Symmetry Breaking Of The Energy-level Structure And The Distribution Of Population In A Atom-molecule Conversion System In A Double-well Potential

Ultracold physics has always been a focus field. Since the first experimental preparation of the Bose-Einstein condensates (BEC) in dilute atomic gases in the 1990s, much attention has been paid on the ultracold physics. While the pure atomic BEC in double-well potential, which has been regard as a classical model for studying ultracold physics, also attracts considerable interest since many intriguing quantum phenomena appears, such as quantum tunneling, self-trapping and Josephson effects. On the other hand, the ultracold molecules and even molecular condensates have also been predicted and created in the experiment. Hence a natural question arises about the possible new properties or quantum phenomena once the conversion of ultracold atoms to molecules is finished in double-well potential. Therefore, in this paper, we present a four-mode system, in which the transformation of ultracold atoms to molecules by external field is performed in double-well potential. In the absence of the interparticle interactions, we study macro-symmetry breaking phenomena of the energy level structures and the population distributions.In the first chapter, we mainly introduce the ultracold atoms, the related experimental techniques and the research progress, including the Bose-Einstein condensation of the atoms, the quantum degenerate fermi gas, and the techniques of laser cooling, atomic trapping and evaporation cooling.In the second chapter, we introduce the ultracold molecule and the related experimental technique, including the techniques of direct cooling and indirect cooling and the research progress of ultracold moleculesIn the third chapter, we start from the basic principle, and mainly introduce the mean field approximation theory and the mode of pure atomic BEC in double-well potential. In addition, the Josephson oscillation and macroscopic quantum trapping have also been introduced.In the forth chapter, we construct a new four-mode model that the transformation process of ultracold atoms to molecules is finished in double-well potential. We mainly study the energy level structures and the population distributions. It is found that, when the interparticle interactions are not considered, as the coupling parameter of the external field increases, the eigenenergy splits and the two or three new energy level structures appear. Each loop energy level is quadruple-degenerated, and its width increases with the increasing of the coupling parameter. In addition, on these loop energy levels, the asymmetric population distributions appear, i.e., the number of particles in one potential well is absolutely higher than the other well. This phenomenon is similar to the macroscopic quantum self-trapping when atoms are loaded in a double-well trapping potential. The difference is that it is caused by the non-linearity with coupling two atoms to one molecule but not atomic interactions.In the fifth chapter, we give a brief summary.