Physicists have discovered a quantum effect that allows them to produce X-ray photons with energies above the limit predicted by standard laser physics theory. In an experiment with helium atoms, the researchers caused two electrons to release energy simultaneously. The results show that interactions between electrons can alter limits that for decades were considered fundamental to one method of generating short X-ray pulses.

The work was carried out by an international team of scientists from TU Wien and the University of California San Diego. The results were published in the journal Nature Photonics.

How a laser generates X-ray pulses

When an intense laser pulse interacts with an atom, it can knock an electron out of it. The laser's electric field accelerates the freed particle and then directs it back toward the atom. Upon returning, the electron releases its accumulated energy as light with a frequency far higher than that of the original laser light.

This process is called high-harmonic generation. It makes it possible to produce extremely short light pulses, including in the X-ray range, and has played an important role in the development of attosecond physics—a field that studies processes on timescales measured in attoseconds.

“The mechanism behind the generation of short X-ray pulses has long been known,” explains Professor Tenio Popmintchev of TU Wien's Institute of Photonics.

In the 1990s, Ferenc Krausz developed pioneering experiments that used this mechanism. His research contributed to the development of attosecond physics, achievements in which were recognized with the 2023 Nobel Prize in Physics.

However, the conventional process has a limitation. According to theory, the energy of the emitted photons cannot exceed a certain maximum, which depends on the interaction between the laser field and the electron. Above this threshold, the radiation intensity drops sharply. Until now, this limitation has been considered within the framework of a mechanism involving a single electron.

Two electrons change the rules

The researchers decided to test whether this limit could be exceeded if two electrons were involved in the process. For the experiment, they exposed helium atoms to intense pulses of ultraviolet light.

Unlike the more familiar scenario in which a laser ejects and returns a single electron, here the electrons were released sequentially. Their behavior nevertheless remained quantum-correlated: the motion of one particle could not be considered entirely independently of the motion of the other.

By carefully adjusting the parameters of the ultraviolet pulses, the physicists were able to make both electrons return to the atom simultaneously.

“Using ultraviolet control pulses, we can arrange for both electrons to return to the atom at exactly the same moment,” says Dimitar Popmintchev, a postdoctoral researcher in Tenio Popmintchev's group at TU Wien.

As a result, the energy of the two electrons is released simultaneously. This creates the conditions for generating a single X-ray photon with a higher energy and, accordingly, a higher frequency than the conventional single-electron model allows.

The new mechanism thus makes it possible to exceed what was previously considered the upper limit of high-harmonic generation in a single-electron process.

An unexpected signal in the spectrum

The experiment provided observable evidence of the new mechanism. Analyzing the spectrum of the coherent radiation, the scientists discovered an additional region of intense emission—a so-called plateau—at photon energies far above the theoretically predicted limit.

This additional plateau was weaker than the main signal but extended far beyond the usual energy range.

The response of different atoms provided an important clue. The unusual effect was observed in helium but did not appear in the same way in experiments with argon and neon.

According to the researchers, the difference is related to the particular characteristics of electron interactions in these atoms. In helium, correlations between the two electrons play an especially important role and allow their motion to be coordinated so that energy is released simultaneously. Under the experimental conditions, the outer electrons of argon and neon did not exhibit similar behavior.

These results support the explanation that exceeding the usual energy limit is specifically due to the joint participation of two quantum-correlated electrons.

A new tool for studying quantum systems

The discovery is important not only because it makes it possible to produce higher-energy X-ray photons. It could also give physicists a new way to investigate electron interactions within atoms, molecules, and solid materials.

Coherent X-ray radiation can serve as a sensitive spectroscopic probe of electron correlations. By examining the shape of the spectrum, the maximum photon energy, and changes in the radiation as the polarization of the laser light is rotated, researchers will be able to obtain information about the behavior of interacting electrons.

Such processes unfold on attosecond timescales. One attosecond is (10^{-18}) seconds—one billionth of a billionth of a second. Studying phenomena over such short periods is essential to understanding how electrons move and influence one another in quantum systems.

Looking ahead, the scientists hope to extend this approach to more complex systems—molecules and solid materials in which electrons interact particularly strongly. This could help improve our understanding of the properties of quantum materials and lead to new methods for controlling their behavior.

High-harmonic generation, once one of the tools that helped establish attosecond physics, could now help researchers study not only the motion of individual electrons but also the complex interactions between multiple quantum particles. Such research could expand our knowledge of quantum systems, including those of interest for quantum computing and the creation of nanomaterials with tailored properties.