Seminarium Fizyki Materii Skondensowanej

Ultra-cold atomic gases in optical lattices are experimental realizationof interacting quantum many-body systems in very clean form. The systemparameters can be precisely controlled and, as a result, strongcorrelation regime can be reached, which shares a lot of similarities withstrongly interacting electronic systems in solid-state physics.Understanding of the behavior of such systems is a challenge fortheoretical approaches. I will present a method being a combination ofBogoliubov theory and quantum rotor model, which makes it possible toanalyze spatial correlations between atoms as a function of latticegeometry and system parameters. This allows me to calculate variousquantities, like time-of-flight absorption images or single-particlespectral functions, also in presence of additional external factors(synthetic magnetic field) and compare them with available experimentalresults.