Tunneling in Degenerate Atomic Gases

The experimental achievement of Bose-Einstein condensation in cold alkali atomic gases in 1995 has started a period of fertile research at the intersection of atomic physics, quantum optics, and condensed matter. In this thesis, various tunneling effects in both bosonic and fermionic gases are investigated. The first part of this work deals with bosons in different Josephson-type experimental setups. After a brief general introduction we establish, in Chapter 2, a mapping between the phase and the Bogoliubov representation for the Josephson oscillations; in Chapter 3 we calculate the Josephson coupling constant for the condensate in the external Josephson effect. Chapter 4 deals with Josephson effects at the level of depletion: we describe in detail the oscillatory dynamics of the virtual quasiparticles. The next Chapter is a stability analysis for the formation of vortices in the Kibble-Zurek scenario. Finally, Chapter 6 contains a discussion on the time-evolution of the many-body states in the absence of tunneling. The second part of the thesis (Chapter 7- Chapter 9) deals with fermionic systems below the BCS critical temperature. The first two of these Chapters explore the possibility of driving transitions between hyperfine states with lasers. In Chapter 7 we show that these transitions could be used to investigate the coherence of the Cooper pairs. In Chapter 8 we imagine an internal Josephson experiment which uses a pair of lasers to drive transitions between two superfluids. Finally, in Chapter 9 we examine the properties of vortices formed in trapped Cooper-paired fermionic gases.U of I Onlythesi