Physicists observe quantum space-time limit for first time

Physicists have for the first time observed a fundamental quantum limit on how precisely the position and time evolution of a single electron can be measured simultaneously, according to a study published in Nature Photonics on July 3, 2026. uni-regensburg.de nature.com

A New Quantum Constraint

The research, conducted by a team at the University of Regensburg’s RUN (Regensburg Center for Ultrafast Nanoscopy) led by Professors Jascha Repp, Rupert Huber, Franz Giessibl, and Klaus Richter, in collaboration with Angel Rubio’s group at the Max Planck Institute in Hamburg, demonstrates that atomic-scale lightwave-driven scanning tunneling microscopy with attosecond time resolution can track individual electrons tunneling through a barrier — but only up to a point. nature.com idw-online.de

The team found that achieving greater spatial resolution in imaging an electron’s position comes at the cost of temporal precision, and vice versa. This trade-off represents what the researchers call the “space-time limit” — a constraint distinct from the well-known Heisenberg uncertainty principle, which governs position and momentum. Instead, the newly confirmed limit applies to position and time, revealing an intrinsic property of quantum mechanical electron wave functions. idw-online.de uni-regensburg.de

How It Was Done

The researchers used lightwave-driven scanning tunneling microscopy, which employs single cycles of terahertz and mid-infrared light to probe tunneling electrons with sub-angstrom spatial resolution and attosecond temporal precision. Upon excitation, electrons were observed tunneling through the microscope’s junction, and the team tracked their intrinsic quantum motion at scales where the space-time limit becomes apparent. nature.com uni-regensburg.de

The paper, titled “Tracking electrons at the space-time limit,” lists authors including K. Richter, F. J. Giessibl, F. P. Bonafé, M. A. Huber, A. Rubio, J. Repp, and R. Huber. idw-online.de

Implications for Quantum Technologies

The findings carry consequences for the development of future quantum technologies. By establishing a measurable boundary on what can be known about an electron’s behavior in space and time, the work provides a framework for understanding electron tunneling dynamics at their most fundamental level. This could inform the design of quantum devices that rely on precisely controlled electron behavior at atomic scales.