| The theoretical prediction of Bose-Einstein Condensation (BEC) dates back to 1925 A. Einstein predicted the occurrence of a phase transition in a gas of non-interacting atoms. In general, a gas of such bosons can develop a macroscopic population of its lowest energy state below a critical temperature when all the particles will lose their individual characteristics. In 1995, E. A. Cornell and C. E. Wieman's group in Colorado University first observed Bose-Einstein Conden-sation in dilute 87Rb atoms, and later on W. Ketterle in MIT and R. G. Hulet in Rice succeeded in the atomic BECs of 23Na atoms and 7Li atoms, respectively. After the experimental realization of atomic BEC, the study of quantum gases in conditions of high degeneracy has become an emerging field of physics, attract-ing the interest of scientists from different areas. From 1997 to 2001, due to the discoveries of laser cooling and trapping atoms (1997), and atomic Bose-Einstein condensation (2001), this field was awarded by two Nobel Prize in physics, which is not a coincidence although the total history of this area is only more than ten years. In this thesis, we aim to show a variety of theoretical ways to solve the bottlenecks in the production of ultracold polar molecules.Currently, achieving ultracold atomic BEC has been a mature exciting fron-tier in the field of atomic, molecular and optical physics, and meanwhile ultracold molecular BEC, being another challenging direction, is expected to be celebrated as another milestone that promises to greatly spur activities at the forefront of physics research. It is clear that there are many roads to ultracold molecules. Di-rect cooling methods are based on cooling preexisting chemical stable molecules. Advantages include wide applicability and large yield. However, the typical tem-perature is only a few mK. An alternative way is to couple a pair of degener-ate atoms by Feshbach resonance or photoassociation, namely, indirect cooling method, which is proposed to be the most promising way of creating molecules in vibrational ground levels. Then final temperature reaches a few hundred nK (not yet to the critical temperature below), and the corresponding phase-space density is as high as 1012cm-3. Recently, Prof. J. Ye and D. S. Jin from JILA succeeded in achieving fermionic 40K87Rb molecules in the lowest rovibrational level. How-ever, the technique they applied is called"coherent two-photon Raman transfer", which is based on a magnetic Fano-Feshbach resonance. Whether molecules can be further compressed to increase its phase-space density and cooled down to the critical temperature is still a debated question.In the present work, we focus on how to produce ground-state molecules by photoassociation. In photoassociation process, pairs of free atoms are coupled into excited-state molecules via a pump laser. While generally speaking, due to the small free-bound Franck-Condon(FC) factor, an extremely strong laser power is required for an efficient transfer. To solve this problem, it is possible to apply another magnetic field, which may increase the photoassociation rate by orders of magnitude near Feshbach resonance. However, magnetic induced collision relax-ation will cause a big particle loss. Based on the above achievements, our group first propose to use all-optical stimulated Raman adiabatic passage to overcome the weakness in photoassociation. Two new schemes--chainwise and R-type models are designed for lowering pump laser with the help of extra light fields. To our knowledge, bound-bound FC factor is far larger than free-bound one, so that extra lights are easily controllable. Our scheme is a generalized approach which can be widely used in most of atom-molecule conversion systems. We think these new proposals may bring us one step closer to the final molecular condensation. Cold molecular physics will likely jump to be a new research highlight as well as an important frontier within atomic physics, optics and condensed matter physics community.
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