TU Wien slides high-harmonic X-rays continuously between the comb's fixed teeth

The leverage is in the multiplication. High harmonics come out as integer multiples of the laser that drives them ^[3]. Taking those integer multiples at face value, the gap between neighbouring teeth is one driving frequency. An output sitting at the Nth multiple moves N times as far as its driver does, so crossing a whole gap needs a change of 1/N in the drive frequency: 5 percent at the twentieth multiple ^[16]. The team went at the laser rather than the X-rays, and a comparatively small shift in laser wavelength is enough to bridge the entire gap to the next harmonic ^[10].

"For decades, high-harmonic light has behaved a little like a guitar with fixed frets," said Tenio Popmintchev, a professor at the Institute of Photonics at TU Wien ^[7]. "What we have now built is more like a slide guitar in the X-ray range: We can move continuously between the harmonics, in either direction, and select exactly the energy we need," he said ^[8].

Producing that shift in a high-power infrared pulse is the difficult part. The ytterbium laser's light acquires its new spectrum from a strong nonlinear interaction with the gas inside the hollow guide ^[11].

"Spectral broadening, such as the kind we produce in our gas-filled waveguide, would normally mean losing control of the pulse," said Dimitar Popmintchev, the study's first author ^[15]. He is at the Institute of Photonics at TU Wien.

The conversion step restores that control. Visible light can be controlled accurately enough to oscillate at a pace that fits the emerging X-rays. Only when that phase matching holds do the illuminated atoms jointly produce a brighter beam with a narrower linewidth instead of uncoordinated waves that partly cancel each other ^[13]. Tuning to an exact energy helps only if the emitted line is narrow enough to sit on the resonance. There is a second gain: under visible driving, each atom's electrons are accelerated and recombine within a shorter interval than with infrared pulses. That is fast enough that quantum diffusion of the electron wave packet has less time to reduce efficiency ^[14].

The paper does not report photon energies, a tuning range in energy units or a beam flux. The only application it names is exciting an atomic resonance that requires one very specific frequency ^[17]. For that class of experiment the frequency problem is the one being solved, since the shift now covers the entire gap between two neighbouring teeth ^[6]. Choosing between a tabletop driver and a storage-ring beamline still turns on photons per second at the energy you picked.