Abstract In atomic, molecular, and optical physics experiments investigating photoinduced reactions in the gas phase, methods that determine which of multiple products correlate are crucial. A major challenge is that instabilities in experimental parameters, such as the laser intensity, influence the event rate, so that false correlations are induced. For correlation at high and fluctuating event rate, which is common in experiments employing Free-Electron Lasers (FELs), covariance-based methods are widely used. However, they can only infer correlation between two or three reaction products. In higher dimensions, cumulant mapping can be applied, but only if any event rate fluctuations are negligible. There is yet no method valid for correlation in higher dimensions and at high and fluctuating event rate. To fill this gap, we present a new method: parametric cumulant mapping . Parametric cumulant mapping can infer correlation between any number of reaction products and at arbitrary and even unknown event rate fluctuations. It is theoretically deduced as a generalization of cumulant mapping to correct for fluctuations, and its functionality is demonstrated in simulations. A general formula of the parametric cumulant is given, and explicit expressions in up to four dimensions are presented. Python and Matlab code for computing parametric cumulants in any dimension is provided as supplementary data. We also show that the established method of partial covariance, typically used at linear laser-light fluctuations, is a special case of parametric cumulants.
Brandt et al. (Thu,) studied this question.