Modeling X-ray Superfluorescence by Stochastic Differential Equations

Supervisors: Prof. Nina Rohringer (DESY, UHH), Jun.-Prof. Mathias Trabs (UHH)

This is an interdisciplinary project between the natural and mathematical sciences to develop a theoretical description of x-ray collective spontaneous emission (superfluorescence and superradiance) in terms of stochastic differential equations with subsequent applications to  experimental data. In experiments performed at modern x-ray sources, such as x-ray free electron lasers (XFEL), matter can be driven into highly excited states, where population inversion is created between valence and inner-core electronic shells, or on nuclear resonances. The ensuing short-wavelength emission of such a highly excited system will be of collective natureand exhibits unique properties. It combines the microscopic, quantum mechanical origin of the emission process with a macroscopically large number of ultimately emitted photons. The theoretical description of superfluorescence/superradiance is challenging and so far poorly developed –especially for the x-ray domain. We address this open problem based on the mathematical formalism of stochastic differential equations (SDE). More precisely, the solution of the underlying Fokker-Planck equation can be equivalently characterized as the distribution of the solution process of a SDE. Based on that simple observation, x-ray superfluorescence can be described via stochastic ordinary or partial differential equations that can be studied using tools from stochastic analysis. The developed theory will be verified against data from previous and future measurements at various XFEL sources and samples. In particular, it will be applied to investigate coherence and quantum properties of superfluorescent/superradiantradiation. This may pave the way for novel spectroscopic and/or imaging applications at XFEL that can benefit from the unique properties of the radiation.