Dynamik von Ein-Dimensional-Gasen von Bosonen und Fermionen

Understanding relaxation processes in quantum systems is an important open problem in several fields of physics. Ultracold atom experiments offer a unique opportunity to address this problem as they can prepare isolated many- body quantum systems, manipulate them in out-of-equilibrium configurations, and observe their transient dynamics. The proposed research project will study the dynamics of a mixture of ultracold bosons and fermions, using the agility of an atom chip to control the dimensionality of the system (3d and 1d), and to perform non- equilibrium and equilibrium experiments with the quantum gases. We will first investigate the influence of a distinguishable and controllable 3d gas of fermions ( 40K atoms) on the non-equilibrium dynamics of a rapidly split 1d Bose gas ( 87Rb atoms). Without the presence of the fermions, the relaxation of the split 1d bosonic system can undergo pre-thermalization to a state which does not correspond to the thermal equilibrium. In the presence of a distinguishable heat bath (the 3d Fermi gas), the 1d bosonic system is expected to reach thermal equilibrium. The first aim of this project is to study the frontier between the two different relaxation regimes and to characterize the onset of the pre-thermalized state. The information about the dynamical states of the system will be obtained through noise analyses of matter-wave interference patterns. In order to access further information about the dynamics of the Bose-Fermi mixture, we will then develop two different methods to detect a single 1d degenerate Fermi gas. The first method will be based on observations of the modifications to the coherence properties of an equilibrium bosonic interferometer induced by the presence of the Fermi gas. Our goal is to achieve sensitivity to low numbers (< 100) of fermions using the many-body bosonic system as a probe for the 1d Fermi gas. The second detection method will use a light-sheet fluorescence imaging setup aiming at detecting single fermions. This detector will be used to measure density distributions and correlation functions of the 1d Fermi gas in free expansion. Such measurements will allow further insight into the non-equilibrium dynamics of the Bose-Fermi mixture, and will complement analyses performed on the Bose gas using matter-wave interferometry. With these tools, we will address important questions about the link between the relaxation and transient states of a non- equilibrium many-body quantum system and its initial state, which are relevant to both fundamental physics and applications.