טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBakman Alexandra
SubjectEffects of Interactions on the Dynamics of Driven Cold
Atoms
DepartmentDepartment of Physics
Supervisor Professor Emeritus Shmuel Fishman (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

The quantum fidelity was introduced by A.Peres in 1984 to study fingerprints of classically chaotic behavior in the quantum dynamics of the corresponding systems. It is defined as an overlap of the perturbed and unperturbed quantum states and indicates the stability of quantum motion. Peres proposed that not knowing the exact Hamiltonian due to the imperfect decoupling of the physical system from the environment, was a mechanism causing irreversibility in both classical and quantum

cases. The fidelity is defined as the magnitude of the overlap between the wave functions of systems starting from the same initial state and subjected to slightly different Hamiltonians, evolved for a certain time.

The fidelity has been investigated in several experimental studies. In quantum information, it was used to measure the decoherence of superposition states due to their interaction with the environment. This decoherence is one of the main obstacles in realizing processing schemes in this field. These states are a coherent superposition of the two magnetic-insensitive hyperfine Zeeman ground states of the Rubidium 85 atoms.

In the present work the signatures of classical dynamics in the fidelity near elliptic fixed points and of weak interactions between particles are characterized for periodically kicked systems. In particular, spectral analysis of the fidelity for states subjected to Hamiltonians with slightly different kicking strengths is performed. The relation between the dynamics of a kicked system and the dynamics of a harmonic

oscillator with some corrections is developed and used to understand the mechanism for generation of the different frequencies of the fidelity.

The largest frequency of the fidelity stems from the classical rotation around the fixed elliptic point in phase space. The smallest frequency we found results from the difference between the frequencies of rotation around the fixed point due to the slight difference in the Hamiltonians. Both frequencies are of purely classical origin and are obtained in presence of interactions as well as in their absence.

An intermediate frequency we found is of a semi classical origin and is not found in absence of interactions. This frequency results of the interplay between the width oscillations of the wave function (or Wigner function) due to the weak interactions and its rotation around the elliptic fixed point. The frequency has been found analytically and verified numerically.