Coherent Control Of Quantum State Transfer With Femtosecond Lasers

The hydrogen atom, because of its simple and representative structure, can be used to solve a number of quantum problems analytically. As a very important atom in quantum mechanics, it is an ideal system for quantum simulations, as well as for experimental verification of theoretical results. Compared to other heavier atoms, the hydrogen atom in nondegenerate excited states has longer period during the laser action and is easier to be coherent controlled with femtosecond laser pulses, therefore the hydrogen atom is the most suitable atom to obtain hybrid orbitals. Hybrid orbitals are great, they can explain many structures of molecules and atoms and can aid our understanding of molecular shapes, bond lengths and energies, charge distributions and electric dipoles and so on. In this Master Thesis, I show that the procession of the hydrogen atom lends itself for simulations of laser sculpting of sp, sp2 and sp3 hybrid orbitals, by means of femtosecond laser pulses. The simulations provide optimal control parameters for experimental preparations of these hybrid orbitals. The total laser pulse consist of a series of several sub-pulses with Gaussian shapes. I have analyzed their shapes and the resulting time evolutions of the populations of the excited states and the related electric dipoles.The main part of this thesis includes the following three sections:First, according to the superposition of s, p orbitals to build the state-selective generation expressions of the hybrid orbitals,Second, according to the related theoretical methods of light-matter interaction to study the interaction beyween a femtosecond laser pulse and a two-level system. And then calculate the required Hamiltonian matrix elements of the system. Furthermore, optimize the parameters of the femtosecond laser pulses.Third, coherent controlling quantum states to transfer exactly by means of femtosecond laser pulses obtained at the second step, then successful preparation of the nine different hybrid orbitals of the hydrogen atom, with analysis of the time evolutions of the state populations and the electric dipoles.