Three-body Interaction In Double-well Trapped Bose-Einstein Condensates

The Bose-Einstein condensate (BEC) has been an attractive research subject for many theoretical and experimental studies, and the mean-field theory provides a practical framework for the investigation of BEC. However, most previous studies of the BEC system only considered the two-body interaction in the system, and the three-body interaction was only taken into consideration in a single trap for analyzing the characterization of Bose-Einstein Condensates. In this thesis, we study the three-body interaction in double-well trapped Bose-Einstein Condensates. The elastic and inelastic collisions, that is, the real and imaginary parts of three-body interaction coefficients are discussed. We investigate the stability, macroscopic quantum self-trapping(MQST), and chaotic behaviors of two Bose-Einstein Condensates (BECs) in a double-well potential with three-body interactions. Furthermore, when the three-body interaction is real, we also analyze the chaotic behavior of the system movement with a periodically time-varying atomic scattering length; when the three-body interaction is imaginary, the effects of the three-body recombination losses on the condensates are studied.This thesis consists of four chapters. In the first chapter, we briefly introduce the two-mode approximation, and the history, the current state of art of research and applications of three-body interactions in the BEC. The second chapter investigates the real three-body interaction coefficients. We first discuss the stability of this system. The stabilities of the stationary state solutions are studied with a linear stability theorem. The result demonstrates that the stationary state relative population will show instability when the physical parameters are adjusted to some critical values. Moreover, the stationary state macroscopic quantum self-trapping is also found. At the end of the chapter, we analyze the chaotic behavior of the system with a periodically time-varying atomic scattering length. By calculating the well-known Melnikov function of this system, we obtain the chaotic regions in the parameter space.The third chapter studies the features of the system movement with the...