| Popis: |
A data-analytical approach that can extract the history and dynamics of complex systems from noisy snapshots on timescales much shorter than the uncertainty with which the data were recorded is described; the approach is demonstrated by extracting the dynamics on the few-femtosecond timescale from experimental data recorded with 300-femtosecond timing uncertainty. When reconstructing climate histories from ice cores or ultrafast dynamics from X-ray free-electron laser (XFEL) experiments, the uncertain time stamps can muddle the sequence of events, making it difficult to recover accurate dynamical information. These authors introduce a data analysis technique, based on nonlinear Laplacian spectral analysis, that circumvents this problem and is capable of extracting dynamical information from noisy data despite the timing uncertainties. They demonstrate reconstruction of few-femtosecond dynamics using XFEL data with 300-femtosecond timing uncertainty. In principle, this approach could be useful in all measurements plagued by time uncertainty, so might find applications from geoscience to gravitational physics. Imperfect knowledge of the times at which ‘snapshots’ of a system are recorded degrades our ability to recover dynamical information, and can scramble the sequence of events. In X-ray free-electron lasers, for example, the uncertainty—the so-called timing jitter—between the arrival of an optical trigger (‘pump’) pulse and a probing X-ray pulse can exceed the length of the X-ray pulse by up to two orders of magnitude1, marring the otherwise precise time-resolution capabilities of this class of instruments. The widespread notion that little dynamical information is available on timescales shorter than the timing uncertainty has led to various hardware schemes to reduce timing uncertainty2,3,4. These schemes are expensive, tend to be specific to one experimental approach and cannot be used when the record was created under ill-defined or uncontrolled conditions such as during geological events. Here we present a data-analytical approach, based on singular-value decomposition and nonlinear Laplacian spectral analysis5,6,7, that can recover the history and dynamics of a system from a dense collection of noisy snapshots spanning a sufficiently large multiple of the timing uncertainty. The power of the algorithm is demonstrated by extracting the underlying dynamics on the few-femtosecond timescale from noisy experimental X-ray free-electron laser data recorded with 300-femtosecond timing uncertainty1. Using a noisy dataset from a pump-probe experiment on the Coulomb explosion of nitrogen molecules, our analysis reveals vibrational wave-packets consisting of components with periods as short as 15 femtoseconds, as well as more rapid changes, which have yet to be fully explored. Our approach can potentially be applied whenever dynamical or historical information is tainted by timing uncertainty. |
