Adiabatic guiding of matter waves

Abstract: Recent efforts in the field of ultracold atoms have goneinto creating wave guides of sub-micron sizes. In this thesis,the quantum dynamics of matter waves in such confiningpotential structures with minima extended in space isinvestigated. A general framework based upon the separation ofthe wave function for the quantum particle using a discrete setof mode functions is introduced to reduce the dimensionality ofthe problem. Conditions for propagation in the form ofindependent modes, i.e. adiabatic propagation, are determinedfor the case of matter waves with spatially varying width andfound to be connected to the diffraction of matter wavesthrough a dimensionless parameter, the Fresnel parameter.Further, the analysis is extended to include situationswhere a transition to completely non-adiabatic dynamics takesplace. Here it is found that focusing of matter waves due toenergy redistribution at the end of adiabatic guiding isdetermined by the Fresnel parameter found earlier. In theadiabatic regime, the essential dynamics in the directiontransverse to the minimal valley of the guiding potentialstructure occurs at a time-scale much shorter than that ofchanges in the propagating direction. As a result of this,reection of matter waves is likely to occur unless the changesare made over very long distances.The formalism of adiabatic propagation is also applied thesituation of splitting of matter waves in potential structures.It is found that the adiabaticity criteria are identical tothose for a single guide of spatially varying width. Aformulation of adiabatic splitting in terms of states localizedclose to either of the two minima is developed. The inuence oflongitudinal localization on the splitting of coherentsuperposition states is examined and found to be described by asimple analytical expression.