A free-electron laser experiment reported a pair of attosecond soft-X-ray pulses whose timing could be adjusted and whose relative phase — the alignment of their wave cycles — showed signs of being tunable. The work is an arXiv preprint, and its numerical estimate of phase fluctuation came from start-to-end simulations rather than a direct experimental numerical measurement.
A pair of short X-ray pulses
The setup used a shaped electron beam in a split, cascaded undulator arrangement. It reused the first stage’s microbunching — a structured pattern in the electron beam — to seed a detuned second free-electron-laser stage. The reported platform was LCLS-II, a superconducting accelerator.
The first isolated attosecond pulse had a 3-to-4 electronvolt bandwidth and approximately 15 microjoules of average energy. Its average duration was estimated at 500 attoseconds, while total pulse energy reached nearly 30 microjoules.
The average spectrum contained two roughly Gaussian lobes separated by 6 electronvolts, with bandwidths of a few electronvolts and similar peak intensities.
Timing could be moved in tiny steps
To characterize timing, researchers used angular streaking, a method that reads the direction and momentum of krypton 3d photoelectrons, measured shot by shot with an array of 16 time-of-flight spectrometers. They compared streaked and unstreaked shots using partial and relative covariance, a test of whether count patterns move together.
The shot-averaged correlations persisted and were treated as evidence of a stable pulse-to-pulse delay. The delay-undulator scan covered 0 to 1 femtosecond in 250-attosecond steps.
Measured delay versus expected undulator slippage was well fit by a line with slope 1 and an offset of 2.80 ± 0.03 femtoseconds.
Both pulses remained present during the scan, but reported pulse energy fell from more than 30 microjoules to just over 20 microjoules at a 1-femtosecond delay.
Phase control showed up in the spectrum
Changing the inter-undulator phase shifter produced periodic changes in amplification of the first pulse. Settings separated by π produced roughly mirror-image difference spectra, a qualitative pattern consistent with tunable relative phase.
Start-to-end simulations modelled four phase-shifter configurations, with 50 runs for each configuration using different random shot-noise seeds.
In those simulations, the RMS phase-difference fluctuation was 1.31 ± 0.04 radians without filtering. After spectral-shape filtering to a double-Gaussian fit with r² > 0.99, the estimate was 0.81 ± 0.03 radians. The lower figure therefore depends on the filtering step.
The same start-to-end model showed two pulses separated by around 2.5 femtoseconds under the zero-added-delay configuration.
A source result, not yet an application
Taken together, the timing correlations, delay scan, phase-shifter spectra and simulations were interpreted by the authors as evidence for mutually phase-stable pulse pairs with direct control over both delay and relative phase. The reported evidence comes from source generation and diagnostics, not from a demonstrated coherent-control experiment in a molecule or other quantum system.
The direct experimental phase result was qualitative, while the numerical phase estimates were simulation-based and depended on random shot-noise seeds and spectral filtering. The report also does not state how many experimental shots went into the averaged timing correlations.
The delay scan did not keep relative phase fixed, so delay and phase were not independently varied throughout that scan. The work leaves open whether the source’s phase stability and pulse energy will remain suitable across broader soft-X-ray energy separations and delay settings, or whether phase fluctuations can be reduced without spectral filtering.
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