Study Of Chaos In Bose-Einstein Condensates

The realization of Bose-Einstein in a dilute atomic gas has attracted enormous attention in recent decades. It has provided physicists with a new fertile ground for exploring many aspects of this fascinating phenomenon including chaos, superfluidity, quantum phase transition and Josephson effect. In the framework of mean-field theory the Bose-Einstein condensates are governed by the Gross-Pitaeviskii equation. Based on the Gross-Pitaeviskii equation we shall study chaos in Bose-Einstein condensates which are loaded into a traveling optical lattice and a weakly open Bose-Einstein condensates with attractive interaction in a magnento-optical double-well trap. Meanwhile, we also discussed the problem of chaos control in the tight binding Bose-Einstein condensates by using the period parameter modulation control method.In this paper, we mainly studied the space-time evolution properties of the Bose-Einstein condensates held in a traveling optical lattice. When the damp is in our considerations, we discussed the Melnikov chaos of the system analytically, and presented the chaotic region in parametrical space. Features of the transient chaos are studied through numerical method. The transition procession from transient chaos to stationary one has been numerically simulated. In this procession, we find that the final attractors of the transient chaos undergo a series of period-doubling bifurcations.We also investigated the dynamics of a weakly open Bose-Einstein condensates with attractive interaction in a magnento-optical double-well trap. A set of time-dependent equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. We revealed that the system could transit among chaotic self-trapping states of the Lorenz model and the macroscopic quantum self-trapping .