Multiphoton Process Of Molecules In Intense Infrared Laser Fields

In this thesis, Multiphoton process and control of molecules in intense infrared laser fields have been studied. Study on the theory of non-linear multiphoton process is an active subject in molecular dynamics.Molecular dynamics is a new subject between in modern physics and in chemistry. Based on the theory of modern physics (especially in molecular physics, atomic physics and laser physics) and experimental technology, it is used to study the movement between molecules and interactions.Recently, the development of molecular dynamics is the relationship between the microstructures of molecules and macro-properties of objects. The microstructures and characters of molecules are correlative with multiphoton process closely, the multiphoton excitation can create ultra-excited states, induce counter-relaxation process of electrons. Using ultra-short infrared shaped laser, the selective vibrational dissociation can be achieved, namely, the strong bond of molecules can be broken firstly while the weak bond does not changed. Many new experimental researches have been reported and those are all relative with characters of high excited states of molecules, non-linear optical properties, the interactions of vibrations and rotations, and the non-adiabatic effect. However, study of multiphoton excitation and dissociation is important to the creation of high-power laser, separation of isotopes, control of chemical reaction, etc. In conclusion, study on the dynamical problems of molecules in intense infrared laser fields has a deep significance.In the intense infrared laser field, vibration of molecule is anharmonic, the perturbation theory is not suitable to the problem, and the Schrodinger equation about the problem is complicate and difficult to be solved. At the beginning of 80 decade, the theory of multiphoton developed rapidly for the invention of a computer with high efficiency. There are several theoretical methods proposed, Coulter transformation method, Floquet method and Lie-algebra method. The concrete descriptions include classical, semi-classical and quantum description. In this thesis, we take the semi-classical description, the molecule is treated quantum mechanically and the external field is assumed to be classical. Coulter transformation method and Floquet theory have been used to study multiphoton process for many years, however, both of them have shortcomings about applications: Coulter transformation method proposes a unitary transformation to decompose the couple term, it needs several transformations when the Hamiltonian of the system becomes complicate, the derivations of formula always difficult, and from the corresponding references, this method is only suitable to the transitions of the low excited states. Floquet method is based on these two theoretical explanations. Recently, there are two general nonperturbative approaches been widely used in the study of multiphoton processes. The first is the stationary treatment of the time-dependent Schrodinger equation. The development of generalized Floquet formalisms allows the reduction of the periodical or quasiperiodical time-dependent Schrodinger equation into a set of time-independent coupled equations or Floquet matrix eigenvalue problem. But the Floquet method has usually been used to discuss the atomic problems, and it becomes complicated for the molecules. Till now, little analytical work has been done to study multiphoton process of molecules, however, Lie-algebra method give the possibility to deal the problem. Lie group and Lie algebra theory are firstly proposed by Marius Sophus Lie, which become from the research of differential equations. Lie-algebra theory is introduced following the foundation of matrix mechanics, and it is used widely for the development of the fundamental quantum mechanics. In 1980s, Iachello, Levine et al. introduced Lie-algebra method from nuclear physics to molecular physics successfully. For the past years the application of time-dependent problems of the dynamical Lie algebraic approach are advanced. Algebraic methods have been extensively used to study problems in nuclear physics, molecular physics and quantum optics etc.. The problems of vibrationally excited states and potential energy surfaces for small polyatomic molecules have been solved successfully and accurately. This approach is recently used to study the interacting quantum system, the dynamical symmetries and its breaking in nanophysics, Tavis-Cummings problem and decoherence in a general three-level system, the dynamical entanglement of vibrations etc.. Lie-algebra method to study multiphoton process of molecules in intense infrared laser fields has three main advantages:(i) Lie-algebra method is still appropriate for the intense laser case. In thispaper, Lie algebra quadratic anharmonic model is used to represent an isolated linear triatomic molecular system, and the coupled interaction between the molecule and the laser field is given under the semiclassical dipole approximation. The time-evolution can be expressed a product of a finite number of exponential operators if the operators in Hamiltonian close under commutation. The parameters in time-evolution operator satisfy a set of differential equations, and the laser term is included in the parameters, so Lie-algebra method is sill effective at the intense laser fields' case.(ii) We can obtain the explicit expression of the time-evolution operatordirectly, which represents avoiding the complex process of solving the time-dependent Schrodinger equation, and the computation time is saved. The dynamical parameters such as transition probability, averaged absorbed energy can be obtained if the time-evolution operator is known, then the dynamical natures of the system can be discussed.(iii) The analytic expression of transition probability can be obtained using the explicit expression of the time-evolution operator. Using this method, we can study the transition properties of high excited states and dissociations. In this paper, we have mainly done the following work:1. Multiphoton excitation of molecules in usual intense laser fields. We take the linear triatomic molecules HCN and DCN as examples. Firstly, we have computed the stretch spectrum of HCN and DCN molecules, and gotten a good agreement with the observed values; it shows the theoretical model of the linear triatomic molecule introduced here is appropriate. Secondly, the vibrational transition probabilities from the ground state to the different excited states as a function of laser frequency and time have been computed, and the averaged absorbed energies at different laser intensity have been given. Then we have discussed the characters of multiphoton excitations, and our results are consistent with the other researches.2. Multiphoton selective excitation of molecules in the chirped and shaped laser fields. We study the three-, four-, and five-photon selective excitation of HCN and DCN molecules by a chirped and shaped laser field. The optimal laser parameters have been given in the paper and discussed the influence on the selectivity of the laser shape. This study also shows our method is effective to study the multiphoton process of triatomic molecules in intense laser fields.3. The state-selective vibrational excitation of diatomic molecules and bond-selective vibrational excitation of triatomic molecules. This study is important for example for promoting the rates or for controlling mode selectivity of chemical reactions or control the pathways of chemical reactions by selectivity exciting a specific bond vibrationally. Based on the method which has been optimized and reduced, we take a comparison with other accurate numerical results, and we get a good agreement. It shows the optimized method has a good numerical accuracy. Then we have studied control for small molecules by intense laser pulses. There are two main problems have been studied: one is the influence of the laser frequency on the state-selective vibrational excitation, the other is the problem of intramolecular vibrational redistribution(IVR), which occurs on the picosecond scale, making selective excitation difficult; and the bond-selective vibrational excitation of triatomic molecules at the different laser shape.In conclusion, we have successfully studied multiphoton process for small molecules by the Lie-algebraic method. The results are in good agreement with the other researches, quantitatively and qualitatively. Furthermore, the bending motions and rotations can be taken into account and this method can also be extended to study the tetra-atomic molecular case. The method can be applied and expanded further.This thesis is divided into five chapters: The first chapter is introduction, which chiefly introduces the definition and the development of multiphoton process of molecules, the importance of the research, the general theory and method and gives the advantages of Lie-algebra method. In the second chapter, we give the basic ideals and the detailed derivations of formula about Hamiltonian of the system, the time-evolution operator and the transition probability. In the next chapter, we take the concrete examples to study multiphoton process of triatomic molecules, give the results of multiphoton vibrational excitation and multiphoton selective vibrational excitation. In the fourth chapter, after we optimized the method and reduced the computation, we study control for small molecules by intense laser fields, and discuss the state-selective vibrational excitation of diatomic molecules and bond-selective vibrational excitation of triatomic molecules. In fifth chapter, we give some important conclusions of this thesis and make a brief illustration to some problems which can be handled by the Lie-algebra method.