Scientists at the X-ray free-electron laser SwissFEL have realised a long-pursued experimental goal in physics: to show how electrons dance together. The technique, known as X-ray four-wave mixing, opens a new way to see how energy and information flow within atoms and molecules. In the future, it could illuminate how quantum information is stored and lost, eventually aiding the design of more error-tolerant quantum devices. The findings are reported in Nature.

Much of the behaviour of matter arises not from electrons acting alone, but from the ways they influence each other. From chemical systems to advanced materials, their interactions shape how molecules rearrange, how materials conduct or insulate and how energy flows.

In many quantum technologies – not least quantum computing – information is stored in delicate patterns of these interactions, known as coherences. When these coherences are lost, information disappears – a process known as decoherence. Learning how to understand and ultimately control such fleeting states is one of the major challenges facing quantum technologies today.

Until now, although many techniques let us study how individual electrons behave, we have mostly been blind to these coherences. Scientists at SwissFEL from the Paul Scherrer Institute PSI and Swiss Federal Institute of Technology in Lausanne (EPFL), in collaboration with the Max Planck Institute of Nuclear Physics in Germany and University of Bern, have now developed a way to access them using a technique known as X-ray four-wave mixing.

“We learn how the electrons dance with each other – whether they hold hands, or if they dance alone,” says Gregor Knopp, senior scientist in the Center for Photon Sciences at Paul Scherrer Institute PSI, who led the study. “This gives us a new view on quantum phenomena and can change how we understand matter.”

Like NMR, but with X-rays

Conceptually, X-ray four-wave mixing is similar to nuclear magnetic resonance (NMR), which today is used daily in hospitals for MRI scans. Both techniques use multiple pulses to create and read out coherences in matter.

The process of four-wave mixing is also already well-established using infrared and visible light, where it allows scientists to investigate how molecules move, vibrate and interact with one another – with applications ranging from optical communications to imaging biological samples.

X-rays bring this same kind of powerful approach to a smaller scale and allow us to step into the world of the electrons. “Whereas other approaches tell us about how atoms or molecules as a whole interact with each other or with their surroundings, with X-rays we can zoom right in to the electrons,” says Ana Sofia Morillo Candas, first author of the paper.

This ability to zoom in on the interactions between electron has the potential to provide completely new insights not only into quantum information, but also into many other areas – for example biological molecules or materials for solar cells and batteries.

The impossible experiment

Turning this kind of X-ray experiment into reality, however, remained almost impossible to achieve until now – even decades after it was first envisioned.

In four-wave mixing, three incoming light waves interact with matter to produce a fourth wave. “In general, to do four-wave mixing, you have to split, delay and recombine different beams of light,” explains Morillo Candas. “This is difficult with X-rays because the wavelength is so short – you have to be unbelievably exact.” Put simply, the challenge of manipulating three X-ray beams is like trying to throw three darts from a kilometre away and have them land on the dartboard within nanometres of each other.

This precision alone is not enough: the X-ray four-wave mixing signal that is generated is also extremely weak. To see it at all, the experiment needs extremely bright and ultrashort bursts of X-ray light – something only large X-ray free-electron laser facilities such as SwissFEL can offer. “Scientists have been dreaming about this experiment since SwissFEL was first built ten years ago,” says Knopp.

A light in the night

The success relied on a trick borrowed from experiments with ordinary laser light rather than X-rays: an aluminium plate with four tiny holes. The X-ray beams pass through three holes and – if the experiment is successful – a new X-ray signal appears at the fourth.

“It’s conceptually a simple solution,” says Knopp, who has a background working with optical laser light. “If you do these experiments with infrared or visible light, this is how you would do it.” This approach is very different to previous attempts made at X-rays four-wave mixing, but to Knopp, it seemed like the obvious method to try. “We were amazed when we saw how large the signal was,” he adds.

It was the middle of the night, when Morillo Candas, at that time a postdoc at PSI, saw the signal in the control room of the Maloja experimental station at SwissFEL. She remembers: “It glowed like a light on the screen. To anyone else, it would look like nothing. But we jumped for joy.”

From a first signal to a mainstream imaging technology

This first successful demonstration of X-ray four-wave mixing was achieved in a noble gas, neon: a comparatively well understood system without complicated electron interactions – the ideal testbed in which to spot the elusive four-wave mixing signal.

Now that the proof of principle has been achieved, scientists will be able to move forward to more complex systems. Both Morillo Candas and Knopp believe that the simplicity of their solution makes it unusually robust and will speed up its adoption.

The next steps at SwissFEL will be to study more complex gases and eventually liquids and solids, where the electrons within molecules interact in richer ways.

But this is likely to be only the beginning for the technique. Eventually, it could be used as an imaging method that reveals where coherences live and where they break down inside a material or a device – in other words, where quantum information is stored and where it is lost. This could give designers clues on how to build more stable qubits and reduce errors in future quantum computers – insights that are simply not available today.

“If in the 1960s you had asked ‘can you do an NMR of my knee’, the answer would have been ‘what?’ But the start was the same – a first signal,” says Knopp. “This is where we are now. I think if we fast forward, one day X-ray four-wave mixing could be a mainstream technique for imaging tiny quantum devices.”

Text: Paul Scherrer Institute / Miriam Arrell