| The dynamics of atomic Bose-Einstein condensates in a time-varying potential field is an universal problem in research directions such as atomic optics and quantum simulation,quantum chaos,quantum state control and precise measurement.However,the complexity of this dynamical system makes its theoretical research mainly rely on the method of numerical simulation of the time-dependent Gross–Pitaevskii(G-P)equation,which is difficult to qualitatively analyze and physically explain its dynamical behaviors.In this paper we propose an analytical method for the mean field dynamics of periodically driven atomic condensates in conservative potential fields.In our research,by using the action-angle transform usually used in the study of classical conservative mechanical systems and resonant frequency approximation,the G-P equation is transferred into the Floquet phase space.In this special phase space,the dynamical equations are no longer time-dependent,which can significantly reduce the difficulty of theoretical analysis.The contents of the thesis are as follows,1.In our research,the atomic condensate in a one-dimensional infinite-square well subjected to time-dependent perturbation is used as a model,and the Floquet phase space is constructed by means of action-angle transform and resonant frequency approximation.In the Floquet phase space,the periodic perturbation in time becomes a periodic lattice potential in space,whose shape is dependent on the multiple resonance of the perturbation frequency.By solving the time-independent G-P equation containing the periodic lattice potential,the main dynamics of the atomic condensate can be obtained.2.In our research,by selecting proper modulation potential fields and driving with one or two times the resonant frequency,it is found that the periodic perturbation driven by one time of the resonant frequency becomes a harmonic potential in the Floquet phase space,and when it is driven by twice the resonant frequency,it will become a double well potential.By solving the coherent oscillation of the atomic condensate in the harmonic potential and the dynamics of the atomic condensate in the physical space,the differences and connections of the atomic condensate dynamics in different spaces are revealed,and it is proved that the motion in the Floquet phase space will determine main dynamical features of the atomic condensates in the physical space.Then through the classical dynamics(Josephson oscillation and self-trapping effect)of the double-well model,the principle of complex dynamics of atomic condensates driven by a time-dependent perturbation in physical space are revealed.At the same time,the influence of different types of many-body interactions of the atomic condensate on the motion is also discussed. |
