Spektralne lastnosti superfluorescence v daljnem ultravijoličnem in rentgenskem področju

Superfluorescence is a nonlinear process in light-matter interaction that leads to amplification of spontaneously emitted radiation from a target with inverted population of atomic or ionic excited states. While this process has been extensively studied in the optical domain, experimental observation in the extreme ultraviolet and X-ray spectral regions has only recently become possible with the development of free-electron lasers. However, despite successful measurements of the characteristic superfluorescence yield at short wavelengths, agreement between experimental results and theoretical predictions has thus far only been qualitative. The main goal of this work is to address some of the open problems in theoretical modeling of superfluorescence. To this end, we first develop a model of light-matter interaction in a three-level system, which is based on a solution of combined propagation equations for quantum correlation functions and semiclassical Maxwell-Bloch equations. This model is employed to study X-ray superfluorescence in K$alpha$ emission from a zinc target. After verifying the validity of the model and comparing it to the existing frameworks for describing superfluorescence, we investigate the spectral properties of emitted radiation for the case of pumping with sub-femtosecond free-electron laser pulses, which have been only recently produced at X-ray wavelengths. The improved model with quantum correlation functions still cannot provide quantitative predictions for realistic experimental setups, so in the second part of the thesis we present a formalism that describes the four-dimensional spatio-temporal evolution of a multi-level atomic system pumped by coherent light and subject to incoherent processes. The model is based on Maxwell-Bloch equations with added stochastic noise terms to simulate random fluctuations of spontaneous emission. After describing the general formalism and its numerical implementation, the model is used to simulate X-ray superfluorescence in K$alpha_1$ emission from a copper nitrate solution, and XUV superfluorescence from resonantly excited helium gas. In both examples, the range of considered parameters matches current experimental capabilities of free-electron lasers.Superfluorescenca je nelinearen kolektiven sevalni pojav, za katerega je značilno ojačanje svetlobe, ki jo spontano izseva tarča z invertirano zasedenostjo. Čeprav je ta proces v vidnem območju podrobno raziskan, lahko superfluorescenco v daljnem ultravijoličnem in rentgenskem spektralnem področju opazujemo šele od nedavne iznajdbe laserjev na proste elektrone. Kljub uspešnim meritvam značilne odvisnosti fotonskega pridelka od jakosti vzbujanja tarče, pa smo lahko z dosedanjimi teoretičnimi modeli poustvarili le kvalitativne značilnosti tega procesa. Glavni cilj pričujočega dela je nasloviti nekatera izmed odprtih vprašanj pri teoretičnem opisu superfluorescence. Tako v prvem delu disertacije razvijemo model interakcije svetlobe s snovjo, ki temelji na reševanju kombinacije enačb za propagacijo kvantnih korelacijskih funkcij in semiklasičnih Maxwell-Blochovih enačb. Model uporabimo za obravnavo superfluorescence pri valovni dolžini K$alpha$ v cinku, pri čemer smo v skladu z najnovejšimi eksperimentalnimi zmožnostmi trajanje črpalnih sunkov močne svetlobe omejili na nekaj sto atosekund. Kljub nekaterim izboljšavam glede na prejšnje teoretične opise superfluorescence, model s kvantnimi korelacijskimi funkcijami še ne more zagotoviti kvantitativnih napovedi za realistične eksperimentalne postavitve. V drugem delu disertacije zato predstavimo večji teoretični okvir, ki opiše štiridimenzionalni prostorsko-časovni razvoj večnivojskega atomskega sistema, ki ga vzbuja koherentna svetloba in je podvržen nekoherentnim procesom. Razširjeni model temelji na reševanju Maxwell-Blochovih enačb z dodanimi stohastičnimi členi, ki ustvarijo naključne fluktuacije polarizacije atomov in simulirajo vpliv spontane emisije. Najprej opišemo splošne značilnosti formalizma in njegovo numerično implementacijo, nato pa model uporabimo za obravnavo superfluorescence pri valovni dolžini K$alpha_1$ v raztopini bakrovega nitrata ter za opis ojačanja ultravijolične fluorescence v resonantno vzbujenem heliju. V obeh primerih obseg parametrov, ki jih obravnavamo, sovpada z aktualnimi tehničnimi zmožnostmi laserjev na proste elektrone