Quantitative uncertainty analysis of extracting attosecond delays from spectrally overlapping RABBIT experiments


Date

2025-07-14

Publication Type

Journal Article

ETH Bibliography

yes

Citations

Altmetric

Data

Abstract

A two-dimensional spectrogram with oscillations along the temporal dimension and partially overlapping peaks along the spectral dimension is the typical outcome of interferometric measurements, e.g. the reconstruction of attosecond beating by interference of two-photon transitions experiment of complex systems. It is necessary to retrieve the oscillation phases of the individual components in order to extract the attosecond photoionisation time delays. One can use either the global-fit method (simulating the oscillations of each component and adding them together) or the complex-fit method (first Fourier transforming along the temporal dimension and then fitting the Fourier coefficients at the relevant frequency in the spectral dimension). Here, we prove that the two methods are mathematically equivalent in the frame of least-squares fitting, and we derive the formula for the variance of the extracted phases based on the Poisson distribution. The fitting and the uncertainty formula are not limited to specific peak shapes. For the special case of two Gaussian peaks, there is a relatively simple expression for the phase uncertainty. The method can be further extended to fitting with peaks that have known phase structures or peaks with relative phase constraints. The uncertainty formula (with multiple peaks and a background) is verified by numerical simulations, and the results show that phase retrieval is possible as long as the peaks do not fully overlap (having exactly the same shape, position and phase structure), although the uncertainty rises with the degree of overlap. We also find that the correctness of fitting relies on properly assigning all the peaks in the energy domain, which is particularly important for extracting the phase from a relatively weak peak overlapped with other peaks.

Publication status

published

Editor

Book title

Volume

58 (13)

Pages / Article No.

135601

Publisher

IOP Publishing

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

attosecond interferometry; RABBIT; photoionisation delays; uncertainty analysis; phase retrieval

Organisational unit

03888 - Wörner, Hans Jakob / Wörner, Hans Jakob check_circle

Notes

Funding

- Time-resolved measurements of intermolecular Coulombic decay ()

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