Theoretical Study On Dissipative Dynamics In Bose-Einstein Condensates

Since the birth of quantum dynamics, study of open quantum system has never been stopped. Research works on open quantum system are related to quantum information, quantum optics, atom molecule physics, condense physics and many other branches of physics. In recent years, accurate model and manipulating open quantum system becomes more and more active. These research works include theoretical proposal and experimental progress in realising important quantum state through stochastic process, reaching quantum limited accuracy, etc. Bose-Einstein condensate is the main subject to be discussed in the thesis. A variety of complicated physics principles and quantum effects are included in the system and decoherence is easily taken place in such a system. The focus of this thesis is on quantum self-trapping effect and dissipative dynamics properties of the system. Particle losses on atom-molecule conversion system, quantum self-trapping effect in double well potential, and effect of distance selective dissipation on dynamics of BEC in driven optical lattice are discussed separately. The thesis is composed of six chapters, and our main work is included in the chapter from3to6.In Chapter1and Chapter2, we introduce research background of the thesis and basic conception related to our thesis. Research history of quantum open system and Bose-Einstein condensate are introduced. Basic knowledge and conception are given, including qubit, Bose distribution, mean-field approximation and Gross-Pitaevskii equation in BEC system, two-mode approximation and Josephson model.In Chapter3, dissipative dynamics for atom-molecule conversion BEC is discussed. With mean-field approximation and phase space analysis, types and positions of fixed points are derived as a function of time. Regimes divided by parameters are then specified and dynamic properties of regimes are different from each other. Transitions between regimes may occur during dissipation.In Chapter4, quantum decoherence on dynamics of BEC in double well potential is discussed. Under mean-field approximation, fixed points in classical phase space are calcu-lated. We find type of the fixed points changes from elliptic to attractor or repeller upon decoherence, which reflects meta-stable property of the system. In Chapter5, effect of distance selective dissipation on dynamics of BEC in driven optical lattice is investigated. Through mean-field approximation and numerical simulation, it is demonstrated that under dissipation atoms can transport in a diffusionless way in the lattice. when reduced to double-well model, steady states of the system can be derived analytically.In the last Chapter, time-dependent self-trapping effect for BEC in double well potential is investigated. With help of time-dependent self-trapping, system can be trapped in its own instantaneous eigenstate. Population difference between wells can be controlled by adjusting coupling constant and parameters of driving field.Finally, conclusions and discussion are given.