Text from the interactive explanation

Experimental demonstration of attosecond hard X-ray pulses

Ichiro Inoue, River Robles, Aliaksei Halavanau, Veronica Guo, Thomas M. Linker Andrei Benediktovitch, Andrei Benediktovitch, Stasis Chuchurka, Matthew Seaberg, Yanwen Sun, Diling (author) Zhu, David Cesar, Yuantao Ding, Vincent Esposito, Paris Franz, Nicholas Sudar, Zhen Zhang, Taito Osaka, Gota Yamaguchi, Yasuhisa Sano, Kazuto Yamauchi, Jumpei Yamada, Uwe Bergmann, Matthias F. Kling, C. Pellegrini, Makina Yabashi, Nina Rohringer, Takahiro Sato, Agostino Marinelli

Nature Photonics · 2026 · Inoue, Robles et al.

Could an X-ray flash finish its picture before it starts damaging what it photographs? That needs hard X-ray pulses lasting only attoseconds , and until this experiment nobody could prove such a flash was really that short. The trick: a sliver of copper that bursts into an avalanche of light only when the flash is brief enough.

Simulated view. Flash length (100 as of light is 30 nm thick), the 150 nm focus and the 400 as core-hole lifetime are drawn to scale; atoms are drawn sparsely, time is slowed about 1015×, and the trip through the 20 µm foil is fast-forwarded. Photon counts per shot come from the paper's simulation (Figs. 3 and 8) with random counting noise; *peak core holes come from the simplified leaky-bucket model explained in chapter 03. Try it: drag the duration from 100 as to 1 fs. The energy stays the same, yet the avalanche nearly dies.

01 · Two kinds of fast

To photograph an electron, you need two kinds of fast

An attosecond is a billionth of a billionth of a second. It is to one second what one second is to about 32 billion years, more than twice the age of the universe. Electrons inside atoms and molecules rearrange on this timescale, and physicists want to film it.

A camera for that needs two things. First, a flash short enough to freeze the motion: in 100 attoseconds even light travels only 30 nanometres. Second, light with a wavelength small enough to show atoms. That means hard X-rays . The X-ray photons in this experiment each carry 9.05 keV of energy and have a wavelength of 0.137 nm, about the spacing between atoms.

Build the camera

An electron cloud sloshes across a small molecule about once per femtosecond (1 fs = 1000 as). Choose the light and the flash length, then look at the photo.

Blurred in space.

Where attosecond flashes existed (photon energy per flash photon, approximate ranges)

The authors describe their result as extending the photon-energy reach of attosecond techniques by about one order of magnitude.

Lasers have made attosecond flashes of extreme-ultraviolet light for over two decades, and X-ray free-electron lasers recently made them in soft X-rays. Hard X-ray flashes this short had been reported, but their length was only inferred indirectly. This paper presents the first direct experimental evidence for them.

What you just sawHard X-rays give the sharpness; attoseconds freeze the motion. Only a flash with both can photograph electrons moving.

02 · One spike, not many

Making a single flash, and why nobody could time it

The flashes come from the Linac Coherent Light Source (LCLS) at SLAC in California, an X-ray free-electron laser . A bunch of electrons, accelerated to about 10 GeV, zig-zags through an undulator, a long row of alternating magnets, and gives off X-rays. Light and electrons push on each other, so the emission amplifies itself, starting from random noise in the bunch. The result is a pulse made of random spikes.

Normally a pulse holds many spikes spread over several femtoseconds. To get just one, the team reshaped the electron bunch. They split the laser pulse that creates the electrons into two parts with a slight gap. The small dip in electron current grows into a single, very dense spike: about 10–20 kiloamperes squeezed into less than a femtosecond. A gradual change along the undulator (a "taper") lets only that spike lase.

Shape the lasing window

Shrink the part of the electron bunch that is allowed to lase. A new random shot fires every two seconds.

Multi-spike pulse.

In the experiment about 6.5% of shots showed a single smooth spectrum about 20 eV wide (Fig. 1b,c below); only those shots were analysed.

Even a perfectly smooth single-spike spectrum can't say how long the flash lasts. A spectrum lists which X-ray "colours" (photon energies) are present, not the order in which they arrive.

Same colours, different lengths

Keep the spectrum fixed at 20 eV wide and add chirp, so the colours arrive one after another instead of all at once.

Pulse duration91 as

Spectrometer sees20 eV wide, unchanged

A pulse with 20 eV of bandwidth can be as short as 91 attoseconds, but only if all its colours arrive together. The same spectrum can also belong to a pulse ten times longer. So a spectrum gives only a lower limit on duration. In soft X-rays, physicists time flashes by "streaking" the electrons they knock loose with an infrared laser. For hard X-rays, no such stopwatch existed.

What you just sawA spectrum only says "at least this short". To show "no longer than this", the team needed a clock that responds to the flash's length itself.

