Researchers at the Regensburg Center for Ultrafast Nanoscopy and the Max Planck Institute in Hamburg have experimentally demonstrated a fundamental limit of space and time. The team, led by Profs. Jascha Repp, Rupert Huber, Franz Giessibl, Klaus Richter, and Angel Rubio, found that an electron's location and its behavior over time cannot both be determined with arbitrary precision. This relationship, called the "space-time limit," differs from Heisenberg's uncertainty principle, which does not restrict position and time in the same way.
The researchers used ultrafast lasers to observe electrons tunneling from a metal tip toward a silver surface across distances of only a few atomic diameters. By controlling the timing between two laser pulses separated by a precisely controlled interval, lead author Simon Maier and colleagues could directly observe electron motion occurring on attosecond timescales. One attosecond equals one-billionth of a billionth of a second.
The electrons traveled as quantum waves, passing through an energy barrier via quantum tunneling. Quantum simulations performed by Rubio's team closely reproduced the experimental findings and revealed that electrons lagged behind the light field by approximately 500 attoseconds.
The team discovered a tradeoff between spatial and temporal precision. As Raffael Spachtholz explains: "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." This constraint emerges from how controlling electron motion over extremely short intervals changes the spatial distribution of quantum wave packets.
The researchers placed a single atom on the surface to confine electron wave packets to extremely small regions before laser pulses arrived. Even when electrons received substantial energy, their wave packets remained sufficiently localized for microscopy with atomic spatial resolution and attosecond time resolution.
The discovery could enable technologies operating far faster than today's electronics. One possibility involves using precisely controlled electron wave packets to influence chemical reactions through single electron transfers.