A free-electron laser has produced a pair of attosecond soft-X-ray pulses whose spacing and relative phase can be varied, according to a laboratory preprint. The work tests a cascaded X-ray free-electron-laser method designed to produce mutually phase-stable pulse pairs with tunable timing and phase. The supplied front matter identifies the document as arXiv version 2, dated 4 September 2026.
The demonstration was carried out at LCLS-II with 3.5 GeV electron beams and an 8 kHz repetition rate. The first isolated pulse was reported with a 3 to 4 eV bandwidth, about 15 µJ average energy and an estimated average duration of 500 attoseconds.
How the pair was made
The researchers then used a shorter second-stage undulator with only three detuned segments. That stage emitted a second pulse from the same microbunching structure as the first, bringing the reported total pulse energy to nearly 30 µJ.
For timing, the team used angular streaking with krypton 3d photoelectrons and a circularly polarized infrared laser. An array of 16 time-of-flight spectrometers measured the photoelectron momenta shot by shot. The delay was estimated by correlating counts from two momentum regions and comparing shot-averaged covariance for timed and mistimed measurements.
Timing the two pulses
The adjustable delay was scanned from 0 to 1 femtosecond in 250-attosecond steps. Both pulses remained present throughout the reported settings, but the pulse energy fell from more than 30 µJ to just over 20 µJ at a 1-femtosecond delay. The scan therefore changed the separation and the reported energy together, an important qualification when the range is described.
In the timing analysis, the measured-delay relationship was well fit by a line with a slope of 1 and an offset of 2.80 plus or minus 0.03 femtoseconds. That fit connects the delay inferred from the photoelectron data with the delay setting used in the undulator scan.
Reading the phase
The researchers examined relative phase, or how the two pulses' wave patterns line up, through changes in their spectra as the phase shifter was adjusted. Experimental and simulated spectra behaved in qualitatively similar ways: settings separated by pi produced mirror-image difference spectra, while simulations were consistent with the relative spectral phase changing with the phase-shifter setting. Those comparisons are the basis for describing the phase relationship as tunable.
The same analysis also found shot-to-shot phase differences fluctuating in simulations. Before filtering, the reported root-mean-square phase-difference fluctuation was 1.31 plus or minus 0.04 radians. The study describes spectral-shape filtering and a double-Gaussian selection criterion of r-squared greater than 0.99 as a way to reduce that variation. After the later filtering step, the reported RMS fluctuation was 0.81 plus or minus 0.03 radians.
Supporting simulations
The spectral comparisons were accompanied by start-to-end simulations. The methods identify ASTRA for the photoinjector, elegant for beam propagation to the undulators and GENESIS 1.3 v4 for the free-electron-laser simulations.
Taken together, the authors interpret the timing measurements, spectral comparisons and simulations as evidence that the method produces mutually phase-stable pulse pairs with control over delay and relative phase. The reported scan also keeps the central trade-off in view: as the delay reached 1 femtosecond, the pulse energy was just over 20 µJ rather than more than 30 µJ at the shorter-delay end.
Paper data and sources
Original title: Mutually phase-stable tunable attosecond soft X-ray attosecond pulses from a free-electron laser
Authors: River Robles, David Cesar, Taran Driver et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text