Analysis of femtosecond pump-probe photoelectron-photoion coincidence measurements applying Bayesian probability theory

Abstract

Ultrafast dynamical processes in photoexcited molecules can be observed with pump-probe measurements, in which information about the dynamics is obtained from the transient signal associated with the excited state. Background signals provoked by pump and/or probe pulses alone often obscure these excited state signals. Simple subtraction of pump-only and/or probe-only measurements from the pump-probe measurement, as commonly applied, results in a degradation of the signal-to-noise ratio and, in the case of coincidence detection, the danger of overrated background subtraction. Coincidence measurements additionally suffer from false coincidences, requiring long data-acquisition times to keep erroneous signals at an acceptable level. Here we present a probabilistic approach based on Bayesian probability theory that overcomes these problems. For a pumpprobe experiment with photoelectron-photoion coincidence detection, we reconstruct the interesting excited-state spectrum from pump-probe and pump-only measurements. This approach allows us to treat background and false coincidences consistently and on the same footing. We demonstrate that the Bayesian formalism has the following advantages over simple signal subtraction: (i) the signal-to-noise ratio is significantly increased, (ii) the pump-only contribution is not overestimated, (iii) false coincidences are excluded, (iv) prior knowledge, such as positivity, is consistently incorporated, (v) confidence intervals are provided for the reconstructed spectrum, and (vi) it is applicable to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, the Bayesian approach allows us to run experiments at higher ionization rates, resulting in a significant reduction of data acquisition times. The probabilistic approach is thoroughly scrutinized by challenging mock data. The application to pump-probe coincidence measurements on acetone molecules enables quantitative interpretations about the molecular decay dynamics and fragmentation behavior. All results underline the superiority of a consistent probabilistic approach over ad-hoc estimations. The software implementation of the Bayesian formalism presented in this paper is provided at https://github.com/fslab-tugraz/PEPICOBayes/. * m.rumetshofer@tugraz.at † M.R. and P.H. contributed equally to this work. arXiv:1709.04456v3 [physics.atom-ph]

Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

“…µν and the detection failure probabilitiesξ e = 1 − ξ e and ξ i = 1 − ξ i . In the second line, we use that P(E ν , M µ , SC|q, λ 1 , I) was already derived in Appendix 1 of [22]. The appearing integrals are of the type:…”

“…according to Appendix 2 of [22]. We now turn to the second term in Equation (14), Since the PDF is the same for both experiments, α and β, we suppress the index ρ in the following considerations.…”

“…In the simulation, we have two different ion masses µ ∈ {p, f}, called parent (p) and fragment (f). We use the test spectra related to the ones reported in [22,26]. The electronic spectrum of the parent has a step-like form, and the electronic spectrum of the fragment consists of Gaussian peaks; see Figure 3.…”

“…We recently presented a Bayesian approach to PEPICO, which treats both coincidences and background subtraction on the same footing [22,29]. In this work, we extend our theory to the prevalent experimental situation of unstable laser intensity, i.e., ionization rates fluctuating from pulse to pulse.…”

“…Yet, here, it has to be considered that the pump-only, the probe-only, and the pump-probe measurements have different ionization rates. Since the statistics of the coincidences depend on the ionization rates, the statistics of sole pump-only and probe-only measurements differ from those in the pump-probe measurement, and simple subtraction turns out not to be an unbiased estimator any longer [22].…”