Scientists just broke a textbook rule of physics

Scientists have pushed X-ray generation beyond a long-accepted limit in laser physics, revealing a surprising quantum effect that conventional theory does not account for. By directing powerful ultraviolet lasers at helium atoms, researchers produced X-rays with substantially higher energies than the standard model predicts. The breakthrough depends on an unusual interaction between two electrons that allows them to release their energy together. The discovery comes from a collaboration between TU Wien and the University of California San Diego and builds on research that helped establish the field of attosecond physics. Laser techniques developed at TU Wien in the 1990s contributed to advances recognized by the 2023 Nobel Prize in Physics. For decades, scientists have understood that directing laser light at certain atoms can cause them to emit extremely short pulses of much higher-frequency light, including X-rays. However, the established theory predicts a maximum energy for these emissions based on the properties of the incoming laser. Beyond this boundary, known as the energy cutoff, X-ray production becomes extremely weak. The new experiment demonstrates that this familiar limit can be exceeded when two electrons interact in a particular way. The findings were published in Nature Photonics. How Lasers Generate Powerful X-Ray Pulses "The mechanism behind short X-ray pulses has been well known for a long time," says Prof. Tenio Popmintchev from the Institute of Photonics at TU Wien. "The laser tears a single electron away from the atom. The electron is then accelerated in the laser's electric field until it eventually collides with the atom again. The energy it loses in the process is emitted in the form of light." During this process, the laser's electric field drives the freed electron away from its parent atom before bringing it back. When the electron returns and releases its energy, it generates light at frequencies far higher than those of the original laser beam. Nobel laureate Ferenc Krausz used this mechanism in pioneering experiments during the 1990s. Tenio Popmintchev and his colleagues now work at the same TU Wien institute where Krausz conducted his earlier research, but their latest experiment has pushed the process beyond its previously understood boundaries. "It can be shown that when the electron returns to its atom, it generates a whole range of different frequencies with roughly equal intensity," says Dimitar Popmintchev, postdoc in Tenio Popmintchev's team at TU Wien. "But there is an upper limit. Frequencies above this limit are much weaker; it is simply not possible to exceed a certain maximum frequency." That prediction describes the conventional process involving a single electron. The researchers wanted to find out whether the outcome would change if two electrons participated instead. Two Electrons Break the Expected X-Ray Energy Limit To investigate, the team used intense ultraviolet (UV) laser pulses to interact with helium atoms. Unlike the usual process involving one electron, the experiment allowed both of helium's electrons to be removed in succession. The first electron was released and accelerated by the laser field, followed by the second. Although the electrons were freed at different moments, their behavior remained connected through quantum correlations. This relationship means their motions cannot be treated as entirely independent. By carefully controlling the ultraviolet laser pulses, the researchers could arrange for both electrons to return to the atom simultaneously. "Using UV driving pulses, we can arrange for both electrons to return to the atom at exactly the same time," says Dimitar Popmintchev. "The energy of two electrons is then released all at once. And when more energy is available, a single higher-energy X-ray photon with higher frequency can also be generated." This coordinated release of energy makes it possible to produce X-ray photons that exceed the conventional energy cutoff. Rather than relying on the energy of a single returning electron, the process draws on the combined energy of two interacting electrons. An Unexpected X-Ray Signal Confirms the Discovery The researchers found clear experimental evidence that the two-electron process was producing unusually energetic X-rays. When they examined the spectrum of the emitted coherent radiation, they identified a second region of sustained emission at much higher photon energies than the standard theory predicts. This additional region, known as a plateau, was weaker than the primary emission but extended well beyond the previously established energy range. The unexpected signal appeared only when the researchers used helium. Similar experiments involving argon and neon did not produce the same behavior in their outer electrons. This difference provides important evidence for the proposed explanation. Helium has particularly strong correlations between its two electrons, allowing them to interact in ways that make the simultaneous release of energy possible. The outer electrons of argon and neon did not demonstrate the same effect under the experimental conditions. A New Window Into Quantum Physics Beyond producing higher-energy X-rays, the discovery could give scientists a powerful new way to investigate how electrons interact inside atoms and other materials. The unusual coherent X-ray emission could serve as a highly sensitive spectroscopic "sensor" for electron-electron correlations. By studying the shape of the emitted spectrum, its maximum energy, and how it changes with the polarization of the laser light, researchers could gain information about the behavior of interacting electrons on extraordinarily short timescales. These interactions occur over attoseconds, with one attosecond equal to one billionth of a billionth of a second. Observing processes at such speeds is essential for understanding how electrons move and influence one another in quantum systems. Eventually, the same principle might be extended beyond individual helium atoms to molecules and solid materials in which electrons interact strongly. The technique behind the discovery, known as high-harmonic generation, originally helped make attosecond physics possible. Now, researchers are finding that it can also reveal the complex behavior of multiple interacting quantum particles. These insights could contribute to research on quantum computing and help scientists understand and design advanced nanomaterials with carefully controlled properties.