The project is targeting an opportunity to build on the very recent development of a qualitatively new approach to the problem of three body recombination at thermal energies. Special attention will be made to develop theoretical and computational techniques to study and control elementary processes taking place during combustion of coal and, in a longer time frame, simple hydrocarbons.
Three body collisions play an important role in processes occurring at thermal and ultracold temperatures. New robust theoretical and numerical techniques for calculation of rate coefficients for three body collisions at thermal energies will be developed and applied to several processes important for fundamental science (primordial three body recombination of hydrogen) and applied science (coal combustion). This project will primarily deal with three body collisions of neutral atoms at thermal and low energies (chemical reactions). However, a further development for charged particles is envisaged at a later stage. Principal points of the present project are the following:
(1) Development of techniques for determination of three body rate coefficients at thermal energies. The main effort will be made on the reaction of three body recombination, A+B+C > AB(v,j)+C. The idea is to develop exact (mostly numerical) and theoretical (with minimum numerical calculations) techniques and test them on relatively simple systems.
(2) Methods: (a) Numerical solution of the three body Schrödinger equation, using hyperspherical coordinates with a recently developed efficient technique for the eigenchannel R matrix with slow variable discretization; (b) A simple theoretical two step model for three body recombination: A+B>AB*, AB*+C > AB (v,j)+C + energy. Another type of coordinates, Eckart coordinates, will be employed to solve the three body Schrödinger equation. The Eckart coordinates combine certain advantages of the well established alternatives: hyperspherical and Jacobi coordinates.
Broader Impacts
A number of broader impacts should emerge from the successful completion of the research in this project: (1) the cross disciplinary importance of the developed methods (in physics, chemistry, astrophysics, plasma physics, combustion chemistry, and in the control of combustion); (2) the training of talented graduate students who will have the tools needed to tackle state-of-the-art problems in this subject area.
Research results We have developed a theory for the formation of triatomic and four-atomic molecules (trimers and tetramers) in the presence of laser radiation (photoassociation). Trimers are formed from an atom excited by the laser and a diatomic molecule in a cold gas containing atoms and molecules. The tetramers are formed from two identical diatomic molecules (dimers) with the help of a microwave laser, operating with the frequency selected in such a way that the laser enhances the formation of a bond between two diatomic molecules. Among other applications, the study contributes into the field of quantum computing: One of possible physical realizations of a quantum computer involves an array of diatomic molecules interacting with each other and with the laser field in a way similar to the one discussed in the study. In a larger perspective, the study can be viewed as an effort to develop tools for nanoscale engineering (fabrication) of molecules with desirable properties using lasers. Another problem that we have considered is the preparation of a diatomic molecule in a particular vibrational state. Normally, molecules in a gas phase have different amplitudes of vibrational motion. An ensemble of molecules vibrating with the same amplitude and in phase with each other has several important properties, which could be used in many technological applications, such as laser technology, precision measurement, lithography, and others. It is a difficult problem to prepare an ensemble of molecules in the same vibrational state. We have proposed a process that brings a cold sample of diatomic molecules into a chosen vibrational state. The process employs a laser pulse of a picosecond duration and the phenomenon of resonance coalescence. After the laser pulse is applied, about a half of molecules is brought into the chosen vibrational state, the other molecules are removed from the sample by the laser-driven dissociation. The proposed techniques allows us also to selectively manipulate vibrational states of molecules. The treatment have also been extended to control rotation of molecules, and can, in principle, be extended to larger molecules. This opens an opportunity to create an inverted population (negative temperature) or to use the technique in quantum information applications. Because of limited space, we will only mentioned other research finding made with the grant support. In a collaboration with experimentalists we have studied several atomic and molecular processes important for the formation, evolution and decay of thermal plasma. This study is important because plasma is widely used in different areas of technology and science (thermonuclear fusion reactors, thin-film deposition, medical applications, industrial air cleaning, atmospheric and space science, and others). We have also studied the process of formation of hydrogen molecule in collisions of three hydrogen atoms. The rate of the process determines the rate at which interstellar atomic clouds form molecular clouds and, eventually, form stars. The solution of this problem would also help to solve one of remaining problems in the Universe evolution: the duration of the so-called Dark Age of the Universe. Education The educational and research components are closely related to each other because the grant supported a PhD student and (partially) several master students, who have been working on the research problems discussed above and, at the same time, were learning and acquiring experience in research and teaching. For example, an important educational part of the students' activity was the experience with analyzing the obtained results, preparing the results to be presented to the scientific community. This includes presentations at national conferences and publications in the professional literature: 5 of 14 publications supported by this grant are based on the results obtained by the students; the students have co-authored the publications. As a result, the PhD student supported by this grant has defended his PhD thesis and found a job (post-doctoral position) in the field of his expertise at the University of California at Davis. Two undergraduate students partially supported by this grant have entered PhD programs. The grant allowed us to improve classroom lecturing: During the two last years, the principal investigator has included in one of the courses he teaches (undergraduate quantum mechanics) some recent research developments in the field of quantum information/computation. Many examples from another area supported by this grant, astrophysics, have also been discussed in the classroom. Very often, undergraduate quantum mechanics is taught in a formal way disconnected from the physical world, similar to mathematics. This happens because the postulates of quantum mechanics, discussed at the undergraduate level, are counterintuitive to an unexperienced person and are introduced only with the help of formal mathematics. The inclusion of several topics on quantum information/computation in the course allowed us to show links between the basic principles of quantum mechanics and the cutting edge of active research activity. This helped us to motivate students to study quantum mechanics.