03 · Copper keeps time

A clock made of vanishing electrons

When a 9.05 keV X-ray photon hits a copper atom, it can knock out one of the two innermost electrons (the K shell). That leaves a core hole , a vacancy deep inside the atom. It doesn't last: in about 400 attoseconds an electron from the next shell drops in. Sometimes the released energy leaves as a new X-ray photon called Kα . It comes in two slightly different versions, Kα1 (8048 eV) and Kα2 (8028 eV), normally in a 2 : 1 ratio, flying off in random directions.

One copper atom

Each cycle: an X-ray photon (cyan) arrives, a K-shell electron flies out, the core hole glows (one second here stands for about 400 as), then an L-shell electron drops in. Either a Kα photon leaves in a random direction, or the energy kicks out another electron instead.

Kα1: 0 · Kα2: 0

That 400-attosecond lifetime is the clock. Picture core holes as water in a leaky bucket . The X-ray pulse is the tap; the leak drains holes as fast as electrons refill them. Pour the same amount of water (the same pulse energy) quickly and the level shoots up. Pour it slowly and the bucket leaks nearly as fast as it fills.

The leaky bucket

Same pulse energy every time. Only how fast it is poured changes.

Peak level: 30% of the instant-pour maximum

Why does the level matter? When many atoms hold core holes at the same moment, a Kα photon passing one of them can make it emit an identical copy travelling the same way. This is stimulated emission , the principle behind every laser. Copies make more copies. Along the 20-micrometre foil, a photon born near the entrance can grow into an avalanche: amplified spontaneous emission , or ASE.

From a whisper to an avalanche

The bucket level above sets how many atoms are primed. Watch light cross the 20 µm foil from left to right.

×3 amplification

Because the avalanche grows exponentially, a modest change in the level makes an enormous change in the output. The team measured each pulse's energy, and they knew the focus (150 nm across). So the brightness of the avalanche reveals how fast the energy was poured in: the pulse duration.

How do we know the copper's light really was an avalanche? Look at its colours.

The avalanche's fingerprint

Kα1 : Kα2 ≈ 2 : 1. Ordinary emission: Kα1 is about twice as bright.

In ordinary emission Kα1 is only twice as bright as Kα2. In the measured spectrum it is roughly twenty times brighter. Amplification compounds like interest: the line that grows slightly faster pulls far ahead. This showed the team that the light was amplified, and that the focused X-rays reached an extreme intensity of around 1019 watts per square centimetre.

What you just sawShorter flash → more core holes at once → an exponentially bigger avalanche. Copper turns time into brightness.

04 · A first estimate

A first, rough reading of the clock

For pulses with a clean single-spike spectrum, the copper avalanche switches on steeply above about 1.5 microjoules . Pulses with multi-spike spectra spread the same energy over several spikes, so their peak intensity is lower, and they barely produce any avalanche.

When does copper start to lase?

Threshold intensity fixed at 2×1019 W/cm², measured in an earlier copper experiment with 7 fs pulses.

1.50 µJ ÷ (2×10¹⁹ W/cm² × 150 nm × 150 nm)

duration ≈ 333 as

The answer, roughly 300 attoseconds, is already attosecond territory. But the authors call it rough. It ignores that the pulse lasts about as long as the core hole itself, and that pulses differ from shot to shot. For a real verdict, they compared every single shot with simulations.

05 · Shot by shot

What the copper actually said

Each gray ring below is one real X-ray pulse. Left to right is the energy it delivered; up and down is how many Kα1 avalanche photons reached the detector. Each gridline is ten times the one below it. The coloured bands show what the team's three-dimensional simulation of the avalanche predicts for flashes of 100 as, 400 as and 1 fs. They include the random scatter expected when only a handful of photons is counted.

Your turn as the analyst. Suppose every flash had the same duration. What would the data look like? Pick a hypothesis and compare its simulated shots with the real ones.

Test a hypothesis

Simulated shots use the measured shots' pulse energies and the paper's simulated expectations, with random counting noise. Like the plotted data, each counts at least one photon (zero-photon shots can't be drawn on this scale). Real shots also carry some scatter from the pulse-energy measurement itself.

Two things stand out. Below about 2 µJ only a few photons arrive per shot, and the three bands overlap: counting noise makes single shots unreadable there. On average these shots roughly match the 1 fs prediction; since durations vary from shot to shot, the authors take this to suggest that a fraction of them are shorter than a femtosecond. Above 2 µJ the bands separate, and most real shots fall between the 100 as and 400 as curves . No single duration reproduces how widely they spread.

That is the paper's conclusion: the LCLS produced attosecond hard X-ray pulses , and their length fluctuates from shot to shot , mostly between about 100 and 400 attoseconds.

Read a single shot

A hidden flash of 100 as, 400 as or 1 fs hits the copper. From its energy and photon count, which was it?

