טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentHihinashvili Rivka
SubjectQuantum Accelerator Modes
DepartmentDepartment of Physics
Supervisor Professor Emeritus Shmuel Fishman (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

  Quantum accelerator modes were recently discovered in experiments with laser-cooled atoms. In such experiments, Cesium atoms are subject to very short pulses, or "kicks", and fall freely with the gravitational acceleration in between kicks. The astonishing result is that, as the period of the kicks approaches some specific values of resonance, a portion of the atoms accelerates, with constant acceleration, relative to the free falling frame.

  A subsequently formulated theory explained the appearance of the quantum accelerator modes by employing a pseudo-classical limit, where the detuning from resonance plays the role of Planck’s constant, resulting in an area preserving classical map. This map resembles the standard map up to a constant drift. The stable periodic orbits of this map, and the islands around the stable periodic points, correspond to the acceleration modes of the atoms. An atom whose wave function is trapped in a stable island of this map moves with constant acceleration giving rise to an accelerator mode.

  This is what motivated the exploration of this map's phase diagram, that is, determining for which values of the map's parameters, stable periodic orbits are found. The structure revealed is of wedge like regions in this space, which we call "tongues" (because of the resemblance to the Arnol'd tongues structure). A perturbative analysis yields the structure of the tip of these tongues, while the non-perturbative regime was explored numerically. The research focused on tongues that correspond to periodic orbits of short periods (up to period 3). In particular the stability borders, defining where in the parameter space stable periodic orbits turn into unstable ones (or vice versa), were calculated. Many standard scenarios of the theory of dynamical systems are encountered in the study of this map: period-doubling cascades, pitchfork bifurcations and tripling bifurcations.