Laser-molecule interactions theory

Laser-Molecule Interaction and Optimal Control Theory 805... 

In this chapter, the main theoretical tools used in the work presented in the next two chapters on the laser control of the radiationless decay in pyrazine and of the tunneling dynamics in NHD2, are introduced. After a brief discussion of the main approximations generally made in the study of laser-molecule interactions, presented in Sect. 6.1, we introduce in Sect. 6.2 the most basic tools for the laser control of population transfer in a two-level system. The derivation of an effective Hamiltonian allowing for the description of the interaction of a molecular system with a strong non-resonant laser pulse is presented in Sect. 6.3. TheFloquet theory and the adiabatic Floquet theory are Anally introduced in Sects. 6.4 and 6.5. 

The ENBO method, which is a method for incorporating polarization and higher order electric field-molecule interaction terms into the theory, is discussed in Section IV. Nearly all OCT experiments actually use laser pulses that give rise to strong electric fields that are sufficiently strong to significantly... 

The first theoretical attempts in the field of time-resolved X-ray diffraction were entirely empirical. More precise theoretical work appeared only in the late 1990s and is due to Wilson et al. [13-16]. However, this theoretical work still remained preliminary. A really satisfactory approach must be statistical. In fact, macroscopic transport coefficients like diffusion constant or chemical rate constant break down at ultrashort time scales. Even the notion of a molecule becomes ambiguous at which interatomic distance can the atoms A and B of a molecule A-B be considered to be free Another element of consideration is that the electric field of the laser pump is strong, and that its interaction with matter is nonlinear. What is needed is thus a statistical theory reminiscent of those from time-resolved optical spectroscopy. A theory of this sort was elaborated by Bratos and co-workers and was published over the last few years [17-19]. 

This chapter discusses the apphcation of femtosecond lasers to the study of the dynamics of molecular motion, and attempts to portray how a synergic combination of theory and experiment enables the interaction of matter with extremely short bursts of light, and the ultrafast processes that subsequently occur, to be understood in terms of fundamental quantum theory. This is illustrated through consideration of a hierarchy of laser-induced events in molecules in the gas phase and in clusters. A speculative conclusion forecasts developments in new laser techniques, highlighting how the exploitation of ever shorter laser pulses would permit the study and possible manipulation of the nuclear and electronic dynamics in molecules. 

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

In this chapter we introduce some of the fundamental concepts needed to understand how light interacts with matter. We start by examining a system of classical charged particles that interacts with a pulse of electromagnetic radiation. We then quantize the particle variables and develop the semiclassical theory of light interacting with quantized particles. The details of the derivations are not required for subsequent chapters. However, the resultant equations [Eqs. (1.50) to (1.52)] form the basis for the theoretical development presented in Chapter 2, which deals with both the interaction of weak lasers with molecules and with photodissociation processes. 

The models for the control processes start with the Schrodinger equation for the molecule in interaction with a laser field that is treated either as a classical or as a quantized electromagnetic field. In Section II we describe the Floquet formalism, and we show how it can be used to establish the relation between the semiclassical model and a quantized representation that allows us to describe explicitly the exchange of photons. The molecule in interaction with the photon field is described by a time-independent Floquet Hamiltonian, which is essentially equivalent to the time-dependent semiclassical Hamiltonian. The analysis of the effect of the coupling with the field can thus be done by methods of stationary perturbation theory, instead of the time-dependent one used in the semiclassical description. In Section III we describe an approach to perturbation theory that is based on applying unitary transformations that simplify the problem. The method is an iterative construction of unitary transformations that reduce the size of the coupling terms. This procedure allows us to detect in a simple way dynamical or field induced resonances—that is, resonances that... 

In Floquet theory the exchange of photons can be analyzed from the temporal variation of the relative photon number. In experiments, one measures for instance the difference in intensity of the laser pulse before and after the interaction with the molecules. Denoting the initial condition (at t = to = 0) by 4>(x) % c(0), we describe the exchange of photons by... 

While stable binary actinide carbonyls are still unknown, research in this area focused mainly on the detection and theoretical investigation of unstable molecules such as the monocarbonyl complexes of thorium and uranium. The possible molecular structures U-GO, U-OG, and GUO of carbon monoxide interacting on a uranium metal surface have been studied by density functional theory (DFT).14 GUO has been produced experimentally by reaction of laser-ablated U atoms with CO in excess argon and trapped in a triplet state in solid argon at 7 K.15 Studies of the reaction of thorium atoms with CO have been carried out. The reaction of laser-ablated thorium atoms with carbon monoxide in excess neon gave the first thorium carbonyl complex, Th-GO, which rearranges photochemically to CThO (Scheme l).16... 

In the dipole approximation, the interaction between molecules and a laser light is given by (r, / ) = — E t). where TJ(l) is the electric field and p(r) is the dipole moment. Here, we will consider only one-dimensional systems, i. e., diatomic molecules, with the coordinate x denoting the internuclear distance between the two atoms. In first order perturbation theory, the probability for a transition between the initial state vibrational eigenstate excited potential U ix) is proportional to... 

Excited state properties of molecules are often important parameters in different models of interacting systems and chemical reactions. For example, excited state polarizabilities are key quantities in the description of electrochromic and solva-tochromic shifts [99-103]. In gas phase there has been a series of experiments were excited state polarizabilities have been determined from Laser Stark spectroscopy by Hese and coworkers [104-106]. However, in the experiments most often not all the tensor components can be determined uniquely without extra information from either theory or other experiments. 

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