Quantum Dynamics In A Atom-molecule Bose-einstein Condensate

With the experimental realization of a Bose-Einstein condensate (BEC) in dilute alkali gases, the system of atom-molecule Bose-Einstein condensat- es has stimulated great interest in the field of ultracold physics. Resort to magnetic Feshbach resonance, physicists have been able to manipulate the system by control- ing the interaction between atoms. Particularly, the system shows very rich property near the magnetic field of resonance.As for theoretical research, most efforts pay attention to the system of Fock states, and few articles refer to the situation of coherent states. By quantum means and the Q function of phase space, this thesis will study the evolution dynamics of a two-mode atom-molecule Bose-Einstein condensate system whose initial state is in a Fock state and a coherent state respectively.This thesis is divided into two chapters. The first chapter is a review about the basic contents of BEC, relevant experimental techniques, Gross-Pitaevskii equation (G-P equation) and some important theoretical jobs. In the second chapter, we study the dynamical property of a two-mode atom-molecule Bose-Einstein condensate system. We diagonalize the Hamiltonian first. Using the Q function, we study the temporal evolution dynamics of the system for two different initial states, a Fock state and a coherent state, compare the difference and research the effects of the nonlinear interaction to the evolution dynamics of the system. Else, we refer to the conversion efficiency between atoms and molecules. As the nonlinear interaction can be adjusted easily, the study could give us some useful information for under- standing the nonlinear phenomena in atom-molecule Bose-Einstein condensation systems, manipulating BEC systems and precise measurement.