Dynamics from noisy data with extreme timing uncertainty.

Area of Science:

• Physics
• Chemistry
• Data Science

Background:

• Imperfect timing knowledge in snapshot recordings degrades dynamical information recovery.
• Timing jitter in X-ray free-electron lasers (XFELs) can exceed X-ray pulse duration, limiting time-resolution.
• Existing hardware solutions to reduce timing jitter are costly and experimental-specific.

Purpose of the Study:

• To develop a data-analytical method for recovering system dynamics from noisy snapshots with timing uncertainty.
• To overcome limitations of hardware-based timing jitter reduction methods.
• To demonstrate the algorithm's capability in extracting ultrafast dynamics from experimental data.

Main Methods:

• Singular-value decomposition (SVD).
• Nonlinear Laplacian spectral analysis.
• Application to noisy X-ray free-electron laser data.

Main Results:

• Successfully extracted few-femtosecond timescale dynamics from XFEL data with 300-femtosecond timing uncertainty.
• Revealed vibrational wave-packets with periods as short as 15 femtoseconds in a Coulomb explosion experiment.
• Demonstrated the algorithm's robustness with noisy pump-probe data.

Conclusions:

• A novel data-analytical approach can recover historical and dynamical information despite significant timing uncertainty.
• This method offers a powerful alternative to hardware solutions for timing jitter issues.
• The approach has broad applicability to systems where timing uncertainty compromises data analysis.