טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMichael Sheinman
SubjectDecay of Quantum Accelerator Modes
DepartmentDepartment of Physics
Supervisor Professor Emeritus Fishman Shmuel (Deceased)


Abstract

Cooling and trapping of atoms enables the exploration of quantum mechanical effects of their center of mass motion. One of the most surprising phenomena, that was discovered, was the existence of "Quantum accelerator modes". These modes were found in the experiments with kicked (by a standing electromagnetic wave) cesium atoms. It was found that there is a fraction of the atoms that accelerate, on average, relative to the gravity. This discovery was explained using a pseudo-classical limit. The quantum dynamics far from the classical limit turn out to be described by a fictitious classical map. The accelerator modes result of wave packets trapped in a stable island of this classical map. The decay of these modes results of tunneling out of the island and is the subject of the thesis. Recently it was demonstrated that in spite of the fact that tunneling is a pure quantum phenomenon it is strongly influenced by classical phase space structures. Results that were obtained recently in the studies of tunneling between regular islands, embedded in the chaotic sea, were used to calculate the tunneling rate from a regular island to the chaotic sea. Of particular importance are the classical resonant island chains. The decay rates of the population of the islands, and the related accelerator modes were calculated in the semiclassical approximation and were tested numerically. A nontrivial dependence on Planck's constant is found in the semiclassical limit