We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton...We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.展开更多
The collective excitations of low-dimensional Bose-Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations...The collective excitations of low-dimensional Bose-Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross-Pitaevskii-Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion （adding cubic, quartic, or quintic terra to a harmonic trap） are studied.展开更多
We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both a...We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two- well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference 5etween wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.展开更多
The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one movi...The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10774120 and 10475066, the Natural Science Foundation of Gansu Province under Grant No 3ZS051-A25-013, and the Creation of Science and Technology of Northwest Normal University under Grant No NWNU-KJCXGC-03-17
文摘We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.
基金supported by the Natural Science Foundation of Shaanxi University of Science and Technology under Grant No.SUST-ZX07-32partly by National Natural Science Foundation of China under Grant No.10774120
文摘The collective excitations of low-dimensional Bose-Einstein condensates with two- and three-body interactions in anharmonic potentials are investigated. Using the standard variational approach, the governing equations of motions for the low-energy excitations are obtained by solving time-dependent Gross-Pitaevskii-Ginzburg equation, and the excitation spectrums are calculated in small amplitude limit. The frequency shift and nonlinear mode coupling induced by the anharmonic distortion （adding cubic, quartic, or quintic terra to a harmonic trap） are studied.
基金Supported by the National Natural Science Foundation of China under Grant No 10774120, the Natural Science Foundation of Gansu Province under Grant No 3ZS051-A25-013, and the Natural Science Foundation of Northwest Normal University （NWNU- KJCXGC-03-17）.
文摘We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two- well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference 5etween wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10347006 and 10475066）, and by the Natural Science Foundation of Gansu province （Grant No 3ZS051-A25-013）.
文摘The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.
