Lie Algebraic Approach To The Vibrational Population Of Diatomic Molecule In Infrared Laser Fields

Molecular dynamics is a new subject between modern physics and chemistry. It employs the theory of modern physics (especially in molecular physics, atomic physics and laser physics) and experimental technology to study the movement and interaction among molecules, and help one to understand the essence and laws of the chemical reaction.In this paper, we investigate the vibrational populations of diatomic molecules in infrared fields employing the algebraic approach. The quadratic oscillator model will be applied to study the vibration of diatomic molecules transition process in this article. Since the quadratic Hamiltonian is easy to deal with in mathematics, and the form is similar to the harmonic oscillator, the solution of the related Schr?dinger equation can be obtained simply and the calculating amount is also smaller. Up to now, however, little analytical work has been done to study the light-matter interaction, and Lie algebra method provides the possibility to cope with this problem. Lie group method and Lie algebra method were first proposed by Marius Sophus Lie in the research of differential equations. Lie algebra theory was introduced together with the build of matrix mechanic. In 1950s, its wide application was with the development of the fundamental quantum mechanics. In 1980s, Iachello, Levine et al, introduced Lie-algebra method from nuclear physics to molecular physics successfully. During the past years, the application of time-dependent problems of dynamical Lie-algebra approach has been further developed rapidly. Algebraic method has been extensively used to study some problems in nuclear physics, molecular physics and quantum optics etc. The problems of vibrationally excited state and potential energy surfaces for molecules have been solved successfully and accurately.This paper will be divided into four chapters.First chapter is the introduction, which briefly presents the concept and the development of molecule vibration, infrared absorption and Lie algebra, the importance of the research, the general method of dealing with the light–matter interaction, and gives advantages of the Lie algebra method. The second chapter is the basic theory, which mainly includes theoretical concepts and derivations of formula about of Hamiltonian of the system. First, SU (2) algebra is briefly discussed. Second, the expression of Hamiltonian and the time evolution operator are obtained by this algebra method, and then its group of parameters of differential equation satisfied is gotten. Finally, the analytical expressions of the transition probability are obtained. In the third chapter we use concrete examples to study the influences of frequency, intensity and pulse duration on the vibrational populations, which belong to, respectively, the ground state and the first, the second and the fourth excited state of vibration in NaCl and LiH molecular systems. It is found that because of the interaction between the molecular dipole moment and external field, the energy level is moved. When the laser intensity and pulse duration are fixed, with the increase of vibrational quantum number, the multi-photon resonance transition frequency becomes smaller, which is consistent with the energy level distribution of non-harmonic oscillator. The research also finds that the population of the excited states displays a periodic fluctuation with the change of the laser strength and pulse duration. When laser frequency and pulse duration are given, with vibration level rising gradually, oscillation period of the population becomes smaller. When the frequency of the laser and light intensity are given, with vibration level rising gradually, oscillation period of the population becomes longer.Chapter 4 is a conclusion. We briefly present the application of Lie algebraic method to the research of the light–matter interaction, and its application vistas are prospected.