טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMartiskainen Hanna
SubjectApplicability of the Adiabatic Theory for Atomic Systems
in Strong Laser Fields
DepartmentDepartment of Physics
Supervisor Professor Emeritus Nimrod Moiseyev
Full Thesis textFull thesis text - English Version


Abstract

In this work we study the possibility to extend the adiabatic approximation used in describing different processes of interaction between light and matter in the low frequency regime, to higher frequencies. The adiabatic Hamiltonian is used in the first step of the three-step model which is the most popular approach in the calculations of the high harmonic generation spectra in atto-second laser physics.

A perturbation theory, where the adiabatic Hamiltonian serves as the zero-order Hamiltonian, is derived. The perturbation is the non-adiabatic coupling, and the parameter controlling the strength of this coupling is the laser frequency.

We developed a computational method which enables the calculation of the radius of convergence. The radius of convergence is associated with a non-Hermitian degeneracy in the spectrum of the dressed atom Hamiltonian. These non-Hermitian degeneracies are often called branch points. The branch points we discuss in our work are obtained as the laser frequency is analytically continued into the complex plane.

For a numerical example it is found that the radius of convergence is reduced as the laser intensities are increased.

The method we developed has a numerical advantage in solving the time dependent Schrӧdinger equation for time dependent Hamiltonians for low frequencies. In these cases it is hard, and often impossible, to calculate the quasi-energy Floquet resonance solutions since an extremely large number of Floquet channels are involved in the photo-induced dynamics.