טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentMartiskainen Hanna
SubjectPhoto Induced Dynamics in the Low Frequency Regime
DepartmentDepartment of Physics
Supervisor Professor Emeritus Nimrod Moiseyev
Full Thesis textFull thesis text - English Version


Abstract

The possibility to create extremely short pulses, using high-order harmonics created by a low-frequency driving field, has stimulated studies of photo induced dynamics in the low-frequency regime. Using low-frequency lasers for high-order harmonic generation is attractive because the cut-off limit scales as one over the laser frequency squared. However, the low frequency raised challenges in dynamics calculation in this regime.


In this thesis we present a perturbational approach for the calculations of the quasi-energy spectrum in the low frequency regime, that avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. The second order perturbation correction terms are obtained when -i*\hbar*\partialt serves as a perturbation and \tau=\omega*t is a dimensionless variable.

The second order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement this perturbation approach for calculating atomic and molecular energy shifts (positions) due to the interaction with low frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. The energy widths (inverse lifetimes) can be obtained at the same level of theory.


In addition, we show how the quasi-energies can be calculated using a variational approach by representation of the Floquet Hamiltonian matrix with the adiabatic solutions as a variational basis set. We assume that for weak or moderate laser fields the essential non-adiabatic coupling is between two adiabatic states associated with the ground and the first excited state of the field-free states. The fact that as the laser field is turned on the field-free states are coupled with the continuum and become metastable states, is reflected in the adiabatic states which are time dependent.

We show how accurate quasi-energies of a system driven by a linearly polarized laser field in the low laser frequency regime can be calculated when the laser intensity is held fixed. The use of adiabatic solutions as a basis set reduces the computational effort by many orders of magnitude.

The method we propose is not a perturbative procedure but based on the use of the complex variational principle that enables us to calculate the resonance stark shift solutions that are used as a basis set in our method.


We believe that the new methods we developed can be used for studying the dynamics of a laser-atom/molecule system in the low frequency regime. These are very appealing approaches since they enable the use of computational methods originally developed for molecular electronic structure calculations to calculate the adiabatic states.