Quantum Dynamics Of Two Components Bose-einstein Condensates

Bose-Einstein condensation,as a new matter form,is one of the frontier research focuses in physics.Especially in recent years,scientists have realized successively molecular Bose-Einstein condensates(BECs),Fermi condensates,spin-orbit coupled ultracold atomic gases,BECs in a cavity,and supersolids,which arouses a new round of research upsurge for cold atom physics.The current experimental techniques concerning cold atoms can achieve precise control of interatomic interactions,trap geometry,components,and purity of ultracold quantum gases,which provides new opportunities for exploring the previously inaccessible research subjects in atomic and molecular physics,condensed matter physics,and optics.The main work of the thesis is as follows.First,we have investigated the quantum reflection and interference of spin-dependent BECs in semi infinite potential wells by using the propagation method and the time-of-flight imaging scheme.We obtained the exact analytical solution of the spindependent condensate wave functions in the semi infinite potential wells.It is shown that once the spin-dependent optical lattice is switched off the spin-dependent matter wave packets in different lattice sites interfere with each other during the free expansion.Consequently,the interference fringes with high contrast are formed.At the same time,the expanded spin-dependent matter waves encounter the wall of the semi infinite potential well,which leads to a quantum reflection.There is a double interference between the reflected waves and the freely expanded incident waves,which is characterized by the significant modulation effect in the interference fringes.Second,we have studied the quantum dynamics of kicked and spin-orbit coupled spin-1/2 BECs.In classical physics,the periodically kicked rotor is a well-known paradigm of studying chaos.As a quantum correspondence of the classical kicked rotor,the kicked BECs(generalized quantum kicked rotors)have attracted much research interest in recent years.We have established a quantum dynamics model of the kicked spin-orbit coupled BECs.By calculating the density distribution,energy,momentum and spin polarization of the particles,we have discussed the effects of kick period,kick intensity,spin-orbit coupling strength,interatomic interactions and other parameters on the dynamics of the system.It is discovered that under the specific parameter regions the system can display exotic dynamic properties,such as quasi-periodic motion,dynamical localization,quantum anti-resonance,and quantum beat.In particular,in the absence of many-body interactions the increase of the spin-orbit coupling strength leads to a phase separation of the system and a generation of quantum beat,while in the presence of many-body interactions the increase of spin-orbit coupling strength tends to support a quasi-periodic motion.