—

Below 2 µJ: 0 / 0 · Above 2 µJ: 0 / 0

What you just sawSingle shots below 2 µJ are too faint to read. Above it, the copper clock puts most flashes between 100 and 400 attoseconds, and no two are quite alike.

06 · The flashes

What the flashes are made of

100–400 attoseconds

Most single-spike hard X-ray pulses at 9.05 keV lasted between about 100 and 400 as, with the length changing from shot to shot.

The accelerator agrees

The team simulated the electron beam and the laser from start to finish, 100 times from fresh random noise. The runs produce single-peaked pulses, many of them close to 100 as long with 20–30 eV of bandwidth, consistent with the copper measurement.

10× higher photon energy

Attosecond pulses now reach hard X-rays, about an order of magnitude above the photon energies attosecond techniques could reach before.

Nearly as short as its colours allow

Remember the chirp slider? A pulse can't be shorter than its spectrum allows: for a smooth (Gaussian) pulse, bandwidth × duration ≥ 1.83 fs·eV. Pulses that sit right on this limit are called transform-limited.

20 eV × 100 as = 2.0 fs·eV

The paper: for 100 as pulses the product is about 2 fs·eV, close to the transform limit, so these flashes carry almost no chirp.

07 · Limits

Where the copper clock runs out

Every stopwatch has a finest tick. The copper clock's is set by the core hole's 400-attosecond lifetime. Once a flash is far shorter than that, the bucket fills faster than it can leak, and pouring even faster can't raise the level any more.

Six flashes, one clock

At 3 µJ: ≈ 240 photons expected.

Why it saturates: the leaky-bucket peak level versus flash duration.

In the team's simulations, 25 as and 50 as flashes give practically the same signal. Below about 50 attoseconds copper can only say "shorter than this". The authors suggest targets whose core holes vanish faster, such as L-shell holes in heavier atoms, to time pulses of a few tens of attoseconds. They also note that the analyzer crystal catches only a sliver of the avalanche, so measuring all of it would sharpen each reading. Linking the readings to the accelerator's own monitors could one day estimate pulse lengths without a copper target at all.

08 · Outrunning the damage

Back to the opening question

Hard X-ray lasers already outrun the atoms: femtosecond flashes are over before the atoms in a sample have time to move. The remaining problem is the electrons. Each absorbed X-ray frees a fast photoelectron, which knocks loose more electrons in a cascade lasting a few femtoseconds, scrambling the very electron clouds scientists want to see.

Race the cascade

—

An attosecond flash can be over before that cascade gets going. The authors see this as a path to damage-free, single-shot X-ray measurements, such as imaging the outer (valence) electrons that hold molecules together, or nonlinear X-ray spectroscopy with intense pulses. This paper doesn't take those pictures. It proves that the flashes needed for them exist, and it gives a way to time them.

The big pictureHard X-ray flashes of 100–400 attoseconds, timed by a copper stopwatch. The camera from chapter 01 now has both kinds of fast. Back to the stopwatch ↑

Sources & credits

The paper

Inoue, I., Robles, R., Halavanau, A., Guo, V., Linker, T. M., Benediktovitch, A., Chuchurka, S., Seaberg, M. H., Sun, Y., Zhu, D., Cesar, D., Ding, Y., Esposito, V., Franz, P., Sudar, N. S., Zhang, Z., Osaka, T., Yamaguchi, G., Sano, Y., Yamauchi, K., Yamada, J., Bergmann, U., Kling, M. F., Pellegrini, C., Yabashi, M., Rohringer, N., Sato, T. & Marinelli, A. Experimental demonstration of attosecond hard X-ray pulses. Nature Photonics (2026). doi:10.1038/s41566-026-02026-7 · nature.com/articles/s41566-026-02026-7

Version used here: this page is based on the authors' preprint, arXiv:2506.07968v1 (9 June 2025; doi:10.48550/arXiv.2506.07968), licensed CC BY 4.0. The published article may differ in wording and numbering: the preprint's Figs. 4–8 appear there as Extended Data Figs. 1–5.

Credits

Figures 1, 2, 3, 6 and 8 are reproduced from the preprint (CC BY 4.0) and cropped.

Data in the interactive charts (1,305 measured shots, bin averages, the Fig. 2 spectrum and threshold curves, and the simulated curves and 95% bands) were extracted from the vector graphics of the preprint's Figs. 2, 3 and 8 and re-plotted.

The 3D ride-along view, camera, lasing-window, chirp, atom, leaky-bucket, avalanche, time–bandwidth and damage instruments are explanatory illustrations made for this page. They are not results from the paper. Their stated numbers (400 as core-hole lifetime, 150 nm focus, 9.05 keV, 20 eV bandwidth, Kα energies) come from the paper; the 2 fs cascade time in chapter 08 is an assumed illustrative value.

Fonts: Fraunces, Inter and IBM Plex Mono (SIL Open Font License).