Chapter 13. Tunneling

Aloïs Würger

Gheorghe Sorin Paraoanu

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.

Παναγιωτησ Τροχουτσοσ

The present work consists of eight chapters. The first chapter gives a brief historical overview of the impasses that Classical Physics found in the late 19th and early 20th centuries, and the efforts made in the framework of Old Quantum theory to overcome it, ultimately leading to the foundation of Quantum Engineering in the 1920s. The second chapter shows the ratio of the Schrodinger equation to the classical wave differential equation, the concept of wave function, the physical importance of probability density, continuity equation and probability current density, while indicating the conditions to be met by the wave function. The third chapter examines square dynamic wells as well as the rectangular dynamic barrier, through the study of which the tunnel phenomenon emerges. The reflecting and transit coefficients are also calculated, while the tunnel effect is also being examined in relation to the principle of uncertainty. The fourth chapter presents semi-classical approaches to the solution of the Schrodinger equation, with an emphasis on the WKB approach. The power of the WKB approach is analysed, and applied to a dynamic well, as well as in the case of tunneling through a dynamic barrier, by calculating the transit coefficient. The fifth chapter analyses the time delay in the tunnel phenomenon and examines the concept of minimum transit time. The sixth chapter refers to natural systems where the tunnel phenomenon occurs, such as cold emission of electrons from metals, a-decay and nuclear fusion. Finally, due to the purely undulating nature of the phenomenon, cases of observation are mentioned macroscopicly, such as the case of total internal reflection. The seventh chapter presents a lesson plan for the teaching of the phenomenon in Secondary Education, using information and communication technologies in the educational process, and finally the main conclusions presented resulting from the previous study.