ABCD Formulation Of The Propagation Of The Atom Laser

The realization of atom lasers opens up the new intriguing perspectives in coherent atom optics. These novel atom sources are based on Bose-Einstein condensates (BEC) from which a coherent matter wave beam is extracted, which have coherence, monochrome and high direction. It is important to characterize the qualities and the propagation of these atom beams. The propagation of an atom laser, which is outcoupled from a Bose-Einstein condensate, is investigated within the framework of quantum mechanics. We discussed the propagation of the atom laser beam which had non-conservation quality factor based on the theory of ABCD formulation of propagation of a time-dependent quantum system. The equation for the quasi-continuous atom laser beam wave-function is given by Schrodinger equation, the beam width, divergence curvature radius and quality factor were introduced to represent the atom laser beam whose transverse potential could be separated. For the conservative quality factor system in some direction, we can get the propagator of ABCD formulation. We considered the propagation of the atom laser beam during the interacting with BEC, the propagation with the trap on and the free propagation with the trap off which potential can be separated by x and y. Within the frame of the ABCD formulation of propagator of a time-dependent quantum system, the ABCD law is extended to the so-called effective ABCD system which effective beam quality factor is conservative; we discussed the system like the propagation of the atom laser beam. The effective beam quality factor and the effective parameter are introduced to obtain the effective ABCD formulation of propagator by means of Heisenberg picture. The atom-atom interaction in the atom laser beam makes the beam quality factor nonconservative, and the effective beam quality factor describes the beam quality factor and the atom-atom interaction together.In chapter 1, a review of the atom lasers and the atom laser beams is given. The compare between the atom laser and the optical laser is also represented, which is the foundation of the propagation of an atom laser beam. At the end of this chapter, we list our works about the propagation of an atom laser beam.In chapter 2, a Schrodinger formulation for paraxial light beam propagation ofthe real and comprehensive refractive indexes is represented. The equation for the atom laser beam wave-function is also given by a Schrodinger equation, which is similar to the equation of the time-dependent system. Therefore, it is possible to investigate the propagation of an atom laser beam.In chapter 3, we discussed the propagation of the atom laser beam, with the transverse independent of gravitate direction, which had non-conservation quality factor based on the theory of ABCD formulation of propagation of a time-dependent quantum system. Actually, the atom laser beam with the transverse independent of gravitate direction is included in the conservative system. We also compare our methods and results with Le Coq's.In chapter 4, the interaction between atoms within the atom laser beam will be included in the potential energy, which leads to the non-conservation of the quality factor. An effective quality factor representing both the interaction between atoms within the atom laser and the quality factor is introduced to study the propagation of the atom laser beam. We derive the ABCD formulation of the propagation of an atom laser beam with arbitrary beam profile including the interaction between atoms within the atom laser by means of the theory of quantum mechanics.In chapter 5, there is a summary of the methods in this thesis, together with the further work.