摘要
We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.
We review our recent theoretical advances in the dynamics of Bose Einstein condensates with tunable interactions using Feshbach resonance and external potential. A set of analytic and numerical methods for Gross Pitaevskii equations are developed to study the nonlinear dynamics of BoseEinstein condensates. Analytically, we present the integrable conditions for the Gross Pitaevskii equations with tunable interactions and external potential, and obtain a family of exact analytical solutions for one- and two-component Bose Einstein condensates in one and two-dimensional cases. Then we apply these models to investigate the dynamics of solitons and collisions between two solitons. Numerically, the stability of the analytic exact solutions are checked and the phenomena, such as the dynamics and modulation of the ring dark soliton and vector-soliton, soliton conversion via Feshbach resonance, quantized soliton and vortex in quasi-two-dimensional are also investigated. Both the exact and numerical solutions show that the dynamics of Bose Einstein condensates can be effectively controlled by the Feshbach resonance and external potential, which offer a good opportunity for manipulation of atomic matter waves and nonlinear excitations in Bose Einstein condensates.
基金
Acknowledgements We would like to express our sincere thanks to Z. X. Liangang L. Wu for their original works and figures. This work was supported by the NatiorLM Natural Science Foundation of China （Grant Nos. 10874235, 10934010, and 60978019）, the National Key Basic Research Special Foundation of China （Grant Nos. 2009CB930701, 2010CB922904, and 2011CB921500）.
