for Ultrafast Nanoscopy (RUN) develops and uses ultrafast microscopes to directly capture the motion of electrons, atoms, and molecules in tiny slow-motion images with the greatest spatial and temporal resolution. Ten years ago, in Regensburg, ultrafast scanning tunneling microscopy was used for the first time to determine the motion of a single molecule in space and time.
At these length scales, electrons move roughly a thousand times faster than atoms and molecules, on timescales measured in attoseconds. The differences in scale are staggering. An atom is approximately ten million times smaller than a millimeter, while an attosecond is one billionth of a billionth of a second (10-¹8 seconds).
To put this into perspective, an attosecond relates to a second in much the same way that a second relates to the age of the universe. Even more remarkably, the motion of electrons is governed by the counterintuitive laws of quantum physics rather than the familiar rules of classical mechanics.
To obtain a similar gain in temporal resolution over earlier studies, as well as to directly view and manipulate the quantum dynamics of individual electrons, the researchers created a novel laser system. They use laser pulses to regulate electron transportation on these extreme time scales, allowing electrons to migrate from an atomically sharp metal tip to a silver surface in the span of a few atomic diameters. These electron motions are monitored in current, and temporal information is gained using two light pulses.
By varying the time interval between the two laser pulses, we can directly observe how the electrons respond.
Simon Maier, Study Lead Author, Regensburg Center for Ultrafast Nanoscopy
The electron mobility recorded in this fashion displays signatures on attosecond timescales, implying that light pulses may move electrons on these timescales and can be detected doing so. What distinguishes this is that the electrons do not behave like classical particles. Rather, as quantum mechanical waves, the electrons pass the energy barrier between the tip and the sample, despite the fact that they lack sufficient energy according to conventional physics. They “tunnel” through it, as if they went through a massive wall without breaking it down.
Our measurement can be understood as a high-speed camera for the electron wave packets, since you can see at what point in time the tunneling process takes place.
Katharina Glöckl, Study Co-Author and Doctoral Student, Universität Regensburg
Professor Angel Rubio’s group used complicated simulations to better understand tiny electron dynamics at the “space-time limit.” The calculations describe the experimental data with amazing precision. They also show that the electron does not instantaneously follow the light field, but rather with a 500 attosecond delay.
In this border region of the tiniest spatial and temporal scales, physical boundaries of quantum physics are revealed on numerous levels. The action of laser pulses, for example, cannot be easily attributed to either the wave or photon picture of light, but exhibits characteristics of both, which is precisely what allowed the researchers to probe so far into the "space-time limit.”
When electrons are transported by light pulses over small time scales, the spatial distribution of the electrons is complicated, as represented in quantum mechanics as wave packets.
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.
Raffael Spachtholz, Study Co-Author, Universität Regensburg
The researchers investigated this association by placing a single atom to atomically limit the electron wave packets right before the light pulses arrived. This enabled them to directly identify the link between the geographic and temporal distribution of electron wave packets. Fortunately, despite tremendous excitation, the electron wave packets are spatially defined and crisp enough to allow for atomically resolved imaging on attosecond timescales.
With this latest breakthrough, the team is pushing the limits previously only vaguely suspected spatiotemporal limit of quantum mechanical electron wave functions, to explore for the first time how electrons’ temporal dynamics shape the spatial structure of their wave function. This also offers up whole new avenues for application.
For example, transferring a single electron to a molecule may seem like a negligible charge transfer. However, if that electron is confined to an extremely small region of space and time, it corresponds to extraordinarily high local peak current densities of up to one trillion amperes per square centimeter.
“In the future, we want to use such wave packets to specifically trigger chemical reactions and observe, on the relevant length and time scales, how chemical bonds can be broken or altered,” explained Prof. Jascha Repp enthusiastically.
“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,” added Prof. Rupert Huber.
The two project heads concur that rather than being constrained by nature, the potential uses of electrons near the space-time limit are now mostly determined by human creativity.
Journal Reference:
Maier, S., et al (2026) Tracking electrons at the space-time-limit. Nature Photonics. DOI: 10.1038/s41566-026-01932-0. https://www.nature.com/articles/s41566-026-01932-0